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Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems. (English) Zbl 1170.93349
Summary: This paper is concerned with the problem of adaptive fuzzy output tracking for a class of perturbed strict-feedback nonlinear systems with time delays and unknown virtual control coefficients. Fuzzy logic systems of Mamdani type are used to approximate the unknown nonlinear functions, then the adaptive fuzzy tracking controller is designed by using the backstepping technique and Lyapunov-Krasovskii functionals. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal. An advantage of the proposed control scheme lies in that the number of the online adaptive parameters is not more than the order of the original system. Finally, two examples are used to demonstrate the effectiveness of our results proposed in this paper.
MSC:
93C42Fuzzy control systems
93C40Adaptive control systems
93C73Perturbations in control systems
References:
[1]Boukas, E. K.; Al-Muthairi, N. F.: Delay-dependent stabilization of singular linear systems with delays, Internat. J. Innovative comput. Inform. control 2, No. 2, 283-291 (2006)
[2]Chen, B.; Lam, J.; Xu, S.: Memory state feedback guaranteed cost control for neutral delay systems, Internat. J. Innovative comput. Inform. control 2, No. 2, 293-303 (2006)
[3]Chen, B.; Liu, X. P.: Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping and application to chemical processes, IEEE trans. Fuzzy systems 13, No. 6, 832-847 (2005)
[4]Chen, B.; Tong, S. C.; Liu, X. P.: Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping approach, Fuzzy sets and systems 158, No. 10, 1097-1125 (2007) · Zbl 1113.93068 · doi:10.1016/j.fss.2006.12.012
[5]Freeman, R. A.; Kokotović, P. V.: Robust nonlinear control design, (1996)
[6]Ge, S. S.; Hong, F.; Lee, T. H.: Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients, IEEE trans. Systems man cybernet. — part B 34, No. 1, 499-516 (2004)
[7]Ge, S. S.; Tee, K. P.: Approximation-based control of nonlinear MIMO time-delay systems, Automatica 43, No. 1, 31-43 (2007) · Zbl 1137.93042 · doi:10.1016/j.automatica.2006.08.003
[8]Ge, S. S.; Wang, C.: Uncertain chaotic system control via adaptive neural design, Internat. J. Bifurcation chaos 12, No. 5, 1097-1109 (2002) · Zbl 1051.93523 · doi:10.1142/S0218127402004930
[9]Ho, D. W. C.; Li, J. M.; Niu, Y. G.: Adaptive neural control for a class of nonlinearly parametric time-delay systems, IEEE trans. Neural networks 16, No. 3, 625-635 (2005)
[10]Hong, F.; Ge, S. S.; Lee, T. H.: Practical adaptive neural control of nonlinear systems with unknown time delays, IEEE trans. Systems man cybernet. — part B 35, No. 4, 849-854 (2005)
[11]Hus, C. F.; Lin, C. M.: Fuzzy-identification-based adaptive controller design via backstepping approach, Fuzzy sets and systems 151, No. 1, 43-57 (2005) · Zbl 1142.93357 · doi:10.1016/j.fss.2004.06.015
[12]Jagannathan, S.; Lewis, F. L.: Robust backstepping control of a class of nonlinear systems using fuzzy logic, Inform. sci. 123, 223-240 (2000) · Zbl 0953.93522 · doi:10.1016/S0020-0255(99)00128-0
[13]Kanellakopoulos, I.; Kokotović, P. V.; Marino, R.: An extended direct scheme for robust adaptive nonlinear control, Automatica 27, No. 2, 247-255 (1991) · Zbl 0729.93046 · doi:10.1016/0005-1098(91)90075-D
[14]Kanellakopoulos, I.; Kokotović, P. V.; Morse, A. S.: Systematic design of adaptive controllers for feedback linearizable systems, IEEE trans. Automat. control 36, No. 11, 1241-1253 (1991) · Zbl 0768.93044 · doi:10.1109/9.100933
[15]Krstić, M.; Kanellakopoulos, I.; Kokotović, P. V.: Nonlinear and adaptive control design, (1995)
[16]Lee, H.; Tomizuka, M.: Robust adaptive control using a universal approximator for SISO nonlinear systems, IEEE trans. Fuzzy systems 8, No. 1, 95-106 (2000)
[17]Lewis, F. L.; Yesildirek, A.; Liu, K.: Robust backstepping control of induction motors using neural networks, IEEE trans. Neural networks 11, No. 3, 1178-1187 (2000)
[18]Niculescu, S. L.: Delay effects on stability: A robust control approach[M], (2001)
[19]Niculescu, S. L.: Delay effects on stability: A robust control approach, (2001)
[20]Polycarpou, M. M.; Mark, J. M.: Stable adaptive tracking of uncertain systems using nonlinearly parameterized on-line approximators, Internat. J. Control 70, 363-384 (1998) · Zbl 0945.93563 · doi:10.1080/002071798222280
[21]Sastry, S. S.; Isidori, A.: Adaptive control of linearization systems, IEEE trans. Automat. control 34, No. 11, 1123-1131 (1989) · Zbl 0693.93046 · doi:10.1109/9.40741
[22]Tong, S. C.; Li, H. X.: Fuzzy adaptive sliding mode control for MIMO nonlinear systems, IEEE trans. Fuzzy systems 11, No. 3, 354-360 (2003)
[23]Wang, C.; Hill, D. J.: Learning from neural control, IEEE trans. Neural network 17, No. 1, 130-146 (2006)
[24]Wang, W. Y.; Chan, M. L.; Lee, T. T.; Liu, C. H.: Adaptive fuzzy control for strict-feedback canonical nonlinear systems with H tracking performance, IEEE trans. Systems man cybernet. — part B 30, No. 6, 878-885 (2000)
[25]Yang, Y. S.; Feng, G.; Ren, J. S.: A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems, IEEE trans. Systems man cybernet. — part A 34, No. 3, 406-420 (2004)
[26]Yang, Y. S.; Zhou, C. J.: Robust adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems via small-gain approach, Inform. sci. 170, 211-234 (2005) · Zbl 1068.93037 · doi:10.1016/j.ins.2004.02.022
[27]Zhang, Y.; Peng, P. Y.; Jiang, Z. P.: Stable neural controller design for unknown nonlinear systems using backstepping, IEEE trans. Neural networks 11, No. 6, 1347-1359 (2000)
[28]Zhou, S. S.; Feng, G.; Feng, C. B.: Robust control for a class of uncertain nonlinear systems: adaptive fuzzy approach based on backstepping, Fuzzy sets and systems 151, No. 1, 1-20 (2005) · Zbl 1142.93378 · doi:10.1016/j.fss.2004.05.008