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Performance improvement of robust controllers for polynomially uncertain systems

Title:

Performance improvement of robust controllers for polynomially uncertain systems

Lavaei, Javad and Aghdam, Amir G. (2010) Performance improvement of robust controllers for polynomially uncertain systems. Automatica, 46 (1). pp. 110-115. ISSN 00051098

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Official URL: http://dx.doi.org/10.1016/j.automatica.2009.10.007

Abstract

This paper is concerned with the high-performance robust control of discrete-time linear time-invariant (LTI) systems with semi-algebraic uncertainty regions. It is assumed that a robustly stabilizing static controller is given whose gain depends polynomially on the uncertain variables. The problem of tuning this parameter-dependent gain with respect to a prescribed quadratic cost function is formulated as a sum-of-squares (SOS) optimization. This method leads to a near-optimal controller whose performance is better than that of the initial controller. It is shown that the results derived in the present work encompass the ones obtained in a recent paper. The efficacy of the results is elucidated by an example.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering
Item Type:Article
Refereed:Yes
Authors:Lavaei, Javad and Aghdam, Amir G.
Journal or Publication:Automatica
Date:2010
Digital Object Identifier (DOI):10.1016/j.automatica.2009.10.007
Keywords:Optimal controller synthesis for systems with uncertainties; Robust control; Convex optimization
ID Code:975170
Deposited By: Danielle Dennie
Deposited On:22 Jan 2013 14:12
Last Modified:18 Jan 2018 17:39

References:

Bakhilina and Stepanov, 2001 I.M. Bakhilina, S.A. Stepanov Design of robust linear controllers under parametric uncertainty of the object model Automation and Remote Control, 62 (1) (2001), pp. 101–113

Bliman, 2004 P.A. Bliman An existence result for polynomial solutions of parameter-dependent LMIs Systems & Control Letters, 51 (3–4) (2004), pp. 165–169

Cao and Lam, 2001 Y.Y. Cao, J. Lam A computational method for simultaneous LQ optimal control design via piecewise constant output feedback IEEE Transactions on Systems, Man and Cybernetics, 31 (5) (2001), pp. 836–842

Chesi et al., 2005 G. Chesi, A. Garulli, A. Tesi, A. Vicino Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: An LMI approach IEEE Transactions on Automatic Control, 50 (3) (2005), pp. 365–370

Dullerud and Paganini, 2005 G.E. Dullerud, F. Paganini A course in robust control theory: A convex approach Texts in Applied Mathematics, Springer (2005)

Feron et al., 1996 E. Feron, P. Apkarian, P. Gahinet Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions IEEE Transactions on Automatic Control, 41 (7) (1996), pp. 1041–1046

Foo and Soh, 1993 Y.K. Foo, Y.C. Soh Robust stability bound for systems with structured and unstructured perturbations Automation and Remote Control, 38 (7) (1993), pp. 1150–1154

Gao et al., 2005 H. Gao, J. Lam, L. Xie, C. Wang New approach to mixed H2/H∞ filtering for polytopic discrete-time systems IEEE Transactions on Signal Processing, 53 (8) (2005), pp. 3183–3192

Goncalves et al., 2005 E.N. Goncalves, R.M. Palhares, R.H.C. Takahashi Improved optimisation approach to the robust H2/H∞ control problem for linear systems IEE Proceedings-Control Theory and Applications, 152 (2) (2005), pp. 171–176

Kau et al., 2005 S. Kau, Y. Liu, L. Hong, C. Lee, C. Fang, L. Lee A new LMI condition for robust stability of discrete-time uncertain systems Systems & Control Letters, 54 (12) (2005), pp. 1195–1203

Lavaei and Aghdam, 2006 Lavaei, J., & Aghdam, A.G. (2006). Robust stability of discrete-time systems using sum-of-squares matrix polynomials. In Proc. 2006 American Contr. Conf. (pp. 3828–3830)

Lavaei and Aghdam, 2007a J. Lavaei, A.G. Aghdam Optimal periodic feedback design for continuous-time LTI systems with constrained control structure International Journal of Control, 80 (2) (2007), pp. 220–230

Lavaei and Aghdam, 2007b J. Lavaei, A.G. Aghdam Simultaneous LQ control of a set of LTI systems using constrained generalized sampled-data hold functions Automatica, 43 (2) (2007), pp. 274–280

Lavaei and Aghdam, 2008 J. Lavaei, A.G. Aghdam Robust stability of LTI systems over semi-algebraic sets using sum-of-squares matrix polynomials IEEE Transactions on Automatic Control, 53 (1) (2008), pp. 417–423

Lin et al., 2006 C. Lin, Q.G. Wang, T.H. Lee A less conservative robust stability test for linear uncertain time-delay systems IEEE Transactions on Automatic Control, 51 (1) (2006), pp. 87–91

Lofberg, 2004 Lofberg, J. (2004). A toolbox for modeling and optimization in MATLAB. In Proc. of the CACSD conf. Available online at http://control.ee.ethz.ch/~joloef/yalmip.php

Oliveira and Geromel, 2005 M.C.de Oliveira, J.C. Geromel A class of robust stability conditions where linear parameter dependence of the Lyapunov function is a necessary condition for arbitrary parameter dependence Systems & Control Letters, 54 (11) (2005), pp. 1131–1134

Oliveira et al., 2004 P.J.de Oliveira, R.C.L.F. Oliveira, V.J.S. Leite, V.F. Montagner, P.L.D. Peres H2 guaranteed cost computation by means of parameter dependent Lyapunov functions International Journal of Systems Science, 35 (5) (2004), pp. 305–315

Oliveira and Peres, 2006 R.C.L.F. Oliveira, P.L.D. Peres LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions Systems & Control Letters, 55 (1) (2006), pp. 52–61


Prajna et al., 2004 Prajna, S., Papachristodoulou, A., Seiler, P., & Parrilo, P.A. (2004). SOSTOOLS sum of squares optimization toolbox for MATLAB. Users guide. Available online at http://www.cds.caltech.edu/sostools

Sekaj and Vesely, 2005 I. Sekaj, V. Vesely Robust output feedback controller design: Genetic algorithm approach

IMA Journal of Mathematical Control and Information, 22 (3) (2005), pp. 257–265

Shaked, 2003 U. Shaked An LPD approach to robust H2 and H∞ static output-feedback design IEEE Transactions on Automatic Control, 48 (5) (2003), pp. 866–872

Vesely, 2005 V. Vesely Static output feedback robust controller design via LMI approach Journal of Electrical Engineering, 56 (1–2) (2005), pp. 3–8
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