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Chaos synchronization using fuzzy logic controller. (English) Zbl 1154.34334

Summary: The design of a rule-based controller for a class of master-slave chaos synchronization is presented in this paper. In traditional fuzzy logic control (FLC) design, it takes a long time to obtain the membership functions and rule base by trial-and-error tuning. To cope with this problem, we directly construct the fuzzy rules subject to a common Lyapunov function such that the master-slave chaos systems satisfy stability in the Lyapunov sense. Unlike conventional approaches, the resulting control law has less maximum magnitude of the instantaneous control command and it can reduce the actuator saturation phenomenon in real physic system. Two examples of Duffing-Holmes system and Lorenz system are presented to illustrate the effectiveness of the proposed controller.

MSC:

34C28 Complex behavior and chaotic systems of ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C42 Fuzzy control/observation systems
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[1] Agiza, H. N., Chaos synchronization of Lü dynamical system, Nonlinear Anal., 58, 1-2, 11-20 (2004) · Zbl 1057.34042
[2] Astakhov, V. V.; Anishchenko, V. S.; Kapitaniak, T.; Shabunin, A. V., Synchronization of chaotic oscillators by periodic parametric perturbations, Physica D, 109, 11-16 (1997) · Zbl 0925.58055
[3] Chen, G.; Dong, X., From Chaos to Order: Methodologies, Perspectives and Applications (1998), World Scientific: World Scientific Singapore · Zbl 0908.93005
[4] Chua, L. O.; Yang, T.; Zhong, G. Q.; Wu, C. W., Adaptive synchronization of Chua’s oscillators, Int. J. Bifurcation Chaos, 6, 1, 189-201 (1996)
[5] Escultura, E. E., Dynamic modeling of chaos and turbulence, Nonlinear Anal., 63, 5-7, 519-532 (2005) · Zbl 1159.83374
[6] Fang, J. Q.; Hong, Y.; Chen, G., Switching manifold approach to chaos synchronization, Phys. Rev. E, 59, 2523-2526 (1999)
[7] Feng, G.; Chen, G., Adaptive control of discrete-time chaotic systems: a fuzzy control approach, Chaos Solitons Fractals, 23, 459-467 (2005) · Zbl 1061.93501
[8] C.L. Kuo, T.H. Li, N. Guo, Design of a novel fuzzy sliding-mode control for magnetic ball levitation system, J. Intell. Robotic Syst. (2004), 1-22.; C.L. Kuo, T.H. Li, N. Guo, Design of a novel fuzzy sliding-mode control for magnetic ball levitation system, J. Intell. Robotic Syst. (2004), 1-22.
[9] Lian, K. Y.; Liu, P.; Chiang, T. S.; Chiu, C. S., Adaptive synchronization design for chaotic systems via a scalar Driving signal, IEEE Trans. Circuits Syst. I, 49, 1, 17-27 (2002)
[10] Liao, T. L., Adaptive synchronization of two Lorenz systems, Chaos Solitons Fractals, 9, 1555-1561 (1998) · Zbl 1047.37502
[11] Lu, J.; Zhang, S., Controlling Chen’s chaotic attractor using backstepping design based on parameters identification, Phys. Lett. A, 286, 145-149 (2001)
[12] Nayfeh, A. H., Applied Nonlinear Dynamics (1995), Wiley: Wiley New York
[13] Park, J. H., Synchronization of Genesio chaotic system via backstepping approach, Chaos Solitons Fractals, 27, 1369-1375 (2006) · Zbl 1091.93028
[14] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 8, 821-824 (1990) · Zbl 0938.37019
[15] Shieh, C. S., Nonlinear rule-based controller for missile terminal guidance, IEE Proc. Control Theory Appl., 150, 1, 45-48 (2003)
[16] Slotine, J. E.; Li, W., Applied Nonlinear Control (1991), Prentice-Hall: Prentice-Hall New Jersey · Zbl 0753.93036
[17] Suykens, J. A.K.; Curran, P. F.; Vandewalle, J., IEEE Trans. Circuits Syst. I, 44, 10, 891-904 (1997)
[18] Takeo, F., Chaos and hypercyclicity for solution semigroups to some partial differential equations, Nonlinear Anal., 63, 5-7, 1943-1953 (2005) · Zbl 1226.47009
[19] Tanaka, K.; Ikeda, T.; Wang, H. O., A unified approach to controlling chaos via LMI-based fuzzy control system design, IEEE Trans Circuits Syst. I, 45, 1021-1040 (1998) · Zbl 0951.93046
[20] Wang, C.; Ge, S. S., Adaptive synchronization of uncertain chaotic systems via backstepping design, Chaos Solitons Fractals, 12, 199-206 (2001) · Zbl 1015.37052
[21] Wang, Y.; Guan, Z. H.; Wen, X., Adaptive synchronization for Chen chaotic system with fully unknown parameters, Chaos Solitons Fractals, 19, 899-903 (2004) · Zbl 1053.37528
[22] Wu, C. W.; Yang, T.; Chua, L. O., On adaptive synchronization and control of nonlinear dynamical systems, Int. J. Bifurcation Chaos, 6, 455-471 (1996) · Zbl 0875.93182
[23] Xue, Y. J.; Yang, S. Y., Synchronization of generalized Henon map by using adaptive fuzzy controller, Chaos Solitons Fractals, 17, 717-722 (2003) · Zbl 1043.93519
[24] Yang, X. S.; Duan, C. K.; Liao, X. X., A note on mathematical aspects of drive-response type synchronization, Chaos Solitons Fractals, 10, 1457-1462 (1999) · Zbl 0955.37020
[25] Yau, H. T., Design of adaptive sliding mode controller for chaos synchronization with uncertainties, Chaos Solitons Fractals, 22, 341-347 (2004) · Zbl 1060.93536
[26] Yau, H. T.; Lin, J. S.; Yan, J. J., Synchronization control for a class of chaotic systems with uncertainties, Int. J. Bifurcation Chaos, 15, 7, 2235-2246 (2005) · Zbl 1092.93594
[27] Yau, H. T.; Yan, J. J., Design of sliding mode controller for Lorenz chaotic system with nonlinear input, Chaos Solitons Fractals, 19, 891-898 (2004) · Zbl 1064.93010
[28] Yin, X.; Ren, Y.; Shan, X., Synchronization of discrete spatiotemporal chaos by using Variable structure control, Chaos Solitons Fractals, 14, 1077-1082 (2002) · Zbl 1038.37506
[29] Yu, X.; Song, Y., Chaos synchronization via controlling partial state of chaotic systems, Int. J. Bifurcation Chaos, 11, 6, 1737-1741 (2001)
[30] Zadeh, L. A., Fuzzy logic, IEEE Comput., 21, 4, 83-93 (1988)
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