A decentralized adaptive robust method for chaos control.

This paper presents a control strategy, which is based on sliding mode control, adaptive control, and fuzzy logic system for controlling the chaotic dynamics. We consider this control paradigm in chaotic systems where the equations of motion are not known. The proposed control strategy is robust against the external noise disturbance and system parameter variations and can be used to convert the chaotic orbits not only to the desired periodic ones but also to any desired chaotic motions. Simulation results of controlling some typical higher order chaotic systems demonstrate the effectiveness of the proposed control method.

[1]  W. Freeman.  Simulation of chaotic EEG patterns with a dynamic model of the olfactory system , 1987, Biological Cybernetics.

[2]  A. Babloyantz,et al.  Predictability of human EEG: a dynamical approach , 1991, Biological Cybernetics.

[3]  W. Chang,et al.  Application of an auto-tuning neuron to sliding mode control , 2002 .

[4]  Ding,et al.  Controlling chaos in high dimensions: Theory and experiment. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  C. Sparrow.  An introduction to the Lorenz equations , 1983 .

[6]  Walter J. Freeman,et al.  EEG analysis gives model of neuronal template-matching mechanism for sensory search with olfactory bulb , 1979, Biological Cybernetics.

[7]  Wpmh Maurice Heemels,et al.  Proceedings of the 14th International Symposium of Mathematical Theory of Networks and Systems , 2000 .

[8]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

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

[10]  Ruiqi Wang,et al.  Chaos control of chaotic pendulum system , 2004 .

[11]  Heinz G. Schuster,et al.  Handbook of Chaos Control: SCHUSTER:HDBK.CHAOS CONTR O-BK , 1999 .

[12]  Jacques Martinerie,et al.  Depression as a dynamical disease , 1996, Biological Psychiatry.

[13]  Wei-Der Chang,et al.  Robust adaptive single neural control for a class of uncertain nonlinear systems with input nonlinearity , 2005, Inf. Sci..

[14]  Abbas Erfanian,et al.  Comments on "Sliding Mode Closed-Loop Control of FES: Controlling the Shank Movement , 2008, IEEE Trans. Biomed. Eng..

[15]  Guanrong Chen,et al.  On feedback control of chaotic continuous-time systems , 1993 .

[16]  Heinz G. Schuster,et al.  Handbook of Chaos Control: Foundations and Applications , 1999 .

[17]  F. H. Lopes da Silva,et al.  Chaos or noise in EEG signals; dependence on state and brain site. , 1991, Electroencephalography and clinical neurophysiology.

[18]  M. T. Yassen,et al.  Chaos control of Chen chaotic dynamical system , 2003 .

[19]  Walter J. Freeman,et al.  TUTORIAL ON NEUROBIOLOGY: FROM SINGLE NEURONS TO BRAIN CHAOS , 1992 .

[20]  Homayoun Seraji,et al.  Decentralized adaptive control of manipulators: theory, simulation, and experimentation , 1989, IEEE Trans. Robotics Autom..

[21]  Walter J. Freeman,et al.  Strange attractors that govern mammalian brain dynamics shown by trajectories of electroencephalographic (EEG) potential , 1988 .

[22]  Li-Xin Wang,et al.  A Course In Fuzzy Systems and Control , 1996 .

[23]  Jun-Juh Yan,et al.  Sliding mode control for uncertain unified chaotic systems with input nonlinearity , 2007 .

[24]  C. Elger,et al.  Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss. , 1995, Electroencephalography and clinical neurophysiology.

[25]  Wei Zhang,et al.  Finite-time chaos control via nonsingular terminal sliding mode control , 2009 .

[26]  C. Elger,et al.  CAN EPILEPTIC SEIZURES BE PREDICTED? EVIDENCE FROM NONLINEAR TIME SERIES ANALYSIS OF BRAIN ELECTRICAL ACTIVITY , 1998 .

[27]  Vadim I. Utkin,et al.  A control engineer's guide to sliding mode control , 1999, IEEE Trans. Control. Syst. Technol..

[28]  Teresa Ree Chay,et al.  BURSTING, SPIKING, CHAOS, FRACTALS, AND UNIVERSALITY IN BIOLOGICAL RHYTHMS , 1995 .

[29]  Elena Panteley,et al.  Control of the chaotic Duffing equation with uncertainty in all parameters , 1998 .

[30]  Huijun Guo,et al.  A radial basis function sliding mode controller for chaotic Lorenz system , 2006 .

[31]  A. Babloyantz,et al.  Evidence of Chaotic Dynamics of Brain Activity During the Sleep Cycle , 1985 .

[32]  Pei Yu,et al.  A method for stability and bifurcation control , 2006, IEEE Transactions on Automatic Control.

[33]  Guanrong Chen,et al.  From Chaos to Order - Perspectives and Methodologies in Controlling Chaotic Nonlinear Dynamical Systems , 1993 .

[34]  Xinghuo Yu,et al.  An invariant-manifold-based method for chaos control , 2001 .