Abstract
In this paper, an adaptive fuzzy output feedback fault-tolerant control scheme is developed for a class of nonlinear systems with actuator faults, unmodeled dynamics and without assuming the states being available for control design. Fuzzy logic systems are employed to approximate unknown nonlinear functions, and a fuzzy state observer is established to estimate the unmeasured states. By combining adaptive backstepping technique with changing supplying function technique and the nonlinear fault-tolerant control theory, a novel adaptive fuzzy fault-tolerant output feedback control approach is developed. It is proved that proposed control approach guarantees that all the variables of the closed-loop system are bounded. The simulation results are provided to illustrate the effectiveness of the proposed control approach. Compared with the existing results, the main contributions of this paper are as follows: (1) the proposed control method removes the restrictive assumption that all the states of the controlled system be measured directly; and (2) the proposed control method cannot only compensate for the actuator faults, but also solve the problem of the unmodeled dynamics.
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References
Kristic M, Kanellakopoulos I, Kokotovic PV (1995) Nonlinear and adaptive control design. Wiley, New York
Wang LX (1994) Adaptive fuzzy systems and control. Prentice Hall, Englewood Cliffs, NJ
Chen B, Liu XP, Shi P (2010) Direct adaptive fuzzy control for nonlinear systems with time-varying delays. Inf Sci 180(5):776–792
Chen WS, Jiao LC, Wu JS (2012) Decentralized backstepping output-feedback control for stochastic interconnected systems with time-varying delays using neural networks. Neural Comput Appl 21(6):1375–1390
Zhang TP, Wen H, Zhu Q (2010) Adaptive fuzzy control of nonlinear systems in pure feedback form based on input-to-state stability. IEEE Trans Fuzzy Syst 18(1):80–93
Chen WS, Jiao LC, Wu JS (2012) Globally stable adaptive robust tracking control using RBF neural networks as feedforward compensators. Neural Comput Appl 21(2):351–363
Tong SC, He XL, Li YM, Zhang HG (2010) Adaptive fuzzy backstepping robust control for uncertain nonlinear systems based on small-gain approach. Fuzzy Sets Syst 161(3):771–796
Lee H (2011) Robust adaptive fuzzy control by backstepping for a class of MIMO nonlinear systems. IEEE Trans Fuzzy Syst 19(2):265–275
Zhou Q, Shi P, Lu JJ, Xu SY (2011) Adaptive output feedback fuzzy tracking control for a class of nonlinear systems. IEEE Trans Fuzzy Syst 19(5):972–982
Zhou Q, Shi P, Xu SY, Li HY (2013) Adaptive output feedback control for nonlinear time-delay systems by fuzzy approximation approach. IEEE Trans Fuzzy Syst 21(2):301–313
Tong SC, Li YM (2009) Observer-based fuzzy adaptive control for strict-feedback nonlinear systems. Fuzzy Sets Syst 160(12):1749–1764
Tong SC, Li CY, Li YM (2009) Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst 160(19):2755–2775
Jiang B, Zhang K, Shi P (2011) Integrated fault estimation and accommodation design for discrete-time Takagi–Sugeno fuzzy systems with actuator faults. IEEE Trans Fuzzy Syst 19(2):291–304
Wu HN, Zhang HY (2006) Reliable H ∞ fuzzy control for continuous-time nonlinear systems with actuator failures. IEEE Trans Fuzzy Syst 14(5):609–618
HN Wu, Qiang XH, Guo L (2011) L ∞-gain adaptive fuzzy fault accommodation control design for nonlinear time delay systems. IEEE Trans Syst Man Cybern B 41(3):817–827
Wu LG, Ho D (2009) Fuzzy filter design for nonlinear itô stochastic systems with application to sensor fault detection. IEEE Trans Fuzzy Syst 17(1):233–242
Wu LG, Su XJ, Shi P (2011) Mixed H 2/H ∞ approach to fault detection of discrete linear repetitive processes. J Franklin Inst 348(2):393–414
Li H, Liu H, Gao H, Shi P (2012) Reliable fuzzy control for active suspension systems with actuator delay and faults. IEEE Trans Fuzzy Syst 20(2):342–357
Jiang B, Gao ZF, Shi P, Xu YF (2010) Adaptive fault-tolerant tracking control of near-space vehicle using Takagi–Sugeno fuzzy models. IEEE Trans Fuzzy Syst 18(5):1000–1007
Li XJ, Yang GH (2012) Robust adaptive fault-tolerant control for uncertain linear systems with actuator failures. IET Contr Theory Appl 6(10):1544–1551
Li T, Zhang YC (2011) Fault detection and diagnosis for stochastic systems via output PDFs. J Franklin Inst 348(6):1140–1152
Li T, Guo L, Wu L (2008) Observer-based optimal fault detection using PDFs for time-delay stochastic systems. Nonlinear Anal Real World Appl 9(5):2337–2349
Li T, Guo L (2009) Optimal fault-detection filtering for non-Gaussian systems via output PDFs. IEEE Trans Syst Man Cybern A 39(2):476–481
Ye D, Yang G (2006) Adaptive fault-tolerant tracking control against actuator faults with application to flight control. IEEE Trans Control Syst Tech 14(6):1088–1096
Yang G, Ye D (2006) Adaptive fault-tolerant H ∞ control via state feedback for linear systems against actuator faults. In: Proceedings of the IEEE conference on decision and control, pp 3530–3535
Tao G, Joshi SM, Ma XL (2001) Adaptive state feedback and tracking control of systems with actuator failures. IEEE Trans Autom Control 46(1):78–95
Tang X, Tao G, Joshi SM (2007) Adaptive actuator failure compensation for nonlinear MIMO systems with an aircraft control application. Automatica 43(11):1869–1883
Zhang K, Jiang B, Shi P (2009) A new approach to observer-based fault-tolerant controller design for Takagi–Sugeno fuzzy systems with state delay. Circuits Syst Signal Process 28(5):679–697
Jiang B, Gao ZF, Shi P (2010) Observer-based integrated robust fault estimation and accommodation design for discrete-time systems. Int J Control 83(6):1167–1181
Zhang K, Jiang B, Shi P (2012) Fault estimation observer design for discrete-time Takagi–Sugeno fuzzy systems based on piecewise Lyapunov functions. IEEE Trans Fuzzy Syst 20(1):192–200
Ma LY, Jiang B (2009) Backstepping-based active fault-tolerant control for a class of uncertain SISO nonlinear systems. J Syst Eng Electron 20(6):1263–1270
Wang W, Wen C (2010) Adaptive actuators failure compensation for uncertain nonlinear systems with guaranteed transient performance. Automatica 46(12):2082–2091
Li P, Yang G (2009) Backstepping adaptive fuzzy control of uncertain nonlinear systems against actuator faults. Control Theory Appl 7(3):248–256
Li P, Yang G (2008) Adaptive fuzzy control of unknown nonlinear systems with actuator failures for robust output tracking. In: Proceedings of the American control conference, pp 4898–4903
Li P, Yang G (2011) An adaptive fuzzy design for fault-tolerant control of MIMO nonlinear uncertain systems. Control Theory Appl 9(2):244–250
Jiang ZP, Praly L (1998) Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties. Automatica 34(7):825–840
Jiang ZP (1999) A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics. IEEE Trans Automat Control 44(9):1705–1711
Jiang ZP (1999) A combined backstepping and small-gain approach to adaptive output feedback control. Automatica 35(6):1131–1139
Hua CC, Guan XP, Guan XP (2007) Robust output tracking control for a class of time-delay nonlinear using neural network. IEEE Trans Neural Netw 18(2):495–505
Chadli M, Karimi HR (2013) Robust observer design for unknown inputs Takagi–Sugeno models. IEEE Trans Fuzzy Syst 21(1):158–164
Zhao X, Zhang L, Shi P, Karimi HR (2013) Novel stability criteria for T–S fuzzy systems. IEEE Trans Fuzzy Syst. doi:10.1109/TFUZZ.2013.2254491
Wang B, Shi P, Karimi HR (2013) Fuzzy sliding mode control design for a class of disturbed systems. J Franklin Inst. doi:10.1016/j.jfranklin.2013.01.023
Zhao L, Gao H, Karimi HR (2011) Robust stability and stabilization of uncertain T–S fuzzy systems with time-varying delay: an input–output approach. IEEE Trans Fuzzy Syst. doi:10.1109/TFUZZ.2012.2235840
Lam HK (2011) LMI-based stability analysis for fuzzy-model-based control systems using artificial T-S fuzzy model. IEEE Trans Fuzzy Syst 19(3):505–513
Narimani M, Lam HK (2009) Relaxed LMI-based stability conditions for Takagi–Sugeno fuzzy control systems using regional-membership-function-shape-dependent analysis approach. IEEE Trans Fuzzy Syst 17(5):1221–1228
Lam HK (2009) LMI-based design of sampled-data fuzzy controller for nonlinear systems based on switching T–S fuzzy model. Nonlinear Anal Theory Methods Appl 3(4):418–432
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Nos. 61074014, 61374113, 61203008), Liaoning Innovative Research Team in University (LT2012013).
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Xu, Y., Tong, S. & Li, Y. Observer-based fuzzy adaptive control of nonlinear systems with actuator faults and unmodeled dynamics. Neural Comput & Applic 23 (Suppl 1), 391–405 (2013). https://doi.org/10.1007/s00521-013-1495-7
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DOI: https://doi.org/10.1007/s00521-013-1495-7