Takagi-Sugeno fuzzy receding horizon H∞ chaotic synchronization and its application to the Lorenz system

Abstract In this article, we propose a new H ∞ synchronization method for chaotic systems with external disturbance based on the Takagi–Sugeno (T–S) fuzzy model and receding horizon control. This synchronization method is called a Takagi–Sugeno fuzzy receding horizon H ∞ synchronization (TSFRHHS) method. A new set of matrix inequality conditions on the terminal weighting matrix is proposed for T–S fuzzy chaotic systems wherein non-increasing monotonicity of the optimal cost is guaranteed. Under this set of terminal inequality conditions, the proposed TSFRHHS method guarantees the infinite horizon H ∞ performance for T–S fuzzy chaotic systems with external disturbance. As an application of the proposed synchronization method, the TSFRHHS problem for the Lorenz system is investigated.

[1]  Wook Hyun Kwon,et al.  Stabilizing receding horizon H∞ controls for linear continuous time-varying systems , 2000, IEEE Trans. Autom. Control..

[2]  C. Ahn.  T–S fuzzy ℋ∞ synchronization for chaotic systems via delayed output feedback control , 2010 .

[3]  Choon Ki Ahn,et al.  Adaptive H∞ Anti-Synchronization for Time-Delayed Chaotic Neural Networks , 2009 .

[4]  Choon Ki Ahn,et al.  An H∞ approach to anti-synchronization for chaotic systems , 2009 .

[5]  Zhi-Hong Guan,et al.  Feedback and adaptive control for the synchronization of Chen system via a single variable , 2003 .

[6]  Sung Tae Jung,et al.  Adaptive H∞ synchronization for uncertain chaotic systems with external disturbance , 2010 .

[7]  Lee Sun-Jin.  From Chaos to Order , 2011 .

[8]  W. Kwon,et al.  A modified quadratic cost problem and feedback stabilization of a linear system , 1977 .

[9]  W. Kwon,et al.  On feedback stabilization of time-varying discrete linear systems , 1978 .

[10]  Choon Ki Ahn.  Adaptive Script H∞ Chaos Anti-synchronization , 2010 .

[11]  T. Kailath,et al.  Stabilizing state-feedback design via the moving horizon method , 1982, 1982 21st IEEE Conference on Decision and Control.

[12]  Choon Ki Ahn,et al.  Output feedback ℋ∞ synchronization for delayed chaotic neural networks , 2009 .

[13]  Meng Zhan,et al.  Complete synchronization and generalized synchronization of one-way coupled time-delay systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[15]  Choon Ki Ahn,et al.  Switched Synchronization with a Guaranteed Performance , 2011 .

[16]  Guanrong Chen,et al.  Some observer-based criteria for discrete-time generalized chaos synchronization , 2002 .

[17]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

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

[19]  Chun-Chieh Wang,et al.  A new adaptive variable structure control for chaotic synchronization and secure communication , 2004 .

[20]  C. Ahn.  Neural network ℋ∞ chaos synchronization , 2010 .

[21]  Shihua Chen,et al.  Adaptive control for anti-synchronization of Chua's chaotic system , 2005 .

[22]  Kazuo Tanaka,et al.  Stability analysis and design of fuzzy control systems , 1992 .

[23]  Oh-Min Kwon,et al.  LMI optimization approach to stabilization of time-delay chaotic systems , 2005 .

[24]  Wook Hyun Kwon,et al.  On stability of constrained receding horizon control with finite terminal weighting matrix , 1997, 1997 European Control Conference (ECC).

[25]  Ju H. Park.  Adaptive Synchronization of a Unified Chaotic System with an Uncertain Parameter , 2005 .

[26]  Wook Hyun Kwon,et al.  Receding Horizon Tracking Control as a Predictive Control and its Stability Properties , 1988, 1988 American Control Conference.

[27]  Er-Wei Bai,et al.  Synchronization of two Lorenz systems using active control , 1997 .

[28]  A receding horizon control approach to synchronization for chaotic systems , 2009, 2009 ICCAS-SICE.