2024-03-29T01:11:25Z
https://eprints.maths.manchester.ac.uk/cgi/oai2
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:204
2017-11-08T18:18:29Z
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7375626A656374733D4D5343:4D53435F3630
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74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/204/
Backward Stochastic Partial Differential
Equations with Jumps and Application to
Optimal Control of Random Jump Fields
Oksendal, Bernt
Proske, Frank
Zhang, Tusheng
35 Partial differential equations
60 Probability theory and stochastic processes
93 Systems theory; control
We prove an existence and uniqueness result for a general class of backward stochastic
partial differential equations with jumps. This is a type of equations which appear as adjoint
equations in the maximum principle approach to optimal control of systems described by
stochastic partial differential equations driven by Levy processes.
2006-04-05
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/204/1/psrr12-2005.pdf
Oksendal, Bernt and Proske, Frank and Zhang, Tusheng (2006) Backward Stochastic Partial Differential Equations with Jumps and Application to Optimal Control of Random Jump Fields. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:216
2017-11-08T18:18:29Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3335
7375626A656374733D4D5343:4D53435F3630
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/216/
Stochastic Evolution Equations Driven by
Compensated Poisson Measures: Existence,
Uniqueness and Large Deviation Estimates
Rockner, Michael
Zhang, Tusheng
35 Partial differential equations
60 Probability theory and stochastic processes
93 Systems theory; control
Existence and uniqueness results are established for
solutions of stochastic evolution equations driven by
Poisson point processes. Large deviation estimates are
obtaines for the case of additive Poisson noise.
Examples are provided.
2006-04-12
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/216/1/psrr19-2005.pdf
Rockner, Michael and Zhang, Tusheng (2006) Stochastic Evolution Equations Driven by Compensated Poisson Measures: Existence, Uniqueness and Large Deviation Estimates. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:218
2017-10-20T14:12:06Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3933
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/218/
Control of free length when coiling a helical spring
Readman, M. C.
Muldoon, M. R.
Reynolds, L.
Morris, R.
Bayliss, M.
Wood, D.
Stewart, I.
93 Systems theory; control
The problem of controlling the free-length of a helical spring while it is being
manufactured on an automatic coiling machine is examined. This is a disturbance rejection
problem, and the feedback system is designed to reject disturbances caused by variation of the
wire properties and disturbances generated by the coiler. Fixed, self-tuning and fuzzy self-tuning
control are used to reduce the variance of the coiled and free length of a helical spring. Friction
feedfonvard is proposed to compensate for the varying coefficients of friction of different
materials.
2001-05-03
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/218/1/springs.pdf
Readman, M. C. and Muldoon, M. R. and Reynolds, L. and Morris, R. and Bayliss, M. and Wood, D. and Stewart, I. (2001) Control of free length when coiling a helical spring. IEE Proceedings-Control Theory and Applications, 148 (3). pp. 239-244. ISSN 1350-2379
10.1049/ip-cta:20010426
10.1049/ip-cta:20010426
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:652
2017-10-20T14:12:21Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/652/
The Sensitivity of Computational Control Problems
Higham, Nicholas J.
Konstantinov, Mihail
Mehrmann, Volker
Petkov, Petko
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
It is well-known that many factors contribute to the accurate and
efficient numerical solution of mathematical problems such as
those arising in computational control system design. In simple
terms these are the arithmetic of the machine on which the
calculations are carried out, sensitivity (or conditioning) of the
mathematical model to small changes of the data and the numerical
stability of the algorithms. It happens quite often that these
concepts are confused. We define these concepts and demonstrate
some of the subtleties that often lead to confusion. In particular
we demonstrate with several examples what may happen when a
problem is modularized, i.e., split into subproblems for which
computational modules are available.
For three classical problems in computational control, pole
placement, linear quadratic control and optimal $H_\infty$
control, we then discuss the conditioning of the problems and
point out sources of difficulties. We give some ill-conditioned
examples for which even numerically stable methods fail.
We also stress the need for condition and error estimators that
supplement the numerical algorithm and inform the user about
potential or actual difficulties, and we explain what can be done
to avoid these difficulties.
We finally describe the current status of available condition
estimators in numerical methods for control system design
such as those available in the SLICOT library and we point
out important areas of future research that need
to be adressed.
2004-02
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/652/1/hkmp04.pdf
Higham, Nicholas J. and Konstantinov, Mihail and Mehrmann, Volker and Petkov, Petko (2004) The Sensitivity of Computational Control Problems. IEEE Control Systems Magazine, 24 (1). pp. 28-43. ISSN 0272-1708
10.1109/MCS.2004.1272744
10.1109/MCS.2004.1272744
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1019
2017-10-20T14:12:34Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3439
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D626F6F6B5F73656374696F6E
https://eprints.maths.manchester.ac.uk/1019/
Calculating the $\mathcal{H}_{\infty}$-Norm of Large Sparse Systems via Chandrasekhar Iterations and Extrapolations
Chahlaoui, Y
Gallivan, K.A
Van Dooren, P
15 Linear and multilinear algebra; matrix theory
49 Calculus of variations and optimal control; optimization
65 Numerical analysis
93 Systems theory; control
We describe an algorithm for estimating the $\mathcal{H}_{\infty}$-norm of a large linear time invariant dynamical system described by a discrete time state-space model. The algorithm uses Chandrasekhar iterations to obtain an estimate of the $\mathcal{H}_{\infty}$-norm and then uses extrapolation to improve these estimates.
EDP Sciences, ESAIM
Benbourhim, Mohammed-Najib
Chenin, Patrick
Hassouni, Abdelhak
Hiriart-Urruty, Jean-Baptiste
2007-10-13
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1019/1/proc072008.pdf
Chahlaoui, Y and Gallivan, K.A and Van Dooren, P (2007) Calculating the $\mathcal{H}_{\infty}$-Norm of Large Sparse Systems via Chandrasekhar Iterations and Extrapolations. In: RFMAO 05 - Rencontres Franco-Marocaines en Approximation et Optimisation 2005. ESAIM: Proceedings, 20 . EDP Sciences, ESAIM, France, pp. 83-92.
http://www.edpsciences.org/articles/proc/abs/2007/04/contents/contents.html
10.1051/proc:072008
10.1051/proc:072008
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1025
2017-10-20T14:12:34Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D626F6F6B5F73656374696F6E
https://eprints.maths.manchester.ac.uk/1025/
Benchmark examples for model reduction of linear time invariant dynamical systems.
Chahlaoui, Younes
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
We present a benchmark collection containing some useful real world examples, which can be used to test and compare numerical methods for model reduction. All systems can be downloaded from the web and we describe here the relevant characteristics of the benchmark examples.
Springer Berlin Heidelberg
Benner, Peter
Sorensen, Danny C.
Mehrmann, Volker
2005
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1025/1/fulltext.pdf
Chahlaoui, Younes and Van Dooren, Paul (2005) Benchmark examples for model reduction of linear time invariant dynamical systems. In: Dimension Reduction of Large-Scale Systems. Lecture Notes in Computational Science and Engineering, 45 . Springer Berlin Heidelberg, Berlin, pp. 379-392. ISBN 978-3-540-24545-2 (Print) 978-3-540-27909-9 (Online)
http://www.springerlink.com/content/gg01154ghv54484x/?p=b4b69bfd848b463d9251b83891135aef&pi=0
10.1007/3-540-27909-1
10.1007/3-540-27909-1
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1026
2017-10-20T14:12:34Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D626F6F6B5F73656374696F6E
https://eprints.maths.manchester.ac.uk/1026/
Model reduction of time-varying systems.
Chahlaoui, Younes
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
This paper presents new recursive projection techniques to compute reduced order models of time-varying linear systems. The methods produce a low rank approximation of the Gramians or of the Hankel map of the system and are mainly based on matrix operations that can exploit sparsity of the model. We show the practical relevance of our results with a few benchmark examples.
Springer Berlin Heidelberg
Benner, Peter
Sorensen, Danny C.
Mehrmann, Volker
2006
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1026/1/owf1.pdf
Chahlaoui, Younes and Van Dooren, Paul (2006) Model reduction of time-varying systems. In: Dimension Reduction of Large-Scale Systems. Lecture Notes in Computational Science and Engineering, 45 . Springer Berlin Heidelberg, Berlin, pp. 131-148. ISBN 978-3-540-24545-2 (Print) 978-3-540-27909-9 (Online)
http://www.springerlink.com/content/r2108k3130r941t2/?p=b4b69bfd848b463d9251b83891135aef&pi=1
10.1007/3-540-27909-1_5
10.1007/3-540-27909-1_5
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1027
2017-10-20T14:12:34Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D626F6F6B5F73656374696F6E
https://eprints.maths.manchester.ac.uk/1027/
Model Reduction of Second-Order Systems.
Chahlaoui, Younes
Gallivan, Kyle A
Vandendorpe, Antoine
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
Springer Berlin Heidelberg
Benner, Peter
Sorensen, Danny C.
Mehrmann, Volker
2006
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1027/1/owf2.pdf
Chahlaoui, Younes and Gallivan, Kyle A and Vandendorpe, Antoine and Van Dooren, Paul (2006) Model Reduction of Second-Order Systems. In: Dimension Reduction of Large-Scale Systems. Lecture Notes in Computational Science and Engineering, 45 . Springer Berlin Heidelberg, Berlin, pp. 149-172. ISBN 978-3-540-24545-2 (Print) 978-3-540-27909-9 (Online)
http://www.springerlink.com/content/l322740005241270/?p=625e43787a2f470280c4cf6111b8b12c&pi=2#ContactOfAuthor2
10.1007/3-540-27909-1_6
10.1007/3-540-27909-1_6
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1029
2017-11-07T22:38:45Z
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1031
2017-10-20T14:12:34Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1031/
The Hinfinity-norm calculation for large sparse systems.
Chahlaoui, Younes
Gallivan, Kyle A
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
In this paper, we describe an algorithm for estimating the H∞-norm of a large linear time
invariant dynamical system described by a discrete time state-space model. The algorithm is
designed to be efficient for state-space models defined by {A,B,C,D} where A is a large sparse
matrix of order n which is assumed very large relative to the input and output dimensions of
the system.
2004-07
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1031/1/MTNS04.pdf
Chahlaoui, Younes and Gallivan, Kyle A and Van Dooren, Paul (2004) The Hinfinity-norm calculation for large sparse systems. In: 16th Symp. on the Mathematical Theory of Networks and Systems (MTNS04), 5-9 July 2004, Leuven.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1032
2017-10-20T14:12:34Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1032/
Second Order Structure Preserving Balanced Truncation.
Chahlaoui, Younes
Lemonnier, Damien
Vandendorpe, Antoine
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
2004-07
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1032/1/MTNS04Sec.pdf
Chahlaoui, Younes and Lemonnier, Damien and Vandendorpe, Antoine and Van Dooren, Paul (2004) Second Order Structure Preserving Balanced Truncation. In: 16th Symp. on the Mathematical Theory of Networks and Systems (MTNS04), 5-9 July 2004, Leuven.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1033
2017-10-20T14:12:34Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/1033/
Second Order Balanced Truncation.
Chahlaoui, Younes
Lemonnier, Damien
Vandendorpe, Antoine
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
We consider second-order linear time-invariant systems. The objective of this paper is
to present a new method for constructing a reduced system by preserving the second-order
structure of the original system. This new model reduction method uses a variant of the wellknown
balanced truncation technique applied to second-order gramians. We also compare it
with another existing technique.
2004-07-02
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1033/1/ChahlaouiLVV03.pdf
Chahlaoui, Younes and Lemonnier, Damien and Vandendorpe, Antoine and Van Dooren, Paul (2004) Second Order Balanced Truncation. Linear Algebra and its Applications, 415 (2-3). pp. 373-384. ISSN 0024-3795
10.1016/j.laa.2004.03.032
10.1016/j.laa.2004.03.032
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1034
2017-10-20T14:12:34Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1034/
Recursive Gramian and Hankel map approximation of large dynamical systems.
Chahlaoui, Younes
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
2003
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1034/1/ChahlaouiV03a.pdf
Chahlaoui, Younes and Van Dooren, Paul (2003) Recursive Gramian and Hankel map approximation of large dynamical systems. In: SIAM Conference on Applied Linear Algebra, 15-19 July 2003, Williamsburg, Virginia, U.S.A..
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1035
2017-10-20T14:12:34Z
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7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1035/
Recursive low rank Hankel approximation and model reduction.
Chahlaoui, Younes
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
In this note we present a new updating technique to
estimate a low rank approximation of the Hankel map
of a time-varying system. We obtain error estimates
of our approximation and also explain how to use this
for model reduction of time-varying as well as time
invariant systems.
2003
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1035/1/ChahlaouiV03b.pdf
Chahlaoui, Younes and Van Dooren, Paul (2003) Recursive low rank Hankel approximation and model reduction. In: Eur. Contr. Conf. 2003, 1-4 Sept 2003, Cambridge.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1037
2017-11-07T22:38:45Z
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1038
2017-10-20T14:12:35Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1038/
Model reduction of second order systems
Chahlaoui, Younes
Lemonnier, Damien
Meerbergen, Karl
Vandendorpe, Antoine
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
In this paper we propose new model reduction methods which preserve the polynomial form of a
given second order system. We also give numerical results to illustrate that even when imposing
such restrictions, one still obtains approximation errors which are comparable to those obtained
via balanced truncation. The advantage of our approach is that preserving the system structure
may better reflect the physical properties of the system we want to approximate.
2002
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1038/1/ChahlaouiLMVV02.pdf
Chahlaoui, Younes and Lemonnier, Damien and Meerbergen, Karl and Vandendorpe, Antoine and Van Dooren, Paul (2002) Model reduction of second order systems. In: Math. Th. Netw. Syst. International Symposium, August 2002, University Notre Dame, Illinois.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1039
2017-10-20T14:12:35Z
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7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1039/
Estimating Gramians of large-scale time-varying systems.
Chahlaoui, Younes
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
In this paper we present a Smith-like updating technique to estimate a low rank approximation of the Gramians of a time-varying system. We obtain error estimates of our approximation and also explain how to use this for model reduction of time-varying systems.
2002
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1039/1/ChahlaouiV02.pdf
Chahlaoui, Younes and Van Dooren, Paul (2002) Estimating Gramians of large-scale time-varying systems. In: IFAC World Congress, 2002, Barcelone.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1040
2017-10-20T14:12:35Z
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7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D6F74686572
https://eprints.maths.manchester.ac.uk/1040/
A collection of benchmark examples for model reduction of linear time invariant dynamical systems.
Chahlaoui, Younes
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
In order to test the numerical methods for model reduction we present here a benchmark collection, which contain some useful real world examples reflecting current problems in applications. All simulations were obtained via Matlab and some SLICOT programs of Niconet.
Niconet
2002
Other
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1040/1/ChahlaouiV02a.pdf
Chahlaoui, Younes and Van Dooren, Paul (2002) A collection of benchmark examples for model reduction of linear time invariant dynamical systems. Niconet.
http://www.icm.tu-bs.de/NICONET/reports.html
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1042
2017-10-20T14:12:35Z
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7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3334
7375626A656374733D4D5343:4D53435F3335
7375626A656374733D4D5343:4D53435F3337
7375626A656374733D4D5343:4D53435F3431
7375626A656374733D4D5343:4D53435F3439
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3638
7375626A656374733D4D5343:4D53435F3933
74797065733D746865736973
https://eprints.maths.manchester.ac.uk/1042/
Low-rank approximation and model reduction.
Chahlaoui, Younes
15 Linear and multilinear algebra; matrix theory
34 Ordinary differential equations
35 Partial differential equations
37 Dynamical systems and ergodic theory
41 Approximations and expansions
49 Calculus of variations and optimal control; optimization
65 Numerical analysis
68 Computer science
93 Systems theory; control
The basic idea of model reduction is to represent a complex linear dynamical system by a much simpler one. This may refer to many different techniques, but in this dissertation
we focus on projection-based model reduction of linear systems. The projection is based on the dominant eigen-spaces of energy functions for ingoing and outgoing signals of the system.
These energy functions are called Gramians of the system and can be obtained as the solutions of Stein equations. When the system matrices are large and sparse, it is not
obvious how to compute efficiently these solutions or their dominant eigen-spaces. In fact, direct methods ignore sparsity in the Stein equations and are not very attractive
for parallelization. Their use is then limited if the state dimension N of the system is large.
The complexity of these methods is roughly O(N3) floating point operations and they require about O(N2) words of memory.
This thesis provides some new ideas of recursive projection-based model reduction for time-varying systems as well as time-invariant systems. We present three algorithms for the recursive computation of the projection. These algorithms combine ideas of two classical methods — namely Balanced Truncation and Krylov subspaces — to produce a
low-rank approximation of the Gramians or the input/output map of the system. We show the practical relevance of our results with real world benchmark examples. We also present some new ideas for second order systems. Such systems have a special structure which one wants to preserve in the reduced order model. We show how to adapt our projection based method to such systems.
2003-12-22
Thesis
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1042/1/Chahlaoui_thesis_A4.pdf
Chahlaoui, Younes (2003) Low-rank approximation and model reduction. Doctoral thesis, University Catholic of Louvain, Louvain-La-Neuve, Belgium.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1062
2017-11-08T18:18:31Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/1062/
Symplectic, BVD, and Palindromic Approaches to Discrete-Time Control Problems
Byers, Ralph
Mackey, D. Steven
Mehrmann, Volker
Xu, Hongguo
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
We give several different formulations for the discrete-time linear-quadratic control
problem in terms of structured eigenvalue problems, and discuss the relationships among
the associated structured objects: symplectic matrices and pencils, BVD-pencils and
polynomials, and the recently introduced classes of palindromic pencils and matrix polynomials.
We show how these structured objects can be transformed into each other, and
also how their eigenvalues, eigenvectors and invariant/deflating subspaces are related.
2008-03-26
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1062/1/ByeMMX08_ppt-final_26-03-2008_00-26-49.pdf
Byers, Ralph and Mackey, D. Steven and Mehrmann, Volker and Xu, Hongguo (2008) Symplectic, BVD, and Palindromic Approaches to Discrete-Time Control Problems. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1133
2017-11-07T22:38:45Z
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1179
2017-11-08T18:18:31Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3337
7375626A656374733D4D5343:4D53435F3339
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/1179/
Dynamics of a hybrid thermostat model with discrete sampling
time control
Glendinning, Paul
Kowalczyk, Piotr
37 Dynamical systems and ergodic theory
39 Difference and functional equations
93 Systems theory; control
The dynamics of a simple thermostat model is described. In the model the control system samples the temperature at regular but discrete time intervals rather than by continuous monitoring. The model exhibits quasi-periodic oscillations and banding, where the response falls into two or more bands of phase space representing either better or poorer control. A return circle map is derived which explains the observed dynamics. Some extensions of these results to the case where the flow is nonlinear are also given.
2008-11-06
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1179/1/gk-thermostat.pdf
Glendinning, Paul and Kowalczyk, Piotr (2008) Dynamics of a hybrid thermostat model with discrete sampling time control. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1223
2017-10-20T14:12:41Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3439
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D626F6F6B5F73656374696F6E
https://eprints.maths.manchester.ac.uk/1223/
Calculating the $\mathcal{H}_{\infty}$-Norm of Large Sparse Systems via Chandrasekhar Iterations and Extrapolations
Chahlaoui, Y
Gallivan, K.A
Van Dooren, P
15 Linear and multilinear algebra; matrix theory
49 Calculus of variations and optimal control; optimization
65 Numerical analysis
93 Systems theory; control
We describe an algorithm for estimating the $\mathcal{H}_{\infty}$-norm of a large linear time invariant dynamical system described by a discrete time state-space model. The algorithm uses Chandrasekhar iterations to obtain an estimate of the $\mathcal{H}_{\infty}$-norm and then uses extrapolation to improve these estimates.
EDP Sciences, ESAIM
Benbourhim, Mohammed-Najib
Chenin, Patrick
Hassouni, Abdelhak
Hiriart-Urruty, Jean-Baptiste
2007-10-13
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1223/1/MIMS_ep2008_5.pdf
Chahlaoui, Y and Gallivan, K.A and Van Dooren, P (2007) Calculating the $\mathcal{H}_{\infty}$-Norm of Large Sparse Systems via Chandrasekhar Iterations and Extrapolations. In: RFMAO 05 - Rencontres Franco-Marocaines en Approximation et Optimisation 2005. ESAIM: Proceedings, 20 . EDP Sciences, ESAIM, France, pp. 83-92.
http://www.edpsciences.org/articles/proc/abs/2007/04/contents/contents.html
10.1051/proc:072008
10.1051/proc:072008
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1224
2017-10-20T14:12:41Z
7374617475733D7375626D6974746564
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3337
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/1224/
A posteriori error bounds for discrete balanced truncation
Chahlaoui, Younes
15 Linear and multilinear algebra; matrix theory
37 Dynamical systems and ergodic theory
65 Numerical analysis
93 Systems theory; control
Balanced truncation of discrete linear time-invariant systems is an automatic method once an error tolerance is specified and yields an a priori error bound, which is why it is widely used in engineering for simulation and control. We present some new insight into this method. We derive a discrete version of Antoulas's $\mathcal{H}_2$-norm error formula \cite[p.218]{Ant05} and show how to adapt it to some special cases. This error bound is an a posteriori computable upper bound for the $\mathcal{H}_2$-norm of the error system defined as the system whose transfer function corresponds to the difference between the transfer function of the original system and the transfer function of the reduced system. The main advantage of our results is that we use the information already available in the balanced truncation algorithm in order to compute the $\mathcal{H}_2$-norm instead of computing one gramian of the corresponding error system. There is always a computational restriction on solving high-dimensional Stein equations for gramians. The a posteriori bound gives insight into the quality of the reduced system and can be used to solve many problems accompanying the order reduction operation.
2009-02-06
Article
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1224/1/APE_BT.pdf
Chahlaoui, Younes (2009) A posteriori error bounds for discrete balanced truncation. SIAM Journal on Scientific Computing (SISC). (Submitted)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1226
2017-11-08T18:18:31Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/1226/
First/second order transformation system.
Tentative proof
Chahlaoui, Younes
Van Dooren, Paul
65 Numerical analysis
93 Systems theory; control
A tentative proof for the existence of a transformation from a first order system to a second order form.
2008-07-31
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1226/1/MIMS_ep2008_77.pdf
Chahlaoui, Younes and Van Dooren, Paul (2008) First/second order transformation system. Tentative proof. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1227
2017-11-07T22:38:45Z
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1228
2017-10-20T14:12:41Z
7374617475733D7375626D6974746564
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3337
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1228/
A new approach for MOR of second order Dynamical Systems
Chahlaoui, Younes
15 Linear and multilinear algebra; matrix theory
37 Dynamical systems and ergodic theory
65 Numerical analysis
93 Systems theory; control
We consider a new idea for model reduction of second order dynamical systems.
It is based on a new theorem which shows under which conditions one can recover the second order form of a dynamical system. This theorem adds some constraints on the projection matrices that will be used to construct the reduced
model.
2009
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1228/1/Chahlaoui_Fes.pdf
Chahlaoui, Younes (2009) A new approach for MOR of second order Dynamical Systems. In: Systems Theory: Modelling, Analysis and Control, 25-28 May 2009, Fes, Morocco. (Submitted)
http://www.theoriedessystemes.net/Fes2009/index.html
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1245
2017-10-20T14:12:42Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3630
7375626A656374733D4D5343:4D53435F3933
74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1245/
Symmetry reduction for stochastic hybrid systems
Bujorianu, M. L.
Katoen, J. P.
60 Probability theory and stochastic processes
93 Systems theory; control
This paper is focused on adapting symmetry reduction, a technique that is highly successful in traditional model checking, to stochastic hybrid systems. We first show that performability analysis of stochastic hybrid systems can be reduced to a stochastic reachability analysis (SRA). Then, we generalize the notion of symmetry reduction as recently proposed for probabilistic model checking, to continuous probabilistic systems. We provide a rigorous mathematical foundation for the reduction technique in the continuous case and also investigate its observability perspective. For stochastic hybrid systems, characterizations for this reduction technique are provided, in terms of their infinitesimal generator.
2008-12-09
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1245/1/MBujorianu_CDC47_Cancun.pdf
Bujorianu, M. L. and Katoen, J. P. (2008) Symmetry reduction for stochastic hybrid systems. In: 47th IEEE Conference on Decision and Control 2008, 9-11 Dec 2008, Cancun, Mexico.
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4739086
10.1109/CDC.2008.4739086
10.1109/CDC.2008.4739086
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1258
2017-10-20T14:12:42Z
7374617475733D7375626D6974746564
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3337
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1258/
Model reduction of switched dynamical systems
Chahlaoui, Younes
15 Linear and multilinear algebra; matrix theory
37 Dynamical systems and ergodic theory
65 Numerical analysis
93 Systems theory; control
A hybrid dynamical system is a system described by both differential equations (continuous
flows) and difference equations (discrete transitions). It has the benefit of allowing more flexible
modeling of dynamic phenomena, including physical systems with impact such as the bouncing ball,
switched systems such as the thermostat, and even the internet congestion as examples. Hybrid dynamical
systems pose a challenge since almost all reduction methods cannot be directly applied. Here
we show some recent developments in the area of model reduction of switched dynamical systems.
2009
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1258/1/Chahlaoui.pdf
Chahlaoui, Younes (2009) Model reduction of switched dynamical systems. In: 4th Conference on Trends in Applied mathematics in Tunisia, Algeria and Morocco., 6-8 May 2009, Kenitra, Morocco. (Submitted)
http://tamtam09.au.ma/
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1392
2017-10-20T14:12:47Z
7374617475733D7375626D6974746564
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/1392/
Two efficient SVD/Krylov algorithms for model order reduction of large scale systems
Chahlaoui, Younès
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
We present two efficient algorithms to produce a reduced order model of a time-invariant linear dynamical system by approximate balanced truncation.
Attention is focused on the use of the structure and the iterative construction via Krylov subspaces of both controllability and observability matrices to compute low-rank approximations of the Gramians or the Hankel operator. This allows us to take advantage of any sparsity in the system matrices and indeed the cost of our two algorithms is only linear in the system dimension. Both algorithms efficiently produce good low-rank approximations (in the least square sense) of the Cholesky factor of each Gramian and the Hankel operator. The second algorithm works directly on the Hankel operator, and it has the advantage that it is independent of the chosen realization. Moreover it is also an approximate Hankel norm method. The two reduced order models produced by our methods are guaranteed to be stable and balanced. We study the convergence of our iterative algorithms and the properties of the fixed point iteration. We also discuss the stopping criteria and the choice of the reduced order.
2010-01-10
Article
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1392/1/RLRG_RLRH_ABT.pdf
Chahlaoui, Younès (2010) Two efficient SVD/Krylov algorithms for model order reduction of large scale systems. Electronic Transactions On Numerical Analysis (ETNA). (Submitted)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1393
2017-11-07T22:38:46Z
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1394
2017-10-20T14:12:47Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3337
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D626F6F6B5F73656374696F6E
https://eprints.maths.manchester.ac.uk/1394/
A new approach for MOR of second order Dynamical Systems
Chahlaoui, Younes
Tisseur, Françoise
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
37 Dynamical systems and ergodic theory
65 Numerical analysis
93 Systems theory; control
We consider a new idea for model reduction of second order dynamical systems.
It is based on a new theorem which shows under which conditions one can recover the second order form of a dynamical system. This theorem adds some constraints on the projection matrices that will be used to construct the reduced
model.
Presses Universitaires de Perpignan
El Jai, A.
Afifi, L.
Zerrik, E.
2009
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1394/1/Pages_de_Proceedings_FES2009.pdf
Chahlaoui, Younes and Tisseur, Françoise and Van Dooren, Paul (2009) A new approach for MOR of second order Dynamical Systems. In: Systems Theory: Modelling, Analysis and Control. Presses Universitaires de Perpignan, pp. 153-158. ISBN 2-35412-043-6
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1464
2017-10-20T14:12:49Z
7374617475733D7375626D6974746564
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/1464/
A posteriori error bounds for discrete balanced truncation
Chahlaoui, Younes
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
Balanced truncation of discrete linear time-invariant systems is an automatic method once an error tolerance is specified and yields an a priori error bound, which is why it is widely used in engineering for simulation and control. We present some new insight into this method. We derive a discrete version of Antoulas's $\mathcal{H}_2$-norm error formula \cite[p.218]{Ant05} and show how to adapt it to some special cases. This error bound is an a posteriori computable upper bound for the $\mathcal{H}_2$-norm of the error system defined as the system whose transfer function corresponds to the difference between the transfer function of the original system and the transfer function of the reduced system. The main advantage of our results is that we use the information already available in the balanced truncation algorithm in order to compute the $\mathcal{H}_2$-norm instead of computing one gramian of the corresponding error system. There is always a computational restriction on solving high-dimensional Stein equations for gramians. The a posteriori bound gives insight into the quality of the reduced system and can be used to solve many problems accompanying the order reduction operation.
2010-04-29
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1464/1/LAA_Chahlaoui.pdf
Chahlaoui, Younes (2010) A posteriori error bounds for discrete balanced truncation. Linear Algebra and Its Applications, specia. (Submitted)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1468
2017-10-20T14:12:49Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3638
7375626A656374733D4D5343:4D53435F3933
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/1468/
Making big steps in trajectories
Müller, Norbert
Korovina, Margarita
65 Numerical analysis
68 Computer science
93 Systems theory; control
We consider the solution of initial value problems within the context of hybrid systems and emphasise use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of trajectories up to the area where discontinuous jumps appear, applicable for holomorphic flow functions. Examples with a prototypical implementation illustrate that the algorithm might provide results with higher precision than well-known ODE solvers at a
similar computation time.
2010
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1468/1/big_steps.pdf
Müller, Norbert and Korovina, Margarita (2010) Making big steps in trajectories. Electronic Proceedings in Theoretical Computer Science, 24. pp. 106-119. ISSN 2075-2180
http://published.eptcs.org/
10.4204/EPTCS
10.4204/EPTCS
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1480
2017-10-20T14:12:50Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3439
7375626A656374733D4D5343:4D53435F3630
7375626A656374733D4D5343:4D53435F3933
74797065733D626F6F6B5F73656374696F6E
https://eprints.maths.manchester.ac.uk/1480/
Dealing with stochastic reachability
Bujorianu, M.L.
49 Calculus of variations and optimal control; optimization
60 Probability theory and stochastic processes
93 Systems theory; control
For stochastic hybrid systems, stochastic reachability is very little supported mainly because of complexity and difficulty of the associated mathematical problems. In this paper, we develop two main directions of studying stochastic reachability as an optimal stopping problem. The first approach studies the hypotheses for the dynamic programming corresponding with the optimal stopping problem for stochastic hybrid systems. In the second approach, we investigate the reachability problem considering approximations of stochastic hybrid systems. The main difficulty arises when we have to prove the convergence of the value functions of the approximating processes to the value function of the initial process. An original proof is provided.
IEEE Control Systems Society
2009-12
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1480/1/cdc09_p1_finfin.tex
Bujorianu, M.L. (2009) Dealing with stochastic reachability. In: Proceedings of the 48th IEEE Conference on Decision and Control, CDC 2009. IEEE Control Systems Society, Shanghai, China, pp. 2935-2940.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1489
2017-10-20T14:12:50Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3933
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/1489/
Parameterising Structure Preserving Transformations Connecting Quadratic Matrix Polynomials
Garvey, S.D.
Popov, A.A.
15 Linear and multilinear algebra; matrix theory
93 Systems theory; control
Structure Preserving Transformations in the present definition provide a formal means by which every quadratic system isospectral to a given quadratic system may be determined. This paper presents a parameterisation for these structure preserving transformations which does not require that any of the coefficient matrices is non-singular and which provides a straightforward means to preserve each one of 8 classes of symmetry possible in a quadratic matrix polynomial.
2010-05-08
Article
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1489/1/Garvey_WCLAM_2010.pdf
Garvey, S.D. and Popov, A.A. (2010) Parameterising Structure Preserving Transformations Connecting Quadratic Matrix Polynomials. Western Canada Linear Algebra Meeting 2010, Banff, May 2010, 1 (1).
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1503
2017-11-07T22:38:46Z
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1509
2017-10-20T14:12:51Z
7374617475733D7375626D6974746564
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3334
7375626A656374733D4D5343:4D53435F3933
74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1509/
A Comparison of Multivariable & Decentralized Control Strategies for Robust Humanoid Walking
Dallali, H.
Medrano-Cerda, G.A.
Brown, M.
15 Linear and multilinear algebra; matrix theory
34 Ordinary differential equations
93 Systems theory; control
Bipedal walking is one of the most interesting control problems in humanoids research. Walking is modelled as a hybrid system in the sense that it involves various phases such as single support phase, impacts with the ground (i.e. a state reset) and the double support phase. The control system has to provide good dynamic performance in these different modes to achieve fast walking speeds while guaranteeing its safe and robust operation. Most humanoids use local joint PID loops (decentralized) control systems while the robot is a multivariable system and walking involves significant interactions between the robot links. Hence in this paper a centralized LQR multivariable controller is designed for the robot and analyzed for its stability, robustness to noise and disturbances and dynamic performance. Then, an LQR based iterative algorithm is used to tune the local PID servos. A comparison between the two schemes is done, where it is shown that the multivariable LQR has better robustness and energy efficiency. Finally, both controllers are simulated using the linearized model of a 10 degree of freedom robot called “C-Cub”.
2010-09-08
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1509/1/A_Comparison_of_Multivariable_%26_Decentralized_Control_Strategies_for_Robust_Humanoid_Walking.pdf
Dallali, H. and Medrano-Cerda, G.A. and Brown, M. (2010) A Comparison of Multivariable & Decentralized Control Strategies for Robust Humanoid Walking. In: UKACC International Conference on CONTROL 2010, 7-10 Sept 2010, Coventry, UK. (Submitted)
http://vs-ec-ctacconf.coventry.ac.uk/drupal-6.14/
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1604
2017-10-20T14:12:54Z
7374617475733D7375626D6974746564
7375626A656374733D4D5343:4D53435F3439
7375626A656374733D4D5343:4D53435F3933
74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1604/
Multi-Objective Hybrid Intelligent Optimization of Operational Indices for Industrial Processes and Application
Chai, Tianyou
Ding, Jinliang
Wang, Hong
49 Calculus of variations and optimal control; optimization
93 Systems theory; control
To pursuit the plant-wide optimization of multiple units industrial process, a hybrid
intelligent optimization approach under dynamic environment is proposed. The objective of
optimization is that the production indices de�ned as the performance related to the �nal
product quality, yield, energy and material consumption fall into their target ranges; whilst the
decision variables are operational indices of each unit, which is related to units� intermediate
product quality, e�ciency and consumption. In this context, the domain knowledge of process
engineers are mimicked and combined with the framework in terms of feedback, prediction and
feed-forward schemes so as to realize the required optimization. The e�ectiveness of the proposed
approach has been demonstrated by the practical application results.
2011-09-01
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1604/1/IFAC11_1753_FI.pdf
Chai, Tianyou and Ding, Jinliang and Wang, Hong (2011) Multi-Objective Hybrid Intelligent Optimization of Operational Indices for Industrial Processes and Application. In: 18th IFAC World Congress, August 28 - September 2, 2011, Milano, Italy. (Submitted)
https://ifac.papercept.net/conferences/scripts/abstract.pl?ConfID=30&Number=1753
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Product Scheduling for Thermal Energy Reduction in Papermakig Industries
Ghasemi Afshar, Puya
Brown, Martin
Wang, Hong
Maciejowski, Jan
49 Calculus of variations and optimal control; optimization
93 Systems theory; control
Papermaking is considered as an energy-intensive industry partly due to the fact
that the machinery and procedures have been designed at the time when energy was both cheap
and plentiful. A typical paper machine manufactures a variety of di�erent products (grades)
which impose variable per-unit raw material and energy costs to the mill. It is known that
during a grade change operation the products are not market-worthy. Therefore, two di�erent
production regimes, i.e. steady state and grade transition can be recognised in papermaking
practice. Among the costs associated with paper manufacture, the energy cost is �more variable�
due to (usually) day-to-day variations of the energy prices. Moreover, the production of a grade
is often constrained by customer delivery time requirements. Given the above constraints and
production modes, the product scheduling technique proposed in this paper aims at optimising
the sequence of orders in a single machine so that the cost of production (mainly determined
by the energy) is minimised. Simulation results obtained from a commercial board machine in
the UK con�rm the e�ectiveness of the proposed method.
2011-08-31
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1605/1/IFAC11_1566_FI.pdf
Ghasemi Afshar, Puya and Brown, Martin and Wang, Hong and Maciejowski, Jan (2011) Product Scheduling for Thermal Energy Reduction in Papermakig Industries. In: 18th IFAC World Congress, August 28 - September 2, 2011, Milano, Italy. (Submitted)
https://ifac.papercept.net/conferences/scripts/abstract.pl?ConfID=30&Number=1566
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1636
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https://eprints.maths.manchester.ac.uk/1636/
Two efficient SVD/Krylov algorithms for model order reduction of large scale systems
Chahlaoui, Younès
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
We present two efficient algorithms to produce a reduced order model of a time-invariant linear dynamical system by approximate balanced truncation.
Attention is focused on the use of the structure and the iterative construction via Krylov subspaces of both controllability and observability matrices to compute low-rank approximations of the Gramians or the Hankel operator. This allows us to take advantage of any sparsity in the system matrices and indeed the cost of our two algorithms is only linear in the system dimension. Both algorithms efficiently produce good low-rank approximations (in the least square sense) of the Cholesky factor of each Gramian and the Hankel operator. The second algorithm works directly on the Hankel operator, and it has the advantage that it is independent of the chosen realization. Moreover it is also an approximate Hankel norm method. The two reduced order models produced by our methods are guaranteed to be stable and balanced. We study the convergence of our iterative algorithms and the properties of the fixed point iteration. We also discuss the stopping criteria and the choice of the reduced order.
2011-04-13
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1636/1/pp113-145.pdf
Chahlaoui, Younès (2011) Two efficient SVD/Krylov algorithms for model order reduction of large scale systems. Electronic Transactions On Numerical Analysis (ETNA), 38. pp. 113-145. ISSN 1068-9613
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1637
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74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1637/
PVD�s contributions to numerical methods in systems and
control
Chahlaoui, Younes
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
Paul M. Van Dooren received the engineering degree in computer science and the doctoral degree in applied sciences, both from the Katholieke Universiteit Leuven, Belgium, in 1974 and 1979, respectively. He held research and teaching positions at the Katholieke Universiteit Leuven (1974-1979), the University of Southern California (1978-1979), Stanford University (1979-1980), the Australian
National University (1984), Philips Research Laboratory Belgium (1980-1991), the University of Illinois at Urbana-Champaign (1991-1994), Florida State University (1998) and the Universite Catholique de Louvain (1980-1991, 1994-now)
where he is currently a professor of Mathematical Engineering.
Dr. Van Dooren received the IBM-Belgium Informatics Award in 1974, the Householder Award in 1981 and the SIAM Wilkinson Prize of Numerical Analysis and Scientific Computing in 1989. He is a Fellow of IEEE and of SIAM (Society of Industrial and Applied Mathematics). He received the Francqui Chair in Antwerp in 2010. He is an Associate Editor of several journals in numerical analysis and systems and control theory. His main interests lie in the areas of numerical linear algebra, systems and control theory, and in numerical methods for large graphs
and networks.
In this talk we will review some of his main contributions and we will show some rare moments captured on pictures by some of his students and friends.
2011-05
Conference or Workshop Item
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1637/1/imacs10_Chahlaoui1.pdf
Chahlaoui, Younes (2011) PVD�s contributions to numerical methods in systems and control. In: 10th IMACS International Symposium on Iterative Methods in Scientific Computing Dedicated to Paul Van Dooren on his 60th Birthday, 18-21 May 2011, Marrakech, Morocco.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1638
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https://eprints.maths.manchester.ac.uk/1638/
Model Order Reduction or How to make everything as simple as possible but not simpler
Chahlaoui, Younes
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
Large complex mathematical models are regularly used for simulation and prediction. However, in control design it is common practice to work with as simple models as possible, because they are easier to analyse and evaluate.
There is a strong need for methods and tools that can take a complex model and deduce simple models for various purposes such as control design. A simple but good model captures much knowledge. It points out the basic properties
and can give good insight about the process.
For simple linear time-invariant models there is a well-established theory and commercially available tools for design of controllers with given speci�cations. Real experiments or simulations using more complex models are then used to verify that the designed controller really works well. For nonlinear models the methods are much less developed. It is simple to derive a linearization on symbolic form from a nonlinear model. It is much more dif�cult to give explicit expressions for stationary operating points since these calculations involve nonlinear equation systems.
The main idea in model reduction is that a high-dimensional state vector is actually belonging to a low-dimensional subspace [1, 2, 4]. Provided that the low-rank subspace is known, the original model can be projected on it to
obtain a required low-dimensional approximation [3]. The goal of every model reduction method is to �nd such a low-dimensional subspace.
In this talk I will introduce model reduction and I will overview some of the most used methods.
2011-05
Conference or Workshop Item
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1638/1/Chahlaoui_Mamern11.pdf
Chahlaoui, Younes (2011) Model Order Reduction or How to make everything as simple as possible but not simpler. In: MAMERN11: 4 th International Conference on Approximation Methods and Numerical Modelling in Environment and Natural Resources, 23-26 May 2011, Saidia, Morocco.
http://196.200.156.187/logos/abstract/Chahlaoui_Mamern11.pdf
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1639
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https://eprints.maths.manchester.ac.uk/1639/
Gramian based model reduction of switched dynamical systems
Chahlaoui, Younes
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
See the pdf document.
2011-06
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1639/1/H11Chahlaoui.pdf
Chahlaoui, Younes (2011) Gramian based model reduction of switched dynamical systems. In: Householder Symposium XVIII on Numerical Linear Algebra, 12-17 June 2011, Tahoe City, CA, US.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1649
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CONTROL OF A COMPLIANT HUMANOID ROBOT IN DOUBLE SUPPORT PHASE: A GEOMETRIC APPROACH.
Dallali, H.
Medrano-Cerda, G.
Brown, M.
15 Linear and multilinear algebra; matrix theory
70 Mechanics of particles and systems
93 Systems theory; control
Enhancing energy e�ciency of bipedal walking is an important research problem that has been approached by design of recently developed compliant bipedal robots such as CoMan. While compliance leads to energy e�ciency, it also complicates the walking control system due to further under-actuated degrees of freedom (DoF) associated with the compliant actuators. This problem becomes more challenging as the constrained motion of the robot in double support is considered. In this paper this problem is approached from a multi-variable geometric control aspect to systematically account for the compliant actuators dynamics and constrained motion of the robot in double support phase using a detailed electro-mechanical model of CoMan. It is shown that the formulation of constraint subspace is non-trivial in the case of non-rigid robots. A step-wise numerical algorithm is provided and the e�ectiveness of the
proposed method is illustrated via simulation, using a ten DoF model of CoMan.
2011-01-27
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1649/1/Control_of_CoMan_in_Double_Support.pdf
Dallali, H. and Medrano-Cerda, G. and Brown, M. (2011) CONTROL OF A COMPLIANT HUMANOID ROBOT IN DOUBLE SUPPORT PHASE: A GEOMETRIC APPROACH. Int. J. of Humanoid Robotics (IJHR). (Submitted)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1651
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oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1673
2017-11-07T22:38:46Z
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1674
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https://eprints.maths.manchester.ac.uk/1674/
An interview with Paul Van Dooren
Chahlaoui, Younes
01 History and biography
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
Interviews and dialogues have been a special way to transmit science since Socrates. They are maybe the only way to get the stories behind most discoveries. I was so positively impressed by the interview of Gene Golub by
Nicholas J. Higham [1] that the idea of doing one with Paul Van Dooren obsessed me for a while. After a few attempts to arrange a meeting, I finally got an occasion during the Householder Symposium at Tahoe City. On June 15, 2011, when most participants were on an excursion (Paul did have a kind of cold), we sat in a corner of the Granhall of the Granlibakken Conference Center and we did the interview. This document provides an edited transcript of that dialogue. The bibliography contains some refernces in the
interview.
2011
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1674/1/PVDinterview-cor2.pdf
Chahlaoui, Younes (2011) An interview with Paul Van Dooren. Applied Numerical Mathematics (APNUM), IISIMS (Specia). (Submitted)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1710
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https://eprints.maths.manchester.ac.uk/1710/
An interview with Paul Van Dooren
Chahlaoui, Younes
01 History and biography
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
Interviews and dialogues have been a special way to transmit science since Socrates. They are maybe the only way to get the stories behind most discoveries. I was so positively impressed by the interview of Gene Golub by
Nicholas J. Higham [1] that the idea of doing one with Paul Van Dooren obsessed me for a while. After a few attempts to arrange a meeting, I finally got an occasion during the Householder Symposium at Tahoe City. On June 15, 2011, when most participants were on an excursion (Paul did have a kind of cold), we sat in a corner of the Granhall of the Granlibakken Conference Center and we did the interview. This document provides an edited transcript of that dialogue. The bibliography contains some refernces in the
interview.
2011-11-28
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1710/1/MIMS_ep2011_74.pdf
Chahlaoui, Younes (2011) An interview with Paul Van Dooren. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1755
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https://eprints.maths.manchester.ac.uk/1755/
Multiobjective Meta-Heuristic Product Scheduling for Multi-Machine Manufacturing Systems
Afsahr, Puya
Wang, Hong
90 Operations research, mathematical programming
93 Systems theory; control
Flow line are one of the most commonly encountered layouts in manufacturing industries, where several product types (grades) are manufactured using a sequence of sub-systems or machinery with different tasks. With increasing prices of energy and speci�c customer demands employing effective product scheduling strategies has become essential for manufacturing industries to maintain their business viability. In this paper, a new product scheduling method is proposed for multi-machine, multi-product �ow lines. The objective here is to control the production start time for each grade so that the product delivery time errors are minimised. It is also desired to minimise the overall makespan variability caused by non-Gaussian uncertainties formulated by the entropy of the delivery time errors. Therefore, the proposed product scheduling strategy is a nonlinear multi-objective optimisation problem with non-Gaussian uncertainties. To solve this problem, the nonlinear dynamic �ow line model is converted to a linear dynamic equivalent using a (Max,+) algebraic approach. Then, a Proportional-Integral (PI) scheduling controller is used to control the production start time for each grade. The scheduling controller coef�cients are tuned by a MultiObjective Differential Evolution (MODE) algorithm. Simulation
results show the effectiveness of the proposed technique and a comparison is made between MODE, Genetic Algorithm (GA) and Particle Swarm Optimisation (PSO).
2011-12-12
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1755/1/2011CDC_AfsharWang.pdf
Afsahr, Puya and Wang, Hong (2011) Multiobjective Meta-Heuristic Product Scheduling for Multi-Machine Manufacturing Systems. In: 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), December 12-15, Orlando, FL, USA,.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1756
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https://eprints.maths.manchester.ac.uk/1756/
Fault Detection and Diagnosis for General Discrete-time Stochastic Systems Using Output Probability Density Estimation.
Skaf, Zakwan
AI-Bayati, Ahmad
Wang, Hong
93 Systems theory; control
A new approach of fault detection and diagnosis (FDD) for general stochastic systems in discrete-time is studied.
Our work on this problem is motivated by the fact that
most of the nonlinear control laws are implemented as digital controllers in reality. Different from the formulation of classical FDD problem, it is supposed that the measured information for the FDD is the probability density functions (PDFs) of the system output rather than its measured value. A radial basis function (RBF) neural network technique is proposed so that the output PDFs can be formulated in terms of the dynamic weighting of the RBFs neural network. Feasible criteria to detect and diagnose the system fault are provided by using linear matrix inequality (LMI) techniques. An illustrated example is included to demonstrate the ef�ciency of the proposed
algorithm, and satisfactory results are obtained.
2011-12-12
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1756/1/2011CDC_SkafAiBayatiWang1.pdf
Skaf, Zakwan and AI-Bayati, Ahmad and Wang, Hong (2011) Fault Detection and Diagnosis for General Discrete-time Stochastic Systems Using Output Probability Density Estimation. In: 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), December 12-15, Orlando, FL, USA,.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1757
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https://eprints.maths.manchester.ac.uk/1757/
Minimum Entropy Approach For Robot Manipulator
Skaf, Zakwan
AI-Bayati, Ahmad
Wang, Hong
93 Systems theory; control
In this paper, a new algorithm for an adaptive PI controller for nonlinear systems subject to stochastic non-
Gaussian disturbance is studied. The minimum entropy control
is applied to decrease the closed-loop tracking error on an ILC basis. The key issue here is to divide the control horizon into a number of equal time intervals called batches. Within each interval, there are a �xed number of sample points. The design procedure is divided into two main algorithms, within each batch and between any two adjacent batches. A D-type ILC law is employed to tune the PI controller coef�cients between two adjacent batches. However, within each batch, the PI coef�cients are �xed. A suf�cient condition is established to guarantee the stability of the closed-loop system. An analysis of the ILC
convergence is carried out. Two-link robot manipulator example is included to demonstrate the use of the control algorithm, and satisfactory results are obtained.
2011-12-12
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1757/1/2011CDC_SkafAiBayatiWang2.pdf
Skaf, Zakwan and AI-Bayati, Ahmad and Wang, Hong (2011) Minimum Entropy Approach For Robot Manipulator. In: 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), December 12-15, Orlando, FL, USA,.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1758
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https://eprints.maths.manchester.ac.uk/1758/
Iterative Fault Tolerant Control Based on Stochastic Distribution
Skaf, Zakwan
AI-Bayati, Ahmad
Wang, Hong
Wang, Aiping
93 Systems theory; control
A new design of a fault tolerant control (FTC)-
based an adaptive, �xed-structure PI controller, with constraints
on the state vector for nonlinear discrete-time system subject to
stochastic non-Gaussian disturbance is studied. The objective
of the reliable control algorithm scheme is to design a control
signal such that the actual probability density function (PDF)
of the system is made as close as possible to a desired PDF, and
make the tracking performance converge to zero, not only when
all components are functional but also in case of admissible
faults. A Linear Matrix Inequality (LMI)-based FTC method
is presented to ensure that the fault can be estimated and
compensated for. A radial basis function (RBF) neural network
is used to approximate the output PDF of the system. Thus, the
aim of the output PDF control will be a RBF weight control with
an adaptive tuning of the basis function parameters. The key
issue here is to divide the control horizon into a number of equal
time intervals called batches. Within each interval, there are a
�xed number of sample points. The design procedure is divided
into two main algorithms, within each batch, and between any
two adjacent batches. A P-type ILC law is employed to tune the
parameters of the RBF neural network so that the PDF tracking
error decreases along with the batches. Suf�cient conditions for
the proposed fault tolerance are expressed as LMIs. An analysis
of the ILC convergence is carried out. Finally, the effectiveness
of the proposed method is demonstrated with an illustrated
example.
2011-12-12
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1758/1/2011CDC_SkafAiBayatiWangWang.pdf
Skaf, Zakwan and AI-Bayati, Ahmad and Wang, Hong and Wang, Aiping (2011) Iterative Fault Tolerant Control Based on Stochastic Distribution. In: 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), December 12-15, Orlando, FL, USA,.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1759
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Cell Death: Linear Control Analysis of Eissing's Model
Readman, Mark C.
Kalamatianos, Dimitrios
92 Biology and other natural sciences
93 Systems theory; control
We deconstruct Eissing's intrinsic apoptosis model using linear control theory. In the life steady state the linearised dynamics are shown to be a tightly coupled but unstable multi- variable system. The life steady state is stabilized biochemically by decentralised XIAP and CARP acting as lead controllers. The small gain theorem is used to analyse stability and to give insight into how the inhibitors naturally modulate cell death and highlighting the role played by positive and negative feedback. Finally we use simulations to examine the extent to which recovery is possible once apoptosis has been initiated.
2012-02-27
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1759/2/MCReadmanMEB.pdf
Readman, Mark C. and Kalamatianos, Dimitrios (2012) Cell Death: Linear Control Analysis of Eissing's Model. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1760
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https://eprints.maths.manchester.ac.uk/1760/
Hybrid intelligent parameter estimation based on grey case-based reasoning for laminar cooling process
Xing, Guishan
Ding, Jinliang
Chai, Tianyou
Afshar, Puya
Wang, Hong
90 Operations research, mathematical programming
93 Systems theory; control
In this paper, a hybrid intelligent parameter estimation algorithm is proposed for predicting the strip
temperature during laminar cooling process. The algorithm combines a hybrid genetic algorithm (HGA) with
grey case-based reasoning (GCBR) in order to improve the precision of the strip temperature prediction. In
this context, the hybrid genetic algorithm is formed by combining the genetic algorithm with an annealing
and a local multidimensional search algorithm based on deterministic inverse parabolic interpolation. Firstly,
the weight vectors of retrieval features in case-based reasoning are optimised using hybrid genetic algorithm
in of�ine mode, and then they are used in grey case-based reasoning to accurately estimate the model
parameters online. The hybrid intelligent parameter estimation algorithm is validated using a set of
operational data gathered from a hot-rolled strip laminar cooling process in a steel plant. Experiment results
show the effectiveness of the proposed method in improving the precision of the strip temperature
prediction. The proposed method can be used in real-time temperature control of hot-rolled strip and has
potential for parameter estimation ofdifferenttypesofcoolingprocess.
2012-03
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1760/1/profWang_paper.pdf
Xing, Guishan and Ding, Jinliang and Chai, Tianyou and Afshar, Puya and Wang, Hong (2012) Hybrid intelligent parameter estimation based on grey case-based reasoning for laminar cooling process. Engineering Applications of Arti�cial Intelligence, 25 (2). pp. 418-429.
http://www.sciencedirect.com/science/article/pii/S0952197611002053
http://dx.doi.org/10.1016/j.engappai.2011.10.007
http://dx.doi.org/10.1016/j.engappai.2011.10.007
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1790
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https://eprints.maths.manchester.ac.uk/1790/
Decentralized LQR Joint Servo Design for a Compliant Humanoid Robot via LMI Optimisation
Dallali, Houman
Medrano-Cerda, Gustavo
Brown, Martin
Tsagarakis, Nikos
Caldwell, Darwin
65 Numerical analysis
93 Systems theory; control
Enhancing bipedal walking safety, robustness and
efficiency has led to design of compliant humanoid robots.
However, the links' interactions and coupling effects are often neglected in the design of their trajectory tracking controller.
Moreover, there is not a direct decentralized approach for
designing the PD-PID gains given a multivariable model of
the compliant humanoid robot. This paper proposes an LMI
formulation for designing decentralized PID gains in discrete time. It is shown that this method can be used to design a full state feedback for trajectory tracking which includes the compliance and links' interactions in the feedback design.
Numerical simulations for a compliant compass gait and a 10
DoF humanoid models are provided to illustrate the use of this method.
2012
Conference or Workshop Item
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1790/1/Decent_PID_LMI_LQR_IROS12.pdf
Dallali, Houman and Medrano-Cerda, Gustavo and Brown, Martin and Tsagarakis, Nikos and Caldwell, Darwin (2012) Decentralized LQR Joint Servo Design for a Compliant Humanoid Robot via LMI Optimisation. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. (Submitted)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1808
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74797065733D626F6F6B
https://eprints.maths.manchester.ac.uk/1808/
Stochastic Reachability Analysis of Hybrid Systems
Bujorianu, L. M.
49 Calculus of variations and optimal control; optimization
60 Probability theory and stochastic processes
93 Systems theory; control
Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems.
Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then treats issues representing the different faces of SRA:
· stochastic reachability based on Markov process theory;
· martingale methods;
· stochastic reachability as an optimal stopping problem; and
· dynamic programming.
The book is rounded off by an appendix providing mathematical underpinning on subjects such as ordinary differential equations, probabilistic measure theory and stochastic modeling, which will help the non-expert-mathematician to appreciate the text.
Stochastic Reachability Analysis of Hybrid Systems characterizes a highly interdisciplinary area of research and is consequently of significant interest to academic researchers and graduate students from a variety of backgrounds in control engineering, applied mathematics and computer science.
Springer
2012-03
Book
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1808/1/9781447127949-t1%281%29.pdf
Bujorianu, L. M. (2012) Stochastic Reachability Analysis of Hybrid Systems. Communications and Control Engineering . Springer, London, UK. ISBN 978-1-4471-2794-9
http://www.springer.com/mathematics/applications/book/978-1-4471-2794-9
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2016
2017-10-20T14:13:09Z
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74797065733D746865736973
https://eprints.maths.manchester.ac.uk/2016/
Real option analysis in resilient energy networks
Blair, J.W.
60 Probability theory and stochastic processes
90 Operations research, mathematical programming
93 Systems theory; control
The resilience of future power systems are being challenged in three fronts: (i) decarbonising energy supply will alter supply mix; (ii) shift of previous non-electric demand onto the energy network will require the system to work at higher capacity; and (iii) expected changes in climate will alter demand and performance of electrical network components. This thesis quantitatively assesses the impact of future climate change on the resilience of a power system, in secure and hazardous conditions. This is done through the use of reliability indices and probabilistic security assessment. Dynamical thermal ratings of circuits are used throughout this thesis given their potential for increased capacity over the standard static ratings. The first finding is that the predicted future climate scenarios will result in components with lower thermal ratings then if used currently. Due to this, it is found that the reliability of the system decreases under further climate scenarios. In order to keep a satisfactory level of reliability in the system, a method of temporary overloaded circuits is introduced which doesn't result in a higher risk of component failure. The temporary overload method allows for the rating constraint to be violated provided the temperature constraint isn't. Applying this to the system, and assessing the results under various climate scenarios, it is found that the method is beneficial in terms of economical cost and system reliability. When applied to hazardous conditions, it is found the method has a higher potential to strengthen the reliability of the system in comparison to when used on the 'safe' system.
An approach is taken to aid the system operator in decision making under uncertain conditions. A scenario is devised in which an operator wants to plan the power dispatch for a future time period. This is done through the use of stochastic optimisation, where the uncertainty is encapsulated by the conductor ratings which are calculated using dynamical thermal ratings in which the weather parameters are stochastic. This is developed for a one and two period model, in which the two period model has the first and second period coupled through the addition of a ramp rate constraint in the optimisation. System adequacy indices and probabilistic security indices are added as constraints so the system operator can control the reliability of his system.
2013-04
Thesis
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2016/1/FULL-TEXT.PDF
Blair, J.W. (2013) Real option analysis in resilient energy networks. Masters thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2136
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7375626A656374733D4D5343:4D53435F3933
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https://eprints.maths.manchester.ac.uk/2136/
CICADA Collection
Chahlaoui, Younes
Korovina, Margarita
37 Dynamical systems and ergodic theory
45 Integral equations
60 Probability theory and stochastic processes
65 Numerical analysis
68 Computer science
90 Operations research, mathematical programming
92 Biology and other natural sciences
93 Systems theory; control
This volume is CICADA Collection which contains contributions developed by researches working on
CICADA Project, The University of Manchester. CICADA Project creates a warm and fruitful atmosphere
for research collaboration in many aries of Mathematics, Computer Science, Engineering including hybrid
and dynamical systems, verification of safety critical systems, human robotics, model reduction and high
dimensional systems, max-pus algebra, stochastic hybrid systems, analysis of adaptive systems and control.
This volume presents examples and software which have been developed and used by CICADA community.
2014-05-22
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2136/1/CICADA_Collection2012.pdf
Chahlaoui, Younes and Korovina, Margarita (2014) CICADA Collection. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2246
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https://eprints.maths.manchester.ac.uk/2246/
Polynomial Zigzag Matrices, Dual Minimal Bases,
and the Realization of Completely Singular Polynomials
De Teran, Fernando
Dopico, Froilan
Mackey, D. Steven
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
93 Systems theory; control
Minimal bases of rational vector spaces are a well known
and important tool in systems theory.
If minimal bases for two subspaces of rational $n$-space
are displayed as the rows of polynomial matrices
$Z_1(\la)_{k \times n}$ and $Z_2(\la)_{m \times n}$, respectively,
then $Z_1$ and $Z_2$ are said to be
dual minimal bases
if the subspaces have complementary dimension,
i.e., $k+m = n$,
and $Z_1^{}(\la) Z_2^T(\la) = 0$.
In other words, each $Z_j(\la)$ provides a minimal basis
for the nullspace of the other.
It has long been known that for any dual minimal bases $Z_1(\la)$ and $Z_2(\la)$,
the row degree sums of $Z_1$ and $Z_2$ are the same.
In this paper we show that this is the only constraint on the row degrees,
thus characterizing the possible row degrees of dual minimal bases.
The proof is constructive, making extensive use
of a new class of sparse, structured polynomial matrices
that we have baptized zigzag matrices.
Another application of these polynomial zigzag matrices
is the constructive solution of the following inverse problem for minimal indices --
given a list of left and right minimal indices and a desired degree $d$,
does there exist a completely singular matrix polynomial
(i.e., a matrix polynomial with no elementary divisors whatsoever)
of degree $d$
having exactly the prescribed minimal indices?
We show that such a matrix polynomial exists
if and only if $d$ divides the sum of the minimal indices.
The constructed realization is simple,
and explicitly displays the desired minimal indices
in a fashion analogous
to the classical Kronecker canonical form
of singular pencils.
2015-02-06
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2246/1/zigzag-matrices_MIMS-1.pdf
De Teran, Fernando and Dopico, Froilan and Mackey, D. Steven and Van Dooren, Paul (2015) Polynomial Zigzag Matrices, Dual Minimal Bases, and the Realization of Completely Singular Polynomials. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2389
2017-10-20T14:13:22Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2389/
Polynomial Zigzag Matrices, Dual Minimal Bases,
and the Realization of Completely Singular Polynomials
De Teran, Fernando
Dopico, Froilan
Mackey, D. Steven
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
93 Systems theory; control
Minimal bases of rational vector spaces are a well-known
and important tool in systems theory.
If minimal bases for two subspaces of rational $n$-space
are displayed as the rows of polynomial matrices
$Z_1(\lambda)_{k \times n}$
and $Z_2(\lambda)_{m \times n}$, respectively,
then $Z_1$ and $Z_2$ are said to be
dual minimal bases
if the subspaces have complementary dimension,
i.e., $k+m = n$,
and $Z_1^{}(\lambda) Z_2^T(\lambda) = 0$.
In other words, each $Z_j(\lambda)$ provides a minimal basis
for the nullspace of the other.
It has long been known that for any dual minimal bases $Z_1(\lambda)$ and $Z_2(\lambda)$,
the row degree sums of $Z_1$ and $Z_2$ are the same.
In this paper we show that this is the only constraint on the row degrees,
thus characterizing the possible row degrees of dual minimal bases.
The proof is constructive, making extensive use
of a new class of sparse, structured polynomial matrices
that we have baptized zigzag matrices.
Another application of these polynomial zigzag matrices
is the constructive solution of the following inverse problem for minimal indices --
given a list of left and right minimal indices and a desired degree $d$,
does there exist a completely singular matrix polynomial
(i.e., a matrix polynomial with no elementary divisors whatsoever)
of degree $d$
having exactly the prescribed minimal indices?
We show that such a matrix polynomial exists
if and only if $d$ divides the sum of the minimal indices.
The constructed realization is simple,
and explicitly displays the desired minimal indices
in a fashion analogous
to the classical Kronecker canonical form
of singular pencils.
2015-02-06
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2389/1/zigzag-matrices_MIMS-Sept2015.pdf
De Teran, Fernando and Dopico, Froilan and Mackey, D. Steven and Van Dooren, Paul (2015) Polynomial Zigzag Matrices, Dual Minimal Bases, and the Realization of Completely Singular Polynomials. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2440
2017-11-08T18:18:38Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3334
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2440/
A rational deferred correction approach to PDE-constrained optimization
Güttel, Stefan
Pearson, John W.
34 Ordinary differential equations
65 Numerical analysis
93 Systems theory; control
The accurate and efficient solution of time-dependent PDE-constrained optimization problems is a challenging task, in large part due to the very high dimension of the matrix systems that need to be solved. We devise a new deferred correction method for coupled systems of time-dependent PDEs, allowing one to iteratively improve the accuracy of low-order time stepping schemes. We consider two variants of our method, a splitting and a coupling version, and analyze their convergence properties. We then test our approach on a number of PDE-constrained optimization problems. We obtain solution accuracies far superior to that achieved when solving a single discretized problem, in particular in cases where the accuracy is limited by the time discretization. Our approach allows for the direct reuse of existing solvers for the resulting matrix systems, as well as state-of-the-art preconditioning strategies.
2016-02-16
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2440/1/dccontrol.pdf
Güttel, Stefan and Pearson, John W. (2016) A rational deferred correction approach to PDE-constrained optimization. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2481
2017-11-08T18:18:38Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2481/
Block Kronecker Linearizations of Matrix Polynomials and their Backward Errors
Dopico, Froilán M.
Lawrence, Piers W.
Pérez, Javier
Van Dooren, Paul
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
We introduce a new family of strong linearizations of matrix polynomials---which we call "block Kronecker pencils"---and perform a backward stability analysis of complete polynomial eigenproblems. These problems are solved by applying any backward stable algorithm to a block
Kronecker pencil, such as the staircase algorithm for singular pencils or the QZ algorithm for regular pencils. This analysis allows us to identify those block Kronecker pencils that yield a computed complete eigenstructure which is exactly that of a slightly perturbed matrix polynomial. These favorable pencils include the famous Fiedler linearizations, which are just a very particular case of block Kronecker pencils. Thus, our analysis offers the first proof available in the literature of global backward stability for Fiedler pencils. In addition, the theory developed for block Kronecker pencils is much simpler than the theory available for Fiedler pencils, especially in the case of rectangular matrix polynomials. The global backward error analysis in this work presents for the first time the following key properties: it is a rigorous analysis valid for finite perturbations (i.e., it is not a first order analysis), it provides precise bounds, it is valid simultaneously for a large class of linearizations, and it establishes a framework that may be generalized to other classes of linearizations. These features
are related to the fact that block Kronecker pencils are a particular case of the new family of "strong block minimal bases pencils," which include certain perturbations of block Kronecker pencils; this allows us to extend the results in this paper to other contexts.
2016-05-31
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2481/1/kron-pencils-backerror-fro.pdf
Dopico, Froilán M. and Lawrence, Piers W. and Pérez, Javier and Van Dooren, Paul (2016) Block Kronecker Linearizations of Matrix Polynomials and their Backward Errors. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2504
2017-10-20T14:13:27Z
7374617475733D707562
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7375626A656374733D4D5343:4D53435F3537
7375626A656374733D4D5343:4D53435F3932
7375626A656374733D4D5343:4D53435F3933
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2504/
Embedding and Time Series Analysis
Huke, Jeremy P.
Muldoon, Mark R.
37 Dynamical systems and ergodic theory
57 Manifolds and cell complexes
92 Biology and other natural sciences
93 Systems theory; control
The 1970's and 80's saw a tremendous wave of interest---across the sciences and beyond---in the subject of nonlinear dynamics. Under the heading of `chaos theory' the subject even gripped the public imagination, leading to popular books and television programmes and even a mention in the film \emph{Jurassic Park}. One of the central ideas driving this interest was the realization that the complex, unpredictable behaviour known as chaos might be widespread in physical systems, and possibly even in biological, economic and social systems as well. This kind of behaviour, with its characteristic \emph{sensitive dependence on initial conditions}, had been shown to occur in a range of simple mathematical systems, many of which were conceived as models of physical or biological phenomena. As well as triggering much work on the mathematical theory of nonlinear dynamical systems, this also raised the intriguing question of whether chaotic behaviour could actually be observed in the broad range of experimental situations that the simple models hinted at. But while physicists and engineers were very familiar with experiments designed to investigate the various periodicities within a system, how should they treat the experimental data (or devise the experiments themselves) so as to reveal the characteristic features of chaos, such as the aforementioned sensitive dependence on initial conditions, or the strange attractors, with their fractal structures, that live in the state spaces of some chaotic systems?
2015-06
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2504/1/HukeMuldoon.pdf
Huke, Jeremy P. and Muldoon, Mark R. (2015) Embedding and Time Series Analysis. Mathematics Today, 51 (3). pp. 120-123. ISSN 1361-2042
http://ima.org.uk/_db/_documents/Contents%20%20from%20MT%20June%2015.pdf
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2505
2017-11-08T18:18:38Z
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7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2505/
A rational deferred correction approach to PDE-constrained optimization
Güttel, Stefan
Pearson, John W.
34 Ordinary differential equations
65 Numerical analysis
93 Systems theory; control
The accurate and efficient solution of time-dependent PDE-constrained optimization problems is a challenging task, in large part due to the very high dimension of the matrix systems that need to be solved. We devise a new deferred correction method for coupled systems of time-dependent PDEs, allowing one to iteratively improve the accuracy of low-order time stepping schemes. We consider two variants of our method, a splitting and a coupling version, and analyze their convergence properties. We then test our approach on a number of PDE-constrained optimization problems. We obtain solution accuracies far superior to that achieved when solving a single discretized problem, in particular in cases where the accuracy is limited by the time discretization. Our approach allows for the direct reuse of existing solvers for the resulting matrix systems, as well as state-of-the-art preconditioning strategies.
2016-02-16
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2505/1/dccontrol_IMAJNA.pdf
Güttel, Stefan and Pearson, John W. (2016) A rational deferred correction approach to PDE-constrained optimization. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2506
2017-11-08T18:18:38Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2506/
Strong linearizations of rational matrices
Amparan, A.
Dopico, F.M.
Marcaida, S.
Zaballa, I.
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
This paper defines for the first time strong linearizations of arbitrary rational matrices, studies in depth properties and diferent characterizations
of such linear matrix pencils, and develops infinitely many
examples of strong linearizations that can be explicitly and easily constructed from a minimal state-space realization of the strictly proper
part of the considered rational matrix and the coefficients of the polynomial part. As a consequence, the results in this paper establish a rigorous foundation for the numerical computation of the complete structure of zeros and poles, both finite and at infinity, of any rational matrix by applying any well known backward stable algorithm for generalized eigenvalue problems to any of the strong linearizations explicitly constructed in this work. Since the results of this paper require to use several concepts that are not standard in matrix computations,
a considerable effort has been done to make the paper as self-contained as possible.
2016-10-04
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2506/1/StrongLinearizationsRationalMatrices.pdf
Amparan, A. and Dopico, F.M. and Marcaida, S. and Zaballa, I. (2016) Strong linearizations of rational matrices. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2559
2017-11-08T18:18:39Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3334
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2559/
A rational deferred correction approach to parabolic optimal control problems
Güttel, Stefan
Pearson, John W.
34 Ordinary differential equations
65 Numerical analysis
93 Systems theory; control
The accurate and efficient solution of time-dependent PDE-constrained optimization problems is a challenging task, in large part due to the very high dimension of the matrix systems that need to be solved. We devise a new deferred correction method for coupled systems of time-dependent PDEs, allowing one to iteratively improve the accuracy of low-order time stepping schemes. We consider two variants of our method, a splitting and a coupling version, and analyze their convergence properties. We then test our approach on a number of PDE-constrained optimization problems. We obtain solution accuracies far superior to that achieved when solving a single discretized problem, in particular in cases where the accuracy is limited by the time discretization. Our approach allows for the direct reuse of existing solvers for the resulting matrix systems, as well as state-of-the-art preconditioning strategies.
2016-02-16
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2559/1/dccontrol_IMAJNA_REV1.pdf
Güttel, Stefan and Pearson, John W. (2016) A rational deferred correction approach to parabolic optimal control problems. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2624
2018-02-18T08:35:05Z
7374617475733D707562
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7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2624/
Van Dooren's Index Sum Theorem
and Rational Matrices with Prescribed Structural Data
Anguas, Luis M.
Dopico, Froilán M.
Hollister, Richard
Mackey, D. Steven
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
The structural data of any rational matrix $R(\la)$,
i.e., the structural indices of its poles and zeros
together with the minimal indices of its left and right
nullspaces,
is known to satisfy a simple condition involving certain sums of these indices.
This fundamental constraint was first proved by Van Dooren in $1978$;
here we refer to this result as the ``rational index sum theorem''.
An analogous result for polynomial matrices
has been independently discovered (and re-discovered)
several times in the past three decades.
In this paper we clarify the connection between these
two seemingly different index sum theorems,
describe a little bit of the history of their development,
and discuss their curious apparent unawareness of each other.
Finally, we use the connection between these results
to solve a fundamental inverse problem
for rational matrices ---
for which lists ${\cal L}$ of prescribed structural data
does there exist some rational matrix $R(\la)$
that realizes exactly the list ${\cal L}$?
We show that Van Dooren's condition is the \emph{only} constraint on rational realizability;
that is, a list ${\cal L}$ is the structural data of some rational $R(\la)$
if and only if
${\cal L}$ satisfies the rational index sum condition.
2018-02-18
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2624/1/rational-index-sum_MIMS_Feb2018.pdf
Anguas, Luis M. and Dopico, Froilán M. and Hollister, Richard and Mackey, D. Steven (2018) Van Dooren's Index Sum Theorem and Rational Matrices with Prescribed Structural Data. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2631
2018-03-27T23:16:52Z
7374617475733D707562
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7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2631/
Strong linearizations of rational matrices
Amparan, A.
Dopico, F.M.
Marcaida, S.
Zaballa, I.
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
This paper defines for the first time strong linearizations of arbitrary rational matrices, studies in depth properties and diferent characterizations
of such linear matrix pencils, and develops infinitely many
examples of strong linearizations that can be explicitly and easily constructed from a minimal state-space realization of the strictly proper
part of the considered rational matrix and the coefficients of the polynomial part. As a consequence, the results in this paper establish a rigorous foundation for the numerical computation of the complete structure of zeros and poles, both finite and at infinity, of any rational matrix by applying any well known backward stable algorithm for generalized eigenvalue problems to any of the strong linearizations explicitly constructed in this work. Since the results of this paper require to use several concepts that are not standard in matrix computations,
a considerable effort has been done to make the paper as self-contained as possible.
2016-10-04
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2631/3/StrongLinearizationsRationalMatrices_v2.pdf
Amparan, A. and Dopico, F.M. and Marcaida, S. and Zaballa, I. (2016) Strong linearizations of rational matrices. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2645
2018-06-05T07:47:58Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3135
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2645/
Strong linearizations of rational matrices
Amparan, A.
Dopico, F.M.
Marcaida, S.
Zaballa, I.
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
93 Systems theory; control
This paper defines for the first time strong linearizations of arbitrary rational matrices, studies in depth properties and diferent characterizations
of such linear matrix pencils, and develops infinitely many
examples of strong linearizations that can be explicitly and easily constructed from a minimal state-space realization of the strictly proper
part of the considered rational matrix and the coefficients of the polynomial part. As a consequence, the results in this paper establish a rigorous foundation for the numerical computation of the complete structure of zeros and poles, both finite and at infinity, of any rational matrix by applying any well known backward stable algorithm for generalized eigenvalue problems to any of the strong linearizations explicitly constructed in this work. Since the results of this paper require to use several concepts that are not standard in matrix computations,
a considerable effort has been done to make the paper as self-contained as possible.
2016-10-04
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2645/5/StrongLinearizationsRationalMatrices_rev.pdf
Amparan, A. and Dopico, F.M. and Marcaida, S. and Zaballa, I. (2016) Strong linearizations of rational matrices. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2688
2019-03-17T09:54:14Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2688/
Stability analysis of a chain of non-identical vehicles under bilateral cruise control
Wang, Liang
Tisseur, Francoise
Strang, Gilbert
Horn, Berthold K.P.
65 Numerical analysis
93 Systems theory; control
Bilateral cruise control (BCC) suppresses traffic
flow instabilities. Previously, for simplicity of analysis, vehicles in BCC traffic flow were assumed to be identical, i.e., using the same gains for control. In this study, we analyze the stability of an inhomogeneous vehicular chain in which the gains used by different vehicles are not the same. Not unexpectedly, mathematical analysis becomes more difficult, and leads to a quadratic eigenvalue problem. We study several different cases, and shows that a chain of vehicles under bilateral cruise control is stable even when the vehicles do not all have the same control system properties. Numerical simulations validate the analysis.
2019-03-17
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2688/1/wtsh19.pdf
Wang, Liang and Tisseur, Francoise and Strang, Gilbert and Horn, Berthold K.P. (2019) Stability analysis of a chain of non-identical vehicles under bilateral cruise control. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2747
2020-02-18T10:10:58Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3635
7375626A656374733D4D5343:4D53435F3933
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2747/
A Hamiltonian Decomposition for Fast Interior-Point Solvers in Model Predictive Control
Poupard, Eduardo
Heath, William P.
Güttel, Stefan
65 Numerical analysis
93 Systems theory; control
Optimal decision-making tools are essential in industry to achieve high performance. One of these tools is Model Predictive Control (MPC), which is an advanced control technique that generates an action that affects the controlled variables, while satisfying the process’ operational constraints. At the core of the MPC algorithm lies an optimization problem that is solved by a numerical method at every sample time. New demand for more self-contained modular processes has seen MPC embedded in small-scale platforms. This has prompted a need for custom-made numerical methods that help to efficiently run the computationally demanding optimization algorithms. In this paper, we propose two approaches that factorize the Newton system of the interior-point method (IPM) based on the two-point boundary-value (TPBV) problem structure, rarely explored in MPC. Exploiting the Hamiltonian form of the augmented system, we derive an incomplete LU factorization. A direct method is available to compute the solution of the system using a forward substitution of a series of matrices. An iterative method is also available. We propose a preconditioned Krylov method that converges within a small number of iterations only depending on the number of states.
2020-02-18
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2747/1/p-merged.pdf
Poupard, Eduardo and Heath, William P. and Güttel, Stefan (2020) A Hamiltonian Decomposition for Fast Interior-Point Solvers in Model Predictive Control. [MIMS Preprint]