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Adaptive fuzzy control of switched nonlinear time-varying delay systems with prescribed performance and unmodeled dynamics. (English) Zbl 1423.93198

Summary: This paper considers the problem of adaptive prescribed performance control for a class of switched nonlinear systems with time-varying delays and unmodeled dynamics. Fuzzy logic systems are introduced to deal with the unknown nonlinear terms. Utilizing dynamic surface control and convex combination method, a state-feedback controller is constructed. It is proven that all signals of the closed-loop system are bounded. Finally, simulation results are given to show that the proposed scheme is effective.

MSC:

93C42 Fuzzy control/observation systems
93C40 Adaptive control/observation systems
93C10 Nonlinear systems in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
Full Text: DOI

References:

[1] Guerra, T. M.; Sala, A.; Tanaka, K., Fuzzy control turns 50: 10 years later, Fuzzy Sets Syst., 281, 168-182 (2015) · Zbl 1368.93320
[2] Guerra, T. M.; Vermeiren, L., LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno’s form, Automatica, 40, 5, 823-829 (2004) · Zbl 1050.93048
[3] Guerra, T. M.; Kruszewski, A.; Vermeiren, L.; Tirmant, H., Conditions of output stabilization for nonlinear models in the Takagi-Sugeno’s form, Fuzzy Sets Syst., 157, 9, 1248-1259 (2006) · Zbl 1090.93023
[4] Wang, Y.; Xia, Y.; Ahn, C. K.; Zhu, Y., Exponential stabilization of Takagi-Sugeno fuzzy systems with aperiodic sampling: an aperiodic adaptive event-triggered method, IEEE Trans. Syst. Man Cybern. Syst. (2018)
[5] Sakthivel, R.; Ahn, C. K.; Joby, M., Fault-tolerant resilient control for fuzzy fractional order systems, IEEE Trans. Syst. Man Cybern. Syst. (2018)
[6] Zhou, Q.; Li, H.; Wu, C.; Wang, L.; Ahn, C. K., Adaptive fuzzy control of nonlinear systems with unmodeled dynamics and input saturation using small-gain approach, IEEE Trans. Syst. Man Cybern. Syst., 47, 8, 1979-1989 (2017)
[7] Hale, J., Theory of Functional Differential Equations (1977), Springer: Springer New York · Zbl 0352.34001
[8] Jankovic, M., Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems, IEEE Trans. Autom. Control, 46, 7, 1048-1060 (2001) · Zbl 1023.93056
[9] Yoo, S. J.; Park, J. B.; Choi, Y. H., Adaptive dynamic surface control for stabilization of parametric strict-feedback nonlinear systems with unknown time delays, IEEE Trans. Autom. Control, 52, 12, 2360-2365 (2007) · Zbl 1366.93593
[10] Tong, S.; Li, Y.; Zhang, H., Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays, IEEE Trans. Neural Netw., 22, 7, 1073-1086 (2011)
[11] Li, Y.; Tong, S., Prescribed performance adaptive fuzzy output-feedback dynamic surface control for nonlinear large-scale systems with time delays, Inf. Sci., 292, 125-142 (2015) · Zbl 1355.93100
[12] Zhou, Q.; Wu, C.; Shi, P., Observer-based adaptive fuzzy tracking control of nonlinear systems with time delay and input saturation, Fuzzy Sets Syst., 316, 49-68 (2017) · Zbl 1392.93033
[13] Zhang, T.; Ge, S. S., Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs, Automatica, 43, 6, 1021-1033 (2007) · Zbl 1282.93152
[14] Zhang, T.; Zhu, Q., Adaptive neural network control of nonlinear time-varying delay systems, Control Decis., 26, 2, 263-270 (2011) · Zbl 1240.93192
[15] Gao, H.; Zhang, T.; Xia, X., Adaptive neural control of stochastic nonlinear systems with unmodeled dynamics and time-varying state delays, J. Franklin Inst., 351, 6, 3182-3199 (2014) · Zbl 1290.93161
[16] Ahn, C. K.; Shi, P.; Wu, L., Receding horizon stabilization and disturbance attenuation for neural networks with time-varying delay, IEEE Trans. Cybern., 45, 12, 2680-2692 (2015)
[17] Choi, H. D.; Ahn, C. K.; Shi, P.; Wu, L.; Lim, M. T., Dynamic output-feedback dissipative control for T-S fuzzy systems with time-varying input delay and output constraints, IEEE Trans. Fuzzy Syst., 25, 3, 511-526 (2017)
[18] Ali, M.; Gunasekaran, N.; Ahn, C. K.; Shi, P., Sampled-data stabilization for fuzzy genetic regulatory networks with leakage delays, IEEE/ACM Trans. Comput. Biol. Bioinform., 15, 1, 271-285 (2018)
[19] Charalampos, P.; George, A., Prescribed performance adaptive control for multi-input multi-output affine in the control nonlinear systems, IEEE Trans. Autom. Control, 55, 5, 1220-1226 (2010) · Zbl 1368.93288
[20] Tong, S.; Sui, S.; Li, Y., Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained, IEEE Trans. Fuzzy Syst., 23, 4, 729-742 (2015)
[21] Xia, X.; Zhang, T.; Yi, Y.; Shen, Q., Adaptive prescribed performance control of output feedback systems including input unmodeled dynamics, Neurocomputing, 190, 19, 226-236 (2016)
[22] Zhai, D.; Xi, C.; An, L.; Dong, J.; Zhang, Q., Prescribed performance switched adaptive dynamic surface control of switched nonlinear systems with average dwell time, IEEE Trans. Syst. Man Cybern. Syst., 47, 7, 1257-1269 (2017)
[23] Na, J.; Chen, Q.; Ren, X.; Guo, Y., Adaptive prescribed performance motion control of servo mechanisms with friction compensation, IEEE Trans. Ind. Electron., 61, 1, 486-494 (2014)
[24] Na, J.; Huang, Y.; Wu, X.; Gao, G.; Herrmann, G.; Jiang, J. Z., Active adaptive estimation and control for vehicle suspensions with prescribed performance, IEEE Trans. Control Syst. Technol. (2017)
[25] Cui, G.; Xu, S.; Ma, Q.; Li, Y.; Zhang, Z., Prescribed performance distributed consensus control for nonlinear multi-agent systems with unknown dead-zone input, Int. J. Control, 91, 5, 1053-1065 (2018) · Zbl 1390.93028
[26] Liberzion, D., Switching in Systems and Control (2003), MA: Birkhäuser: MA: Birkhäuser Boston · Zbl 1036.93001
[27] Zhao, X.; Zheng, X.; Niu, B.; Liu, L., Adaptive tracking control for a class of uncertain switched nonlinear systems, Automatica, 52, 4, 185-191 (2014) · Zbl 1309.93081
[28] Jiang, B.; Shen, Q.; Shi, P., Neural-networked adaptive tracking control for switched nonlinear pure-feedback systems under arbitrary switching, Automatica, 61, 119-125 (2015) · Zbl 1327.93246
[29] Niu, B.; Liu, L.; Liu, Y., Adaptive backstepping-based fuzzy tracking control scheme for output-constrained nonlinear switched lower triangular systems with time-delays, Neurocomputing, 175, 759-767 (2016)
[30] Li, Y.; Tong, S.; Liu, L.; Feng, G., Adaptive output-feedback control design with prescribed performance for switched nonlinear systems, Automatica, 80, 225-231 (2017) · Zbl 1370.93124
[31] Tong, S.; Li, Y., Adaptive fuzzy output feedback control for switched nonlinear systems with unmodeled dynamics, IEEE Trans. Cybern., 47, 2, 295-305 (2017)
[32] Li, Y.; Tong, S., Adaptive neural networks prescribed performance control design for switched interconnected uncertain nonlinear systems, IEEE Trans. Neural Netw. Learn. Syst., 29, 7, 3059-3068 (2018)
[33] Zhai, D.; An, L.; Dong, J.; Zhang, Q., Adaptive exact tracking control for a class of uncertain nonlinear switched systems with arbitrary switchings, J. Franklin Inst., 354, 7, 2816-2831 (2017) · Zbl 1364.93414
[34] Huang, S.; Xiang, Z., Finite-time output tracking for a class of switched nonlinear systems, Int. J. Robust Nonlinear Control, 27, 6, 1017-1038 (2017) · Zbl 1369.93287
[35] Zhai, D.; Lu, A.; Dong, J.; Zhang, Q., Adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems: an adaptive statedependent switching law method, IEEE Trans. Syst. Man Cybern. Syst. (2017)
[36] Zhai, D.; Lu, A.; Ye, D.; Zhang, Q., Adaptive tracking control for a class of switched uncertain nonlinear systems under a new state-dependent switching law, Nonlinear Anal. Hybrid Syst., 24, 227-243 (2017) · Zbl 1377.93099
[37] Hou, Y.; Tong, S., Adaptive fuzzy output-feedback control for a class of nonlinear switched systems with unmodeled dynamics, Neurocomputing, 168, 200-209 (2015)
[38] Zhang, L.; Li, Y.; Tong, S., Adaptive fuzzy output feedback control for MIMO switched nonlinear systems with prescribed performances, Fuzzy Sets Syst., 306, 153-168 (2017) · Zbl 1368.93234
[39] El-Farra, N.; Mhaskar, P.; Christofides, P., Output feedback control of switched nonlinear systems using multiple Lyapunov functions, Syst. Control Lett., 54, 12, 1163-1182 (2005) · Zbl 1129.93497
[40] Long, L.; Zhao, J., Adaptive disturbance rejection for strict-feedback switched nonlinear systems using multiple Lyapunov functions, Int. J. Robust Nonlinear Control, 24, 13, 1887-1902 (2014) · Zbl 1301.93092
[41] Long, L., Multiple Lyapunov functions-based small-gain theorems for switched interconnected nonlinear systems, IEEE Trans. Autom. Control, 62, 8, 3943-3958 (2017) · Zbl 1373.93299
[42] Cai, M.; Xiang, Z.; Guo, J., Adaptive finite-time control for a class of switched nonlinear systems using multiple Lyapunov functions, Int. J. Syst. Sci., 48, 2, 324-336 (2017) · Zbl 1359.93410
[43] Jiang, Z. P.; Praly, L., Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties, Automatica, 34, 7, 825-840 (1998) · Zbl 0951.93042
[44] Lin, W.; Qian, C., Adaptive control of nonlinearly parameterized systems: the smooth feedback case, IEEE Trans. Autom. Control, 47, 8, 1249-1266 (2002) · Zbl 1364.93399
[45] Hardy, G.; Littlewood, J.; Pslya, G., Inequalities (1952), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0047.05302
[46] Wang, L. X., Adaptive Fuzzy Systems and Control (1994), Prentice Hall: Prentice Hall Englewood Cliffs, NJ
[47] Zhang, T.; Xia, M.; Yang, Y., Adaptive neural dynamic surface control of strict-feedback nonlinear systems with full state constraints and unmodeled dynamics, Automatica, 81, 232-239 (2017) · Zbl 1372.93125
[48] Hua, C.; Liu, G.; Li, L.; Guan, X., Adaptive fuzzy prescribed performance control for nonlinear switched time-delay systems with unmodeled dynamics, IEEE Trans. Fuzzy Syst., 26, 4, 1934-1945 (2018)
[49] Hua, C.; Liu, P. X.; Guan, X., Backstepping control for nonlinear systems with time delays and applications to chemical reactor systems, IEEE Trans. Ind. Electron., 56, 9, 3723-3732 (2009)
[50] Zhang, X.; Lin, Y., Global stabilization of high-order nonlinear time-delay systems by state feedback, Syst. Control Lett., 65, 89-95 (2014) · Zbl 1285.93076
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