HOSVD Based Canonical Form for Polytopic Models of Dynamic Systems

László Szeidl; Péter Várlaki

doi:10.20965/jaciii.2009.p0052

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JACIII Vol.13 No.1 pp. 52-60

doi: 10.20965/jaciii.2009.p0052

(2009)

Paper:

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HOSVD Based Canonical Form for Polytopic Models of Dynamic Systems

László Szeidl^* and Péter Várlaki^**

^*Budapest Tech Polytechnic Institute, J. von Neumann Faculty of Informatics, H-1034 Budapest, Bécsi út 96/B, Hungary

^**Budapest University of Technology and Economics, Department of Chassis and Lightweight Structures, H-1111 Budapest, Bertalan L. u. 2, Hungary

Received:

June 6, 2007

Accepted:

February 18, 2008

Published:

January 20, 2009

Keywords:

LPV model, polytopic dynamic model, TP model, HOSVD, linear matrix inequalities (LMI)

Abstract

The higher order singular-value-based canonical form of linear parameter varying models we define, extracts a models's most important invariant characteristics. We studied the numerical reconstructibility of the canonical form using a routinely executable tractable uniform method, and present convergency theorems for given numerical reconstruction constraint.

Cite this article as:

L. Szeidl and P. Várlaki, “HOSVD Based Canonical Form for Polytopic Models of Dynamic Systems,” J. Adv. Comput. Intell. Intell. Inform., Vol.13 No.1, pp. 52-60, 2009.

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References

[1] M. Athans, S. Fekri, and A. Pascoal, “Issues on robust adaptive feedback control,” in Plenary paper, Perprints of 16th IFAC Word Congress, Prague, pp. 9-39, 2005.
[2] G. Balas, J. Bokor, and Z. Szabó, “Invariant subspaces for LPV systems and their application,” IEEE Transactions on Automatic Control, Vol.48, No.11, pp. 2065-2069, 2003.
[3] P. Baranyi, D. Tikk, Y. Yam, and R. J. Patton, “From differential equations to PDC controller design via numerical transformation,” Computers in Industry, Elsevier Science, Vol.51, pp. 281-297, 2003.
[4] J. Bokor, P. Baranyi, P. Michelberger, and P. Varlaki, “TP model transformation in non-linear system control,” in 3rd IEEE Int. Conf. on Computational Cybernetics (ICCC), pp. 111-119, (plenary lecture) ISBN: 0-7803-9474-7, Mauritius, Greece, 13-16 April, 2005.
[5] S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, “Linear Matrix Inequalities in Systems and Control Theory,” SIAM books, Philadelphia, 1994.
[6] L. De. Lathauwer, B. De. Moor, and J. Vandewalle, “A multilinear singular value decomposition,” SIAM Journal on Matrix Analysis and Applications, Vol.21, No.4, pp. 1253-1278, 2000.
[7] G. Marsaglia and G. P. H. Styan, “Equalities and inequalities for ranks of matrices,” Linear and Multilinear Algebra, Vol.2, pp. 269-292, 1974.
[8] L. Szeidl, P. Baranyi, Z. Petres, and P. Várlaki, “Numerical reconstruction of the HOSVD based canonical form of polytopic dynamic models,” in 3rd Int. Symposium on Computational Intelligence and Intelligent Informatics (ISCIII 2007), pp. 111-116, Agadir, Morocco, 2007.
[9] K. Tanaka and H. O. Wang, “Fuzzy Control Systems Design and Analysis – A Linear Matrix Inequality Approach,” John Wiley and Sons, Inc., 2001.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] M. Athans, S. Fekri, and A. Pascoal, “Issues on robust adaptive feedback control,” in Plenary paper, Perprints of 16th IFAC Word Congress, Prague, pp. 9-39, 2005.

[2] [2] G. Balas, J. Bokor, and Z. Szabó, “Invariant subspaces for LPV systems and their application,” IEEE Transactions on Automatic Control, Vol.48, No.11, pp. 2065-2069, 2003.

[3] [3] P. Baranyi, D. Tikk, Y. Yam, and R. J. Patton, “From differential equations to PDC controller design via numerical transformation,” Computers in Industry, Elsevier Science, Vol.51, pp. 281-297, 2003.

[4] [4] J. Bokor, P. Baranyi, P. Michelberger, and P. Varlaki, “TP model transformation in non-linear system control,” in 3rd IEEE Int. Conf. on Computational Cybernetics (ICCC), pp. 111-119, (plenary lecture) ISBN: 0-7803-9474-7, Mauritius, Greece, 13-16 April, 2005.

[5] [5] S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, “Linear Matrix Inequalities in Systems and Control Theory,” SIAM books, Philadelphia, 1994.

[6] [6] L. De. Lathauwer, B. De. Moor, and J. Vandewalle, “A multilinear singular value decomposition,” SIAM Journal on Matrix Analysis and Applications, Vol.21, No.4, pp. 1253-1278, 2000.

[7] [7] G. Marsaglia and G. P. H. Styan, “Equalities and inequalities for ranks of matrices,” Linear and Multilinear Algebra, Vol.2, pp. 269-292, 1974.

[8] [8] L. Szeidl, P. Baranyi, Z. Petres, and P. Várlaki, “Numerical reconstruction of the HOSVD based canonical form of polytopic dynamic models,” in 3rd Int. Symposium on Computational Intelligence and Intelligent Informatics (ISCIII 2007), pp. 111-116, Agadir, Morocco, 2007.

[9] [9] K. Tanaka and H. O. Wang, “Fuzzy Control Systems Design and Analysis – A Linear Matrix Inequality Approach,” John Wiley and Sons, Inc., 2001.

HOSVD Based Canonical Form for Polytopic Models of Dynamic Systems

László Szeidl* and Péter Várlaki**

László Szeidl^* and Péter Várlaki^**