Controlling chaotic systems via nonlinear state feedback and linear H ∞ controller design

In this paper, a method for controlling chaotic systems, such as Lorenz system, Chen system and Lu system is described; which is composed by a nonlinear state vector feedback and a linear H∞ controller. With this method the objective is to stabilize chaotic oscillations to a steady state, as well as tracking a desired trajectory. In order to physical implementation a discrete time H∞ controller is used with adjusted sample time, and analogic implementation is used for nonlinear part of the controller. Computer simulations are given and analyzed for the purpose of illustration and verification.

[1]  Tetsushi Ueta,et al.  Control of chaos in a piecewise smooth nonlinear system , 2006 .

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

[4]  L. Chua,et al.  A universal circuit for studying and generating chaos. II. Strange attractors , 1993 .

[5]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[6]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[7]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[8]  Guanrong Chen,et al.  Bifurcation Analysis of Chen's equation , 2000, Int. J. Bifurc. Chaos.

[9]  Guanrong Chen,et al.  On a Generalized Lorenz Canonical Form of Chaotic Systems , 2002, Int. J. Bifurc. Chaos.

[10]  Maciej J. Ogorzalek,et al.  Taming Chaos: Part 11-Control , 1993 .

[11]  Maciej Ogorzalek,et al.  Taming chaos. I. Synchronization , 1993 .

[12]  M. Yassen.  Chaos control of chaotic dynamical systems using backstepping design , 2006 .

[13]  Daizhan Cheng,et al.  Bridge the Gap between the Lorenz System and the Chen System , 2002, Int. J. Bifurc. Chaos.

[14]  S. Boccaletti,et al.  The control of chaos: theory and applications , 2000 .

[15]  Maciejowsk.  Multivariable Feedback Design , 1989 .

[16]  M. T. Yassen,et al.  Feedback and adaptive synchronization of chaotic Lü system , 2005 .

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

[18]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[19]  Rafael González López,et al.  A Symmetric Piecewise-Linear Chaotic System with a Single Equilibrium Point , 2005, Int. J. Bifurc. Chaos.