On the Computation of Robust Control Invariant Sets for Piecewise Affine Systems

In this paper, an alternative approach to the computation of control invariant sets for piecewise affine systems is presented. Based on two approximation operators, two algorithms that provide outer and inner approximations of the maximal robust control invariant set are presented. These algorithms can be used to obtain a robust control invariant set for the system. An illustrative example is presented.

[1]  Computation of piecewise quadratic Lyapunov functions for hybrid systems , 1998, IEEE Trans. Autom. Control..

[2]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

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

[4]  M. Morari,et al.  Stability and stabilization of piecewise affine and hybrid systems: an LMI approach , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[5]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[6]  Alberto Bemporad,et al.  Convexity recognition of the union of polyhedra , 2001, Comput. Geom..

[7]  Bart De Schutter,et al.  Equivalence of hybrid dynamical models , 2001, Autom..

[8]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..

[9]  D. Mayne,et al.  Computation of invariant sets for piecewise affine discrete time systems subject to bounded disturbances , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[10]  Luis Rodrigues Stability analysis of piecewise-affine systems using controlled invariant sets , 2004, Syst. Control. Lett..

[11]  Alberto Bemporad,et al.  Stabilization conditions for model predictive control of constrained PWA systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[12]  Tae Woong Yoon,et al.  Proceedings of the 43rd IEEE Conference on Decision and Control , 2004 .

[13]  Mato Baotic,et al.  Stabilizing low complexity feedback control of constrained piecewise affine systems , 2005, Autom..

[14]  D. Limon,et al.  Enlarging the domain of attraction of MPC controllers , 2005, Autom..