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Adaptive robust fuzzy control for a class of uncertain chaotic systems. (English) Zbl 1176.93040
Summary: In this paper, the output feedback control of uncertain chaotic systems is addressed via an adaptive robust fuzzy approach. Fuzzy logic systems are employed to approximate uncertain nonlinear functions in the chaotic systems. Because only partial information of the system’s states is needed to be known, an observer is given to estimate the unmeasured states. Compared with the existing results in the observer design, the prior knowledge on dynamic uncertainties is relaxed and a class of more general chaotic systems is considered as well as robustness to the approximation error is improved. It can be proven that the closed-loop system is stable in the sense that all the variables are bounded. Simulation example for the unified chaotic systems is given to verify the effectiveness of the proposed method.
MSC:
93C40Adaptive control systems
93C42Fuzzy control systems
References:
[1]Chen, G.R.: Controlling Chaos and Bifurcations in Engineering Systems. CRC Press, Boca Raton (1999)
[2]Ge, S.S., Wang, C.: Adaptive control of uncertain Chua’s circuits. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 47(9), 1397–1402 (2000) · Zbl 1046.93506 · doi:10.1109/81.883337
[3]Ge, S.S., Wang, C.: Uncertain chaotic system control via adaptive neural design. Int. J. Bifurc. Chaos 12(5), 1097–1109 (2002) · Zbl 1051.93523 · doi:10.1142/S0218127402004930
[4]Wang, C., Ge, S.S.: Adaptive backstepping control of uncertain Lorenz system. Int. J. Bifurc. Chaos 11(4), 1115–1119 (2001) · Zbl 1090.93536 · doi:10.1142/S0218127401002560
[5]Jiang, Z.P.: Advanced feedback control of the chaotic Duffing equation. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 49(2), 244–249 (2002) · doi:10.1109/81.983872
[6]Hua, C.C., Guan, X.P.: Adaptive control for chaotic systems. Chaos Solitons Fractals 22(1), 55–60 (2004) · Zbl 1069.93016 · doi:10.1016/j.chaos.2003.12.071
[7]Hua, C.C., Guan, X.P., Shi, P.: Adaptive feedback control for a class of chaotic systems. Chaos Solitons Fractals 23(3), 757–765 (2005) · Zbl 1061.93503 · doi:10.1016/j.chaos.2004.05.042
[8]Chen, B., Liu, X.P., Tong, S.C.: Adaptive fuzzy approach to control unified chaotic systems. Chaos Solitons Fractals 34(4), 1180–1187 (2007) · Zbl 1142.93356 · doi:10.1016/j.chaos.2006.04.035
[9]Hua, C.C., Guan, X.P., Li, X.L., Shi, P.: Adaptive observer-based control for a class of chaotic systems. Chaos Solitons Fractals 22(1), 103–110 (2004) · Zbl 1089.93010 · doi:10.1016/j.chaos.2003.12.072
[10]Tong, S.C., Li, H.X.: Direct adaptive fuzzy output tracking control of nonlinear systems. Fuzzy Sets Syst. 128, 107–115 (2002) · Zbl 0995.93512 · doi:10.1016/S0165-0114(01)00058-6
[11]Tong, S.C., Li, H.X., Wang, W.: Observer-based adaptive fuzzy control for SISO nonlinear systems. Fuzzy Sets Syst. 148(3), 355–376 (2004) · Zbl 1057.93029 · doi:10.1016/j.fss.2003.11.017
[12]Wang, C.H., Lin, T.C., Lee, T.T., Liu, H.L.: Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems. IEEE Trans. Syst. Man Cybern. Part B 32, 583–597 (2002) · doi:10.1109/TSMCB.2002.1033178
[13]Kung, C.C., Chen, T.H.: Observer-based indirect adaptive fuzzy sliding mode control with state variable filters for unknown nonlinear dynamical systems. Fuzzy Sets Syst. 155(2), 292–308 (2005) · Zbl 1140.93411 · doi:10.1016/j.fss.2005.04.016
[14]Wang, J., Qiao, G.D., Deng, B.: Observer-based robust adaptive variable universe fuzzy control for chaotic system. Chaos Solitons Fractals 23(3), 1013–1032 (2005)
[15]Boulkroune, A., Tadjine, M., M’Saad, M., Farza, M.: How to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems. Fuzzy Sets Syst. 159(8), 926–948 (2008) · Zbl 1170.93335 · doi:10.1016/j.fss.2007.08.015
[16]Wang, L.X.: Fuzzy systems are universal approximators. In: IEEE International Conference on Fuzzy Systems, San Diego, pp. 1163–1170 (1992)
[17]Li, T.S., Yang, Y.S., Hu, J.Q., Yang, L.J.: Robust adaptive fuzzy tracking control for a class of perturbed uncertain nonlinear systems with UVCGF. Int. J. Wavelets Multiresolut. Inf. Process. 5(1), 227–239 (2007) · Zbl 1158.93358 · doi:10.1142/S0219691307001604
[18]Li, T.S., Hong, B.G., Shi, G.Y.: DSC-backstepping based robust adaptive NN control for strict-feedback nonlinear systems via small gain theorem. Int. J. Syst. Control Commun. 1(1), 124–145 (2008) · doi:10.1504/IJSCC.2008.019587