Synchronization of Discrete-Time Chaotic Fuzzy Systems by means of Fuzzy Output Regulation Using Genetic Algorithm

The synchronization of chaotic systems, described by discrete-time T-S fuzzy models, is treated by means of fuzzy output regulation theory. The conditions for designing a discrete-time output regulator are given in this paper. Besides, when the system does not fulfill the conditions for exact tracking, a new regulator based on genetic algorithms is considered. The genetic algorithms are used to approximate the adequate membership functions, which allow the adequate combination of local regulators. As a result, the tracking error is significantly reduced. Both the Complete Synchronization and the Generalized Synchronization problem are studied. Some numerical examples are used to illustrate the effectiveness of the proposed approach.

[1]  Jesús A. Meda-Campaña,et al.  Analysis of the Fuzzy Controllability Property and Stabilization for a Class of T–S Fuzzy Models , 2015, IEEE Transactions on Fuzzy Systems.

[2]  John H. Holland,et al.  Outline for a Logical Theory of Adaptive Systems , 1962, JACM.

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

[4]  Alan V. Oppenheim,et al.  Circuit implementation of synchronized chaos with applications to communications. , 1993, Physical review letters.

[5]  Bernardino Castillo-Toledo,et al.  The fuzzy discrete-time robust regulation problem: an LMI approach , 2004, IEEE Transactions on Fuzzy Systems.

[6]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[7]  He,et al.  Analysis and synthesis of synchronous periodic and chaotic systems. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[8]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[9]  Pyragas,et al.  Weak and strong synchronization of chaos. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Kazuo Tanaka,et al.  Parallel distributed compensation of nonlinear systems by Takagi-Sugeno fuzzy model , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[11]  A. Isidori.  Nonlinear Control Systems , 1985 .

[12]  B. Francis.  The linear multivariable regulator problem , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[13]  Tonatiuh Hernandez-Cortes,et al.  A Simplified Output Regulator for a Class of Takagi-Sugeno Fuzzy Models , 2015 .

[14]  Mohamed Laid Hadjili,et al.  A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy Models , 2007, Int. J. Appl. Math. Comput. Sci..

[15]  Guanrong Chen,et al.  Synchronization of chaotic systems from a fuzzy regulation approach , 2009, Fuzzy Sets Syst..

[16]  B. Castillo-Toledo,et al.  A fuzzy output regulator for Takagi-Sugeno fuzzy models , 2003, Proceedings of the 2003 IEEE International Symposium on Intelligent Control.

[17]  E. Solak,et al.  Observer-based control of a class of chaotic systems , 2001 .

[18]  Hans-Paul Schwefel,et al.  Numerical Optimization of Computer Models , 1982 .

[19]  Ricardo Tapia-Herrera,et al.  Tuning of a TS Fuzzy Output Regulator Using the Steepest Descent Approach and ANFIS , 2013 .

[20]  A. Isidori,et al.  Output regulation of nonlinear systems , 1990 .

[21]  Ivan Zelinka,et al.  Evolutionary Algorithms and Chaotic Systems , 2010, Evolutionary Algorithms and Chaotic Systems.

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

[23]  Guanrong Chen,et al.  Integration of Fuzzy Logic and Chaos Theory , 2010 .

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

[25]  E. Solak,et al.  On the Synchronization of Chaos Systems by Using State Observers , 1997 .

[26]  Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos , 2015 .

[27]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[28]  Farid Sheikholeslam,et al.  Stability analysis and design of fuzzy control systems , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

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

[30]  Her-Terng Yau,et al.  Circuit Implementation and Synchronization Control of Chaotic Horizontal Platform Systems by Wireless Sensors , 2013 .

[31]  D. B. Fogel,et al.  Revisiting Bremermann's genetic algorithm. I. Simultaneous mutation of all parameters , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[32]  P. Sangapate.  Adaptive Control and Synchronization of the Shallow Water Model , 2012 .

[33]  B. Castillo-Toledo,et al.  On the output regulation for TS fuzzy models using sliding modes , 2005, Proceedings of the 2005, American Control Conference, 2005..