Robust polytopic invariant sets for discrete fuzzy control systems

TS fuzzy models are exact representations of nonlinear systems in a compact zone (sector nonlinearity). Once a controller is found by Lyapunov methods, determining the set of initial conditions such that the state does not leave the modelling region is an important problem to be solved. Also, determining the set to which the disturbances will steer the system is also necessary to ensure that the size of the modelling region has been correctly estimated. This paper proposes polytopic approximation to such sets based in algorithms from [1]. A Polya-based approach has been introduced in order to (conservatively) transform the nonlinear invariant set problem into a polytopic one.

[1]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[2]  Alberto Bemporad,et al.  Stabilizing Model Predictive Control of Hybrid Systems , 2006, IEEE Transactions on Automatic Control.

[3]  Carlos Ariño,et al.  Maximal closed loop admissible set for linear systems with non-convex polyhedral constraints , 2011 .

[4]  Mato Baotic,et al.  Multi-Parametric Toolbox (MPT) , 2004, HSCC.

[5]  Kazuo Tanaka,et al.  A fuzzy Lyapunov approach to fuzzy control system design , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[6]  J. Suykens,et al.  The efficient computation of polyhedral invariant sets for linear systems with polytopic uncertainty , 2005, Proceedings of the 2005, American Control Conference, 2005..

[7]  David Q. Mayne,et al.  Optimized robust control invariance for linear discrete-time systems: Theoretical foundations , 2007, Autom..

[8]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[9]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[10]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  E. Kerrigan.  Robust Constraint Satisfaction: Invariant Sets and Predictive Control , 2000 .

[12]  Robert Babuska,et al.  Perspectives of fuzzy systems and control , 2005, Fuzzy Sets Syst..

[13]  Antonio Sala,et al.  Local fuzzy modeling: Maximising the basin of attraction , 2010, International Conference on Fuzzy Systems.

[14]  Antonio Sala,et al.  Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem , 2007, Fuzzy Sets Syst..