Abstract
This paper investigates the adaptive fuzzy output feedback control problem for nonlinear non-strict feedback system with input delay. In the control design, the Pade approximation method and fuzzy logic system are used to handle the input delay and unknown functions, and a state observer is designed to approximate the unmeasured states of the system. By backstepping technique, an observer-based adaptive fuzzy control design method is given. The stability of the controlled system and the tracking performance of the system are demonstrated by utilizing the Lyapunov function theory. Finally, a simulation example of electromechanical system is provided to confirm the effectiveness of the proposed control method.
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Li, Z.J., Xiao, S.T., Ge, S.S., Su, H.: Constrained multi-legged robot system modeling and fuzzy control with uncertain kinematics and dynamics incorporating foot force optimization. IEEE Trans. Syst. Man Cybern. Syst. 46(1), 1–15 (2016)
Fan, Y.Q., Wang, Y.H., Wang, W.Q.: Adaptive fuzzy tracking control with compressor and limiters for uncertain nonlinear systems. Int. J. Fuzzy Syst. 16(1), 31–38 (2014)
Wang, C.H., Wang, J.H., Chen, C.Y.: Analysis and design of indirect adaptive fuzzy controller for nonlinear hysteretic systems. Int. J. Fuzzy Syst. 17(1), 84–93 (2015)
Li, Z.J., Deng, J., Lu, R.Q., Xu, Y., Bai, J.J., Su, C.Y.: Trajectory tracking control of mobile robot systems incorporating neural-dynamic optimized model predictive approach. IEEE Trans. Syst. Man Cybern. Syst. 46(6), 740–749 (2016)
Pan, Y.P., Yu, H.Y.: Biomimetic hybrid feedback feedforward neural-network learning control. IEEE Trans. Neural Netw. Learn. Syst. 28(6), 1481–1487 (2017)
Tong, S.C., Li, C.Y., Li, Y.M.: Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst. 160(19), 2755–2775 (2009)
Zhou, Q., Shi, P., Lu, J., Xu, S.Y.: Adaptive output-feedback fuzzy tracking control for a class of nonlinear systems. IEEE Trans. Fuzzy Syst. 19(5), 972–982 (2011)
Pan, Y.P., Er, M.J., Liu, Y.Q., Pan, L., Yu, H.Y.: Composite learning fuzzy control of uncertain nonlinear systems. Int. J. Fuzzy Syst. 18(6), 990–998 (2016)
Zhang, D., Shi, P., Wang, Q.G., Li, Y.: Analysis and synthesis of networked control systems: a survey of recent advances and challenges. ISA Trans. 66, 376–392 (2017)
Liu, Z., Wang, F., Zhang, Y., Chen, X., Chen, C.L.P.: Adaptive fuzzy output-feedback controller design for nonlinear systems via backstepping and small-gain approach. IEEE Trans. Cybern. 44(10), 1714–1725 (2014)
Pan, Y.P., Yu, H.Y.: Composite learning from adaptive dynamic surface control. IEEE Trans. Autom. Control 61(9), 2603–2609 (2016)
Zhang, D., Nguang, S.K., Srinivasan, D., Li, Y.: Distributed filtering for discrete-time T-S fuzzy systems with incomplete measurements. IEEE Trans. Fuzzy Syst. (2017). doi:10.1109/TFUZZ.2017.2725228
Chen, B., Liu, X.P., Ge, S.S., Lin, C.: Adaptive fuzzy control of a class of nonlinear systems by fuzzy approximation approach. IEEE Trans. Fuzzy Syst. 20(6), 1012–1021 (2012)
Wang, H.Q., Chen, B., Liu, K., Liu, X., Lin, C.: Adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis. IEEE Trans. Neural Netw. Learn. Syst. 21(5), 947–958 (2014)
Zhou, Q., Wang, L.J., Wu, C.W., Li, H.Y., Du, H.P.: Adaptive fuzzy control for nonstrict-feedback systems with input saturation and output constraint. IEEE Trans. Syst. Man Cybern. Syst. 47(1), 1–12 (2017)
Chen, B., Zhang, H.G., Lin, C.: Observer-based adaptive neural network control for nonlinear systems in nonstrict-feedback form. IEEE Trans. Neural Netw. Learn. Syst. 27(1), 89–98 (2016)
Tong, S.C., Li, Y.M., Sui, S.: Adaptive fuzzy tracking control design for uncertain non-strict feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 24, 1441–1454 (2016)
Wang, H.Q., Liu, X.P., Liu, K.F., Karimi, H.R.: Approximation-based adaptive fuzzy tracking control for a class of nonstrict-feedback stochastic nonlinear time-delay systems. IEEE Trans. Fuzzy Syst. 23(5), 1746–1760 (2015)
Liu, Z., Lai, G., Zhang, Y., Chen, X., Chen, C.L.P.: Adaptive neural control for a class of nonlinear time-varying delay systems with unknown hysteresis. IEEE Trans. Neural Netw. Learn. Syst. 25(12), 2129–2140 (2014)
Hamdy, M., Ramadan, A.: Design of smith predictor and fuzzy decoupling for MIMO chemical processes with time delays. Asian J. Control 19(2), 1–10 (2017)
Zhou, J., Wang, W., Wen, C.Y.: Adaptive backstepping control of uncertain systems with unknown input time-delay. Automatica 45(6), 1415–1422 (2009)
Lee, C H., Cheng, H.T.: Identification and fuzzy controller design for nonlinear uncertain systems with input time-delay. Int. J. Fuzzy Syst. 11(2), 73–85 (2009)
Zhu, Q., Fei, S., Zhang, T., Zhang, K., Li, T.: Adaptive RBF neural-networks control for a class of time-delay nonlinear systems. Neurocomputing 71(16), 3617–3624 (2008)
Khanesar, M.A., Kaynak, O., Yin, S., Gao, H.: Adaptive indirect fuzzy sliding mode controller for networked control systems subject to time-varying network-induced time delay. IEEE Trans. Fuzzy Syst. 23(1), 205–214 (2015)
Dawson, D.M., Carroll, J.J., Schneider, M.: Integrator backstepping control of a brush DC motor turning a robotic load. IEEE Trans. Control Syst. Technol. 2(3), 233–244 (1994)
Wang, L.X.: Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy Syst. 1(2), 146–155 (1993)
Hamdy, M.: State observer based dynamic fuzzy logic system control for a class of SISO nonlinear systems. Int. J. Autom. Comput. 10(2), 118–124 (2013)
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This work was supported by the National Natural Science Foundation of China (Nos. 61773188, 61573175).
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Wang, N., Tong, S. & Li, Y. Observer-Based Adaptive Fuzzy Control of Nonlinear Non-strict Feedback System with Input Delay. Int. J. Fuzzy Syst. 20, 236–245 (2018). https://doi.org/10.1007/s40815-017-0388-9
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DOI: https://doi.org/10.1007/s40815-017-0388-9