Control of Rabinovich chaotic system based on passive control

This paper discusses the control of three-dimensional continuous Rabinovich attractor by using passive control technique. Based on the property of the passive system, the passive controller is designed and this controller is added to chaotic Rabinovich system for achieving the control of the system. The controller is ensured to the global asymptotical stability of the three dimensional Rabinovich chaotic system via Lyapunov theory. As a result, the control of Rabinovich chaotic system is realized. To confirm the validity of the proposed method, numerical simulations are presented graphically.

[1]  Wei Lin,et al.  Feedback stabilization of general nonlinear control systems: a passive system approach , 1995 .

[2]  M.,et al.  Onset of stochasticity in decay confinement of parametric instability , 2010 .

[3]  Guanrong Chen,et al.  Adaptive Synchronization of Chaotic Systems via State or output Feedback Control , 2001, Int. J. Bifurc. Chaos.

[4]  Sahjendra N. Singh,et al.  Adaptive Control of Chaos in Lorenz System , 1997 .

[5]  Chongxin Liu,et al.  Passive control on a unified chaotic system , 2010 .

[6]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .

[7]  Wen Yu Passive equivalence of chaos in Lorenz system , 1999 .

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

[9]  Donglian Qi,et al.  Passive control of Chen chaotic system , 2004, Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788).

[10]  Günyaz Ablay,et al.  Sliding mode control of uncertain unified chaotic systems , 2009 .

[11]  L. Chua,et al.  The double scroll family , 1986 .

[12]  M. Yassen Controlling chaos and synchronization for new chaotic system using linear feedback control , 2005 .

[13]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.

[14]  Karim Kemih,et al.  Control of nuclear spin generator system based on passive control , 2009 .

[15]  Keiji Konishi,et al.  Sliding mode control for a class of chaotic systems , 1998 .

[16]  Leon O. Chua,et al.  ON ADAPTIVE SYNCHRONIZATION AND CONTROL OF NONLINEAR DYNAMICAL SYSTEMS , 1996 .

[17]  O. Rössler An equation for continuous chaos , 1976 .

[18]  Xiaobing Zhou,et al.  Passivity-based chaos control and synchronization of a four-dimensional chaotic system , 2009, 2009 International Conference on Communications, Circuits and Systems.

[19]  Chongxin Liu,et al.  A new chaotic attractor , 2004 .

[20]  T. Rikitake,et al.  Oscillations of a system of disk dynamos , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.