Abstract
This paper investigates the adaptive fuzzy output-feedback control problem for single-input and single-output switched uncertain nonlinear systems. The addressed systems in this paper have the characteristics of arbitrary switchings, unknown nonlinear dynamics and immeasurable states. A common state observer is designed independent of switching signals. Fuzzy logic systems are utilized to approximate unknown lumped nonlinear dynamics. Based on the framework of backstepping design technique, an adaptive fuzzy output-feedback control scheme is developed. By using the common Lyapunov function theory, the stability of the closed-loop system is proved. The proposed control scheme does not need the assumptions that the states of the controlled system are available for measurement and that the switching signals satisfy the average dwell time. Moreover, it can guarantee that all the closed-loop signals are bounded, and the system output eventually converges to a small neighborhood of the origin. Finally, simulation studies are provided to further check the effectiveness of the proposed control scheme.
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References
B. Chen, X. Liu, Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping and application to chemical processes. IEEE Trans. Fuzzy Syst. 13(6), 832–847 (2005)
J.X. Dong, G.H. Yang, H.G. Zhang, Stability analysis of T-S fuzzy control systems by using set theory. IEEE Trans. Fuzzy Syst. 23(4), 827–841 (2015)
T.T. Han, S.S. Ge, T.H. Lee, Adaptive neural control for a class of switched nonlinear systems. Syst. Control Lett. 58(2), 109–118 (2009)
H. Lee, Robust adaptive fuzzy control by backstepping for a class of MIMO nonlinear systems. IEEE Trans. Fuzzy Syst. 19(2), 265–275 (2011)
H.Y. Li, Y.B. Gao, L.G. Wu, H.K. Lam, Model reduction for interval type-2 takagi-sugeno fuzzy systems. Automatica 61, 308–314 (2015)
H.Y. Li, Y.N. Pan, Q. Zhou, Filter design for interval type-2 fuzzy systems with D stability constraints under a unified frame. IEEE Trans. Fuzzy Syst. 23(3), 719–725 (2015)
H.Y. Li, C.W. Wu, P. Shi, Y.B. Gao, Control of nonlinear networked systems with packet dropouts: interval type-2 fuzzy model-based approach. IEEE Trans. Cybern. 45(11), 2378–2389 (2015)
T. Li, W.X. Zheng, Networked-based generalised H-infinity fault detection filtering for sensor faults. Int. J. Syst. Sci. 5(5), 831–840 (2015)
Y.M. Li, S.C. Tong, T.S. Li, Adaptive fuzzy backstepping control design for a class of pure-feedback switched nonlinear systems. Nonlinear Anal. Hybrid Syst. 16, 72–80 (2015)
Y.M. Li, S.C. Tong, T.S. Li, Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation. IEEE Trans. Cybern. 45(10), 2299–2308 (2015)
Y.M. Li, S.C. Tong, T.S. Li, Observer-based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control direction and unknown dead-zones. IEEE Trans Fuzzy Syst. 23(4), 1228–1241 (2015)
Z. Liu, F. Wang, Y. Zhang, X. Chen, C.P. Chen, Adaptive fuzzy output-feedback controller design for nonlinear systems via backstepping and small-gain approach. IEEE Trans. Cybern. 44(10), 1714–1725 (2014)
F. Long, S.M. Fei, Neural networks stabilization and disturbance attenuation for nonlinear switched impulsive systems. Neurocomputing 71(7), 1741–1747 (2008)
F. Long, S.M. Fei, Z.M. Fu, S.Y. Zheng, Adaptive Neural Network Control for Switched System with Unknown Nonlinear Part by Using Backstepping Approach: SISO Case. Advances in Neural Networks-ISNN (Springer, Berlin, 2006)
L.J. Long, J. Zhao, Adaptive output-feedback neural control of switched uncertain nonlinear systems with average dwell time. IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1350–1361 (2015)
L.J. Long, J. Zhao, \(H_\infty \)control of switched nonlinear systems in-normal form using multiple Lyapunov functions. IEEE Trans. Autom. Control 57(5), 1285–1291 (2012)
R.C. Ma, J. Zhao, Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary swtichings. Automatica 46(11), 1819–1823 (2010)
A.E. Ougli, B. Tidhaf, Optimal type-2 fuzzy adaptive control for a class of uncertain nonlinear systems using an LMI approach. Int. J. Innov. Comput. Inf. Control. 11(3), 851–863 (2015)
Z.H. Peng, D. Wang, H.W. Zhang, G. Sun, Distributed neural network control for adaptive synchronization of uncertain dynamical multi-agent systems. IEEE Trans. Neural Netw. Learn. Syst. 2(8), 1509–1519 (2014)
X.J. Su, P. Shi, L.G. Wu, Michael V. Basin, Reliable filtering with strict dissipativity for T–S fuzzy time-delay systems. IEEE Trans. Cybern. 44(12), 2470–2483 (2014)
X.J. Su, L.G. Wu, P. Shi, C.L. Philip, Model approximation for fuzzy switched systems with stochastic perturbation. IEEE Trans. Fuzzy Syst. 23(5), 1458–1473 (2015)
X.J. Su, L.G. Wu, P. Shi, Y.D. Song, A novel approach to output feedback control of fuzzy stochastic systems. Automatica 50(12), 3268–3275 (2014)
S.C. Tong, C.Y. Li, Y.M. Li, Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst. 160(19), 2755–2775 (2009)
S.C. Tong, Y.M. Li, Observer-based fuzzy adaptive control for strict-feedback nonlinear systems. Fuzzy Sets Syst. 160(12), 1749–1764 (2009)
S.C. Tong, S. Sui, Y.M. Li, Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained. IEEE Trans. Fuzzy Syst. 23(4), 729–742 (2015)
S.C. Tong, S. Sui, Y.M. Li, Observed-based adaptive fuzzy tracking control for switched nonlinear systems with dead-zone. IEEE Trans. Cybern. (2014). doi:10.1109/TCYB.2386912
H.Q. Wang, K.F. Liu, X.P. Liu, B. Chen, C. Lin, Neural-based adaptive output-feedback control for a class of nonstrict-feedback stochastic nonlinear systems. IEEE Trans. Cybern. 45(9), 1977–1987 (2015)
L.X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis (Prentice-Hall, Englewood Cliffs, 1994)
M. Wang, X. Liu, P. Shi, Adaptive neural control of pure-feedback nonlinear time-delay systems via dynamic surface technique. IEEE Trans. Syst. Man Cybern. B Cybern. 41(6), 1681–1692 (2011)
T. Wang, H.J. Gao, J. Qiu, A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control. IEEE Trans. Neural Netw. Learn. Syst. (2015). doi:10.1109/TNNLS.2015.2411671
T. Wang, Y. Zhang, J. Qiu, H.J. Gao, Adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements: IEEE Trans. Fuzzy Syst. 23(2), 302–312 (2015)
J.L. Wu, Stabilizing controllers design for switched nonlinear systems in strict-feedback form. Automatica 45(4), 1092–1096 (2009)
L.G. Wu, Z.G. Feng, W.X. Zheng, Exponential stability analysis for delayed neural networks with switching parameters: average dwell time approach. IEEE Trans. Neural Netw. 21(9), 1396–1407 (2010)
L.G. Wu, X.J. Su, P. Shi, Output feedback control of Markovian jump repeated scalar nonlinear systems. IEEE Trans. Autom. Control. 59(1), 199–204 (2014)
L.G. Wu, X. Yang, H.K. Lam, Dissipativity analysis and synthesis for discrete-time T–S fuzzy stochastic systems with time-varying delay. IEEE Trans. Fuzzy Syst. 22(2), 380–394 (2014)
L.G. Wu, W.X. Zheng, H.J. Gao, Dissipativity-based sliding mode control of switched stochastic systems. IEEE Trans. Autom. Control. 58(3), 785–791 (2013)
Z.G. Wu, P. Shi, H.Y. Su, J. Chu, Network-based robust passive control for fuzzy systems with randomly occurring uncertainties. IEEE Trans. Fuzzy Syst. 21(5), 966–971 (2013)
X. Xie, D. Yue, H. Zhang, Y. Xue, Control synthesis of discrete-time T–S fuzzy systems via a multi-instant homogenous polynomial approach. IEEE Trans. Cybern. (2015). doi:10.1109/TCYB.2015.2411336
H. Yang, B. Jiang, H. Zhang, Stabilization of non-minimum phase switched nonlinear systems with application to multi-agent systems. Syst. Control Lett. 61(10), 1023–1031 (2012)
R.N. Yang, G.P. Liu, P. Shi, C. Thomas, Michael V. Basin, Predictive output feedback control for networked control systems. IEEE Trans. Ind. Electron. 61(1), 512–520 (2014)
R.N. Yang, P. Shi, G.P. Liu, Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts. IEEE Trans. Autom. Control. 56(11), 2655–2660 (2011)
L. Yu, S.M. Fei, F. Long, M. Zhang, J. Yu, Multilayer neural networks-based direct adaptive control for switched nonlinear systems. Neurocomputing 74(1), 481–486 (2010)
L. Yu, S.M. Fei, L.N. Sun, J. Huang, Y.L. Zhu, Fuzzy approximation of a novel nonlinear adaptive switching controller design. Circuit Syst. Signal Process. 34(2), 377–391 (2015)
L. Yu, S.M. Fei, G. Yang, A neural network approach for tracking control of uncertain switched nonlinear systems with unknown dead-zone input. Circuit Syst. Signal Process. 34(8), 2695–2710 (2015)
H. Zhang, G. Feng, H.C. Yan, Q.J. Chen, Sampled-data control of nonlinear networked systems with time-delay and quantization. Int. J. Robust Nonlinear Control. (2015). doi:10.1002/rnc.3343
T.P. Zhang, S.S. Ge, Adaptive neural network tracking control of MIMO nonlinear systems with unknown dead zones and control directions. IEEE Trans. Neural Netw. 20(3), 483–497 (2009)
A.M. Zou, Z.G. Hou, M. Tan, Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach. IEEE Trans. Fuzzy Syst. 16(4), 886–897 (2008)
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This work is supported by the National Natural Science Foundation of China (Nos. 61573175, 61374113), and the Program for Liaoning Excellent Talents in University (LJQ2015048).
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Li, Y., Tong, S. Adaptive Fuzzy Output-Feedback Control for Switched Nonlinear Systems with Arbitrary Switchings. Circuits Syst Signal Process 35, 3152–3171 (2016). https://doi.org/10.1007/s00034-015-0196-0
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DOI: https://doi.org/10.1007/s00034-015-0196-0