Switch control for piecewise affine chaotic systems.

Switch control can be imposed naturally on the piecewise affine system, where the control action switches from an affine subsystem to another according to switch conditions depending on the system states. In this paper we present such piecewise feedback control for stabilizing unstable equilibrium points of piecewise affine systems. The noise effect on the stabilization is also investigated. The original Chua's circuit is used to illustrate our results.

[1]  Kazuo Tanaka,et al.  An approach to fuzzy control of nonlinear systems: stability and design issues , 1996, IEEE Trans. Fuzzy Syst..

[2]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

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

[4]  Abraham Boyarsky,et al.  A new approach to controlling chaotic systems , 1998 .

[5]  Guanrong Chen.  Controlling Chaos and Bifurcations in Engineering Systems , 1999 .

[6]  Anders Rantzer,et al.  Piecewise linear quadratic optimal control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[7]  Jun-ichi Imura,et al.  Characterization of well-posedness of piecewise-linear systems , 2000, IEEE Trans. Autom. Control..

[8]  Erik M. Bollt,et al.  Controlling Chaos and the Inverse Frobenius-Perron Problem: Global stabilization of Arbitrary Invariant Measures , 2000, Int. J. Bifurc. Chaos.

[9]  Tao Yang,et al.  In: Impulsive control theory , 2001 .

[10]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[11]  Gang Feng,et al.  An approach to $H_{\infty}$ controller synthesis of piecewise linear systems , 2002, Commun. Inf. Syst..

[12]  J. How,et al.  Observer-based control of piecewise-affine systems , 2003 .

[13]  Alexander L. Fradkov,et al.  Control of Chaos: Methods and Applications. I. Methods , 2003 .

[14]  Alexander L. Fradkov,et al.  Control of Chaos: Methods and Applications. II. Applications , 2004 .

[15]  Xiaofeng Liao,et al.  Impulsive synchronization of chaotic systems. , 2005, Chaos.

[16]  Tingwen Huang,et al.  Impulsive stabilization and synchronization of a class of chaotic delay systems. , 2005, Chaos.

[17]  L. Rodrigues.  State feedback control of piecewise-affine systems with norm bounded noise , 2005, Proceedings of the 2005, American Control Conference, 2005..

[18]  L. A. Aguirre,et al.  Piecewise affine models of chaotic attractors: the Rossler and Lorenz systems. , 2006, Chaos.