Fuzzy controller based on chaos optimal design and its application

Abstract

In order to overcome difficulty of tuning parameters of fuzzy controller, a chaos optimal design method based on annealing strategy is proposed. First, apply the chaotic variables to search for parameters of fuzzy controller, and transform the optimal variables into chaotic variables by carrier-wave method. Making use of the intrinsic stochastic property and ergodicity of chaos movement to escape from the local minimum and direct optimization searching within global range, an approximate global optimal solution is obtained. Then, the chaos local searching and optimization based on annealing strategy are cited, the parameters are optimized again within the limits of the approximate global optimal solution, the optimization is realized by means of combination of global and partial chaos searching, which can converge quickly to global optimal value. Finally, the third order system and discrete nonlinear system are simulated and compared with traditional method of fuzzy control. The results show that the new chaos optimal design method is superior to fuzzy control method, and that the control results are of high precision, with no overshoot and fast response.

Keywords

fuzzy controller / chaos algorithm / parameter / optimal control

References

[1] KhaledB L, FaouziT. Genetic algorithm for the design of a class of fuzzy controllers: an alternative approach [J]. IEEE Trans on Fuzzy Systems, 2000, 8(4): 324-342

[2] LimM H, RahardjaS, GweeB H. A GA parading for learning fuzzy rules [J]. Fuzzy and Systems, 1996, 82(4): 177-186

[3] MagneS, HansR. GA fuzzy modeling and classification: complexity and performance [J]. IEEE Trans on Fuzzy Systems, 2000, 8(5): 509-522

[4] ZouEn, LiXiang-fei, ChenJian-guoChaotic Control and Optimization Applications [M], 2002, Changsha, National University of Defense Technology Press: 207-216(in Chinese)

[5] WangZi-cai, ZhangTong, WangHong-wei. Simulated annealing algorithm based on chaotic variable [J]. Control and Decision, 1999, 14(4): 381-384(in Chinese)

[6] PanYong-xiang, XuQian-feng, GaoHong-mei. The research of the fuzzy control algorithm optimization based on chaos[J]. Control Theory and Application, 2000, 17(5): 703-706(in Chinese)

[7] ChoiC, LeeJ. Chaotic local search algorithm[J]. Artificial Life and Robotics, 1998, 2(1): 81-384

[8] ZhouC, HeT. Chaotic annealing for optimization[J]. Physical Review E, 1997, 53(3): 2580-2587

[9] ZhouD, YashdaK, YokoyamaR. A method to combine chaos and neural network based on the fixed theory[J]. Transactions of the Institute of Electrical Engineers of Japan, 1997, 117(5): 599-608

[10] HuBao-gang, GeorgeK I M, RaymondG G. New methodology for analytical and optimal design of fuzzy PID controller [J]. IEEE Trans on Fuzzy Systems, 1999, 7(5): 521-538

[11] YouJ, WangL. Simplifying fuzzy rule-based models using orthogonal transformation methods [J]. IEEE Trans on Systems, Man & Cybernetics, 1999, 29B: 13-24

[12] WangL X. Analysis and design of hierarchical fuzzy systems[J]. IEEE Trans On Fuzzy Systems, 1999, 7(6): 617-624

[13] ChaoC T, ChenY J, TengC C. Simplification of fuzzy neural systems using similarity analysis [J]. IEEE Trans on Systems, Man & Cybernetics, 1996, 26B: 344-354

[14] QianFu-cai, FeiChu-hong, WanBai-wu. A hybrid algorithm for finding global minimum [J]. Information and Control, 1998, 27(3): 232-235(in Chinese)

[15] LiBing. Optimization complex function by chaos search [J]. Cybernetics and Systems, 1998, 4(29): 409-419

[16] ChenL, AiharaK. Chaotic simulated annealing by a neural network model with transient chaos[J]. Neural Networks, 1995, 8(6): 915-930