A New Fuzzy Impulsive Control of Chaotic Systems Based on T–S Fuzzy Model

In this paper, fuzzy impulsive control is used for stabilization of chaotic systems based on the Takagi-Sugeno (T-S) model. The stability issue of the general nonlinear impulsive control system is first investigated via comparison criterion. Then, a novel impulsive control scheme is presented for chaotic systems based on the T-S fuzzy model. Some sufficient conditions are given to stabilize the T-S fuzzy model. Our results are proven to be less conservative theoretically and numerically. Moreover, we have also estimated the stable region of the impulsive interval. Finally, the proposed fuzzy impulsive control scheme is successfully applied to stabilize Rössler's system and Chua's circuit. The numerical simulations demonstrate the effectiveness and advantage of our main results.

[1]  Zhi-Hong Guan,et al.  Impulsive synchronization for Takagi-Sugeno fuzzy model and its application to continuous chaotic system [rapid communication] , 2005 .

[2]  Xinzhi Liu,et al.  Impulsive stabilization and control of chaotic system , 2001 .

[3]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Zheng Yong-ai,et al.  Synchronization for Rössler Chaotic Systems Using Fuzzy Impulsive Controls , 2007, Third International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP 2007).

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

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

[7]  Christopher J. Harris,et al.  Fuzzy local linearization and local basis function expansion in nonlinear system modeling , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[8]  Kazuo Tanaka,et al.  A unified approach to controlling chaos via an LMI-based fuzzy control system design , 1998 .

[9]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[10]  Jitao Sun,et al.  A Lie Algebraic Condition of Stability for Hybrid Systems and Application to Hybrid Synchronization , 2009, Int. J. Bifurc. Chaos.

[11]  Xiaofeng Liao,et al.  Complete and lag synchronization of hyperchaotic systems using small impulses , 2004 .

[12]  Yang Liu,et al.  A new approach to practical stability of impulsive functional differential equations in terms of two measures , 2009 .

[13]  Jinde Cao,et al.  Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters. , 2005, Chaos.

[14]  Qidi Wu,et al.  Less conservative conditions for asymptotic stability of impulsive control systems , 2003, IEEE Trans. Autom. Control..

[15]  Xiaofeng Liao,et al.  Impulsive control for T-S fuzzy model based chaotic systems with adaptive feedback , 2009, 2009 International Conference on Communications, Circuits and Systems.

[16]  Guanrong Chen,et al.  Fuzzy impulsive control of chaotic systems based on TS fuzzy model , 2009 .

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

[18]  Jiang-Wen Xiao,et al.  Impulsive control for synchronization of a class of continuous systems. , 2004, Chaos.

[19]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[20]  Yongbin Yu,et al.  Impulsive control for T-S fuzzy model based time-delay chaotic systems , 2008, 2008 International Conference on Communications, Circuits and Systems.

[21]  Xiaohong Zhang,et al.  Impulsive stability of chaotic systems represented by T-S model , 2009 .

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

[23]  Mignon Park,et al.  Design of an adaptive fuzzy model based controller for chaotic dynamics in Lorenz systems with uncertainty , 2002, Inf. Sci..

[24]  Dong Li,et al.  Impulsive Control of T-S Fuzzy Systems , 2007, Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007).

[25]  Zhengguo Li,et al.  Analysis and design of impulsive control systems , 2001, IEEE Trans. Autom. Control..

[26]  Peter Liu,et al.  LMI-based fuzzy chaotic synchronization and communications , 2001, IEEE Trans. Fuzzy Syst..

[27]  S. Zhong,et al.  T-S fuzzy model-based impulsive control of chaotic systems with exponential decay rate , 2007 .

[28]  Yan-Wu Wang,et al.  Impulsive Control for T-s Fuzzy System and its Application to Chaotic Systems , 2006, Int. J. Bifurc. Chaos.

[29]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[30]  Yang Liu,et al.  GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS: A New Approach for Impulsive Stabilization of Liu's System , 2010 .

[31]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[32]  Chun-Mei Yang,et al.  Impulsive control of Lorenz system , 1997 .

[33]  Leon O. Chua,et al.  Conditions for impulsive Synchronization of Chaotic and hyperchaotic Systems , 2001, Int. J. Bifurc. Chaos.