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A new approach to observer-based fault-tolerant controller design for Takagi-Sugeno fuzzy systems with state delay. (English) Zbl 1173.94476
Summary: This paper deals with the problem of active fault-tolerant control (FTC) for time-delay Takagi-Sugeno (T-S) fuzzy systems based on a fuzzy adaptive fault diagnosis observer (AFDO). A novel fuzzy fast adaptive fault estimation (FAFE) algorithm for T-S fuzzy models is proposed to enhance the performance of fault estimation, and sufficient conditions for the existence of the fault estimator are given in terms of linear matrix inequalities (LMIs). Using the obtained on-line fault estimation information, an observer-based fast active fault-tolerant controller is designed to compensate for the effect of faults by stabilizing the closed-loop system. Simulation results of a track trail system and a nonlinear numerical example are presented to illustrate the effectiveness of the proposed method.

94D05Fuzzy sets and logic in connection with communication
93C42Fuzzy control systems
Full Text: DOI
[1] M. Blanke, M. Kinnaert, J. Lunze, M. Staroswiecki, Diagnosis and Fault-Tolerant Control (Springer, Berlin, 2006) · Zbl 1126.93004
[2] Y.Y. Cao, P.M. Frank, Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models. Fuzzy Sets Syst. 124(2), 213--229 (2001) · Zbl 1002.93051 · doi:10.1016/S0165-0114(00)00120-2
[3] J. Chen, R.J. Patton, Robust Model-based Fault Diagnosis for Dynamic Systems (Kluwer Academic, Norwell, 1999) · Zbl 0920.93001
[4] W. Chen, M. Saif, An iterative learning observer for fault detection and accommodation in nonlinear time-delay systems. Int. J. Robust Nonlinear Control 16(1), 1--19 (2006) · Zbl 1127.93335 · doi:10.1002/rnc.1033
[5] B. Chen, X. Liu, S. Tong, Delay-dependent stability analysis and control synthesis of fuzzy dynamic systems with time delay. Fuzzy Sets Syst. 157(16), 2224--2240 (2006) · Zbl 1106.93046 · doi:10.1016/j.fss.2006.01.010
[6] H.H. Choi, LMI-based nonlinear fuzzy observer-controller design for uncertain MIMO nonlinear systems. IEEE Trans. Fuzzy Syst. 15(5), 956--971 (2007) · Zbl 05516320 · doi:10.1109/TFUZZ.2006.890676
[7] M. Corless, J. Tu, State and input estimation for a class of uncertain systems. Automatica 34(6), 757--764 (1998) · Zbl 0932.93008 · doi:10.1016/S0005-1098(98)00013-2
[8] C. Edwards, X.G. Yan, S.K. Spurgeon, On the solvability of the constrained Lyapunov problem. IEEE Trans. Automat. Contr. 52(10), 1982--1987 (2007) · doi:10.1109/TAC.2007.904324
[9] A. Fekih, H. Xu, F.N. Chowdhury, Neural networks based system identification techniques for model based fault detection of nonlinear systems. Int. J. Innov. Comput. Inf. Control 3(5), 1073--1085 (2007)
[10] H. Gao, T. Chen, H estimation for uncertain systems with limited communication capacity. IEEE Trans. Automat. Contr. 52(11), 2070--2084 (2007) · doi:10.1109/TAC.2007.908316
[11] H. Gao, T. Chen, Stabilization of nonlinear systems under variable sampling: A fuzzy control approach. IEEE Trans. Fuzzy Syst. 15(5), 972--983 (2007) · Zbl 05516327 · doi:10.1109/TFUZZ.2006.890660
[12] H. Gao, T. Chen, L. Wang, Robust fault detection with missing measurements. Int. J. Control 81(5), 804--819 (2008) · Zbl 1152.93346 · doi:10.1080/00207170701684823
[13] L. Guo, F. Yang, J. Fang, Multiobjective filtering for nonlinear time-delay systems with nonzero initial conditions based on convex optimization. Circuits Syst. Signal Process. 25(5), 591--607 (2006) · Zbl 1106.93052 · doi:10.1007/s00034-005-0311-8
[14] B. Jiang, M. Staroswiecki, V. Cocquempot, Fault identification for a class of time-delay systems, in Proceedings of the American Control Conference, Anchorage, AK (2002), pp. 2239--2244
[15] B. Jiang, M. Staroswiecki, V. Cocquempot, Fault accommodation for nonlinear dynamic systems. IEEE Trans. Automat. Contr. 51(9), 1578--1583 (2006) · doi:10.1109/TAC.2006.878732
[16] N.P. Karampetakis, Computation of the generalized inverse of a polynomial matrix and applications. Linear Algebra Appl. 252(1--3), 35--60 (1997) · Zbl 0869.65028 · doi:10.1016/0024-3795(95)00695-8
[17] J.H. Kim, C.H. Hyun, E. Kim, M. Park, Adaptive synchronization of uncertain chaotic systems based on T-S fuzzy model. IEEE Trans. Fuzzy Syst. 15(3), 359--369 (2007) · Zbl 05452648 · doi:10.1109/TFUZZ.2006.880007
[18] K.R. Lee, J.H. Kim, E.T. Jeung, H.B. Park, Output feedback robust H control of uncertain fuzzy dynamic systems with time-varying delay. IEEE Trans. Fuzzy Syst. 8(6), 657--664 (2000) · doi:10.1109/91.890325
[19] C.J. Lopez-Toribio, R.J. Patton, Takagi-Sugeno fuzzy fault-tolerant control for a non-linear system, in Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ (1999), pp. 4368--4373
[20] X.J. Ma, Z.Q. Sun, Y.Y. He, Analysis and design of fuzzy controller and fuzzy observer. IEEE Trans. Fuzzy Syst. 6(1), 41--51 (1998) · doi:10.1109/91.660807
[21] S.K. Nguang, P. Shi, H fuzzy output feedback control design for nonlinear systems: An LMI approach. IEEE Trans. Fuzzy Syst. 11(3), 331--340 (2003) · doi:10.1109/TFUZZ.2003.812691
[22] S.K. Nguang, P. Shi, S.X. Ding, Delay-dependent fault estimation for uncertain time-delay nonlinear systems: An LMI approach. Int. J. Robust Nonlinear Control 16(18), 913--933 (2006) · Zbl 1135.93022 · doi:10.1002/rnc.1116
[23] S.K. Nguang, P. Shi, S.X. Ding, Fault detection for uncertain fuzzy systems: An LMI approach. IEEE Trans. Fuzzy Syst. 15(6), 1251--1262 (2007) · Zbl 05516307 · doi:10.1109/TFUZZ.2007.894983
[24] H. Noura, D. Theilliol, D. Sauter, Actuator fault-tolerant control design: Demonstration on a three-tank-system. Int. J. Syst. Sci. 31(9), 1143--1155 (2000) · Zbl 1080.93591 · doi:10.1080/002077200418414
[25] R.J. Patton, J. Chen, C.J. Lopez-Toribio, Fuzny observers for non-linear dynamic systems fault diagnosis, in Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL (1998), pp. 84--89
[26] R. Penrose, A generalized inverse for matrices. Proc. Camb. Philos. Soc. 51, 406--413 (1955) · Zbl 0065.24603 · doi:10.1017/S0305004100030401
[27] A.M. Pertew, H.J. Marquez, Q. Zhao, H observer design for Lipschitz nonlinear systems. IEEE Trans. Automat. Contr. 51(7), 1211--1216 (2006) · doi:10.1109/TAC.2006.878784
[28] M.M. Polycarpou, Fault accommodation of a class of multivariable nonlinear dynamical systems using a learning approach. IEEE Trans. Automat. Contr. 46(5), 736--742 (2001) · Zbl 1006.93074 · doi:10.1109/9.920792
[29] R. Rajamani, Y.M. Cho, Existence and design of observers for nonlinear systems: Relation to distance to unobservability. Int. J. Control 69(5), 717--731 (1998) · Zbl 0933.93019 · doi:10.1080/002071798222640
[30] E.D. Sontag, The ISS philosophy as a unifying framework for stability-like behavior, in Nonlinear Control in the Year 2000 (Springer, Berlin, 2000), pp. 443--467 · Zbl 0989.93083
[31] M. Staroswiecki, H. Yang, B. Jiang, Progressive accommodation of parametric faults in linear quadratic control. Automatica 43(12), 2070--2076 (2007) · Zbl 1138.49029 · doi:10.1016/j.automatica.2007.04.016
[32] D. Theilliol, H. Noura, D. Sauter, Fault tolerant control method for actuator and component faults, in Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL (1998), pp. 604--609
[33] S. Tong, Y. Li, Direct adaptive fuzzy backstepping control for a class of nonlinear systems. Int. J. Innov. Comput. Inf. Control 3(4), 887--896 (2007)
[34] S. Tong, W. Wang, L. Qu, Decentralized robust control for uncertain T-S fuzzy large-scale systems with time-delay. Int. J. Innov. Comput. Inf. Control 3(3), 657--672 (2007)
[35] K. Vijayaraghavan, R. Rajamani, J. Bokor, Quantitative fault estimation for a class of non-linear systems. Int. J. Control 80(1), 64--74 (2007) · Zbl 1115.93040 · doi:10.1080/00207170600921029
[36] H. Wang, S. Daley, Actuator fault diagnosis: An adaptive observer-based technique. IEEE Trans. Automat. Contr. 41(7), 1073--1078 (1996) · Zbl 0858.93040 · doi:10.1109/9.508919
[37] M. Wang, B. Chen, S. Tong, Adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown time delays. Int. J. Innov. Comput. Inf. Control 4(4), 829--837 (2008)
[38] Z. Wang, D.P. Goodall, K.J. Burnham, On designing observers for time-delay systems with non-linear disturbances. Int. J. Control 75(11), 803--811 (2002) · Zbl 1027.93007 · doi:10.1080/00207170210126245
[39] Y. Zhang, S.J. Qin, Adaptive actuator/component fault compensation for nonlinear systems. AIChE J. 54(9), 2404--2412 (2008) · doi:10.1002/aic.11546
[40] K. Zhang, B. Jiang, V. Cocquempot, Adaptive observer-based fast fault estimation. Int. J. Control Autom. Syst. 6(3), 320--326 (2008)