Abstract
This paper presents a fuzzy controller to solve a master-slave chaos synchronization problem. At first, the method of traditional sliding mode control is considered, which utilizes the discontinuous sign function to make the system state reaching a sliding surface. Next, fuzzy rules are determined according to the Lyapunov theorem, and the fuzzy controller is designed for chaos synchronization. Finally, an example of chaos synchronization for an uncertain Duffing-Holmes system is presented to illustrate the validity and feasibility of the proposed controller.
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References
Carroll, T.L., Pecora, L.M.: Synchronizing chaotic system. IEEE Trans. Circ. Syst. I: Fundam. Theory Appl. 38, 453–456 (1991)
Chen, C.L., Lin, W.Y.: Sliding mode control for non-linear system with global invariance. Proc. Inst. Mech. Engrs. 211, 75–82 (1997)
Chen, G., Fong, G.: Chaotification via arbitrarily small feedback controls: theory, method, and applications. Int. J. Bifur. Chaos 10, 549–570 (2000)
Chen, G., Dong, X.: From chaos to order: methodologies, perspectives and applications. World Scientific, Singapore (1998)
Liao, T.-L.: Adaptive synchronization of two Lorenz system. Chaos Solitons & Fractals 9, 1555–1561 (1998)
Lian, K.-Y., Liu, P., Chiang, T.-S., Chiu, C.-S.: Adaptive synchronization design for chaotic systems via a scalar driving signal. IEEE Trans. Circuit Syst. I 49, 17–27 (2002)
Lu, J., Zhang, S.: Controlling Chen’s chaotic attractor using backstepping design based on parameters identification. Phys Lett. A 286, 145–149 (2001)
Lü, J., Chen, S.: Chaotic time series analysis and its application. Wuhan University Press, China (2002)
Nayfeh, A.H.: Applied nonlinear dynamics. Wiley, New York (1995)
Slotine, J.E., Li, W.: Applied nonlinear control. Prentice-Hall, Englewood Cliffs (1991)
Suykens, J.A.K., Curran, P.F., Vandewalle, J.: Robust nonlinear synchronization of chaotic Lur’e system. IEEE Trans. Circuit Syst. I 44, 891–904 (1997)
Tamasevicius: Reproducible analogue circuit for chaotic synchronization. Electron. Lett. 33, 1105–1106 (1997)
Tanaka, K., Ikeda, T., Wang, H.O.: A unified approach to controlling chaos via LMI-based fuzzy control system design. IEEE Trans. Circ. Syst. I 45, 1021–1040 (1998)
Yau, H.-T.: Design of Adaptive Sliding Mode Controller for Chaos Synchronization with Uncertaintie. Chaos Solitons & Fractals 22, 341–347 (2004)
Yau, H.-T., Kuo, C.-L., Yan, J.-J.: Fuzzy Sliding Mode Control for A Class of Chaos Synchronization with Uncertainties. International Journal of Nonlinear Sciences and Numerical Simulation 7(3), 333–338 (2006)
Yin, X., Ren, Y., Shan, X.: Synchronization of discrete spatiotemporal chaos by busing variable structure control. Chaos Solitons & Fractals 14, 1077–1082 (2002)
Zadeh, L.A.: Outline of a New Approach to Analysis of Complex System and Decision Process. IEEE Transactions on Systems, Man, and Cybernetics 3(1), 28–44 (1973)
Zadeh, L.A.: Fuzzy Logic. IEEE Computer 21(4), 83–93 (1988)
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Kuo, CL., Shieh, CS., Lin, CH., Shih, SP. (2007). Design of Fuzzy Sliding-Mode Controller for Chaos Synchronization. In: Park, JW., Kim, T.G., Kim, YB. (eds) AsiaSim 2007. AsiaSim 2007. Communications in Computer and Information Science, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77600-0_5
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DOI: https://doi.org/10.1007/978-3-540-77600-0_5
Publisher Name: Springer, Berlin, Heidelberg
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