Adaptive fuzzy tracking control of switched uncertain nonlinear systems with unstable subsystems

This paper is concerned with the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems where the solvability of the fuzzy tracking control problem for subsystems is unnecessary. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a new adaptive fuzzy tracking control technique for the problem under study is set up. Based on the technique above, we design a switching law and construct adaptive fuzzy controllers of subsystems explicitly by a recursive design algorithm to guarantee that all the signals in the resulting closed-loop system remain bounded and the system output of the closed-loop system converges to a small neighborhood of the reference signal. Multiple Lyapunov functions are exploited to get out of the conservativeness caused by adoption of a common Lyapunov function for all subsystems, which is commonly required when applying the backstepping-like recursive design scheme. A mass-spring-damper system is provided to demonstrate the effectiveness of the proposed design method.

[1]  Jie Huang,et al.  Global Disturbance Rejection of Lower Triangular Systems With an Unknown Linear Exosystem , 2011, IEEE Transactions on Automatic Control.

[2]  Weisheng Chen,et al.  Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign , 2010, Fuzzy Sets Syst..

[3]  Shaocheng Tong,et al.  Adaptive Fuzzy Decentralized Control for Large-Scale Nonlinear Systems With Time-Varying Delays and Unknown High-Frequency Gain Sign , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  Shaocheng Tong,et al.  Adaptive Fuzzy Output Feedback Control of MIMO Nonlinear Systems With Unknown Dead-Zone Inputs , 2013, IEEE Transactions on Fuzzy Systems.

[5]  Bor-Sen Chen,et al.  H∞ tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach , 1996, IEEE Trans. Fuzzy Syst..

[6]  Shaocheng Tong,et al.  Adaptive Neural Output Feedback Controller Design With Reduced-Order Observer for a Class of Uncertain Nonlinear SISO Systems , 2011, IEEE Transactions on Neural Networks.

[7]  Carla A. Schwartz,et al.  A minimum energy approach to switching control for mechanical systems , 1997 .

[8]  Jeng-Tze Huang Hybrid-based adaptive NN backstepping control of strict-feedback systems , 2009, Autom..

[9]  Jun Zhao,et al.  A Small-Gain Theorem for Switched Interconnected Nonlinear Systems and Its Applications , 2014, IEEE Transactions on Automatic Control.

[10]  Abdesselem Boulkroune,et al.  Fuzzy approximation-based indirect adaptive controller for multi-input multi-output non-affine systems with unknown control direction , 2012 .

[11]  Abdesselem Boulkroune,et al.  State and output feedback fuzzy variable structure controllers for multivariable nonlinear systems subject to input nonlinearities , 2014 .

[12]  Shaocheng Tong,et al.  Adaptive Fuzzy Control via Observer Design for Uncertain Nonlinear Systems With Unmodeled Dynamics , 2013, IEEE Transactions on Fuzzy Systems.

[13]  Shuzhi Sam Ge,et al.  Adaptive neural control of uncertain MIMO nonlinear systems , 2004, IEEE Transactions on Neural Networks.

[14]  Xiaoping Liu,et al.  Direct adaptive fuzzy control of nonlinear strict-feedback systems , 2009, Autom..

[15]  Tua Agustinus Tamba,et al.  Adaptive backstepping for stabilization of switched nonlinear systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[16]  Wei Lin,et al.  Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework , 2002, IEEE Trans. Autom. Control..

[17]  Tsu-Tian Lee,et al.  Adaptive fuzzy control for strict-feedback canonical nonlinear systems with H infin tracking performance , 2000, IEEE Trans. Syst. Man Cybern. Part B.

[18]  Guangming Xie,et al.  Controllability of switched linear systems , 2002, IEEE Trans. Autom. Control..

[19]  Abdesselem Boulkroune,et al.  Indirect adaptive fuzzy control scheme based on observer for nonlinear systems: A novel SPR-filter approach , 2014, Neurocomputing.

[20]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Backstepping Output Feedback Control of Uncertain MIMO Pure-Feedback Nonlinear Systems , 2012, IEEE Transactions on Fuzzy Systems.

[21]  Pierre Riedinger,et al.  On the Convergence of Linear Switched Systems , 2011, IEEE Transactions on Automatic Control.

[22]  Bin Jiang,et al.  Robust Adaptive Tracking Control of the Underwater Robot with Input Nonlinearity Using Neural Networks , 2010 .

[23]  Shuzhi Sam Ge,et al.  Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form , 2008, Autom..

[24]  Tong Shao-cheng,et al.  Fuzzy adaptive observer backstepping control for MIMO nonlinear systems , 2009 .

[25]  Daizhan Cheng,et al.  STABILIZATION OF SWITCHED LINEAR SYSTEMS , 2008 .

[26]  Bing Chen,et al.  Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems , 2008, Fuzzy Sets Syst..

[27]  Cong Wang,et al.  Identification and Learning Control of Ocean Surface Ship Using Neural Networks , 2012, IEEE Transactions on Industrial Informatics.

[28]  Shuzhi Sam Ge,et al.  Adaptive neural control for a class of switched nonlinear systems , 2009, Syst. Control. Lett..

[29]  Okyay Kaynak,et al.  Robust and adaptive backstepping control for nonlinear systems using RBF neural networks , 2004, IEEE Transactions on Neural Networks.

[30]  Alessandro Pisano,et al.  Switched Observers for Switched Linear Systems With Unknown Inputs , 2011, IEEE Transactions on Automatic Control.

[31]  Licheng Jiao,et al.  Adaptive Backstepping Fuzzy Control for Nonlinearly Parameterized Systems With Periodic Disturbances , 2010, IEEE Transactions on Fuzzy Systems.

[32]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[33]  Shaocheng Tong,et al.  Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems , 2009, Fuzzy Sets Syst..

[34]  Jun Zhao,et al.  $H_{\infty}$ Control of Switched Nonlinear Systems in $p$-Normal Form Using Multiple Lyapunov Functions , 2012, IEEE Transactions on Automatic Control.

[35]  Shaocheng Tong,et al.  A Combined Backstepping and Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control , 2009, IEEE Transactions on Fuzzy Systems.

[36]  Shaocheng Tong,et al.  A Novel Robust Adaptive-Fuzzy-Tracking Control for a Class of NonlinearMulti-Input/Multi-Output Systems , 2010, IEEE Transactions on Fuzzy Systems.

[37]  Jun Zhao,et al.  Adaptive disturbance rejection for strict‐feedback switched nonlinear systems using multiple Lyapunov functions , 2014 .

[38]  Wei Lin,et al.  A remark on partial-state feedback stabilization of cascade systems using small gain theorem , 2003, IEEE Trans. Autom. Control..

[39]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[40]  Jenq-Lang Wu,et al.  Stabilizing controllers design for switched nonlinear systems in strict-feedback form , 2009, Autom..

[41]  Jun Zhao,et al.  On stability, L 2 -gain and H 8 control for switched systems , 2008 .

[42]  Abdesselem Boulkroune,et al.  Design of a unified adaptive fuzzy observer for uncertain nonlinear systems , 2014, Inf. Sci..

[43]  Jun Zhao,et al.  Output-feedback stabilisation for a class of switched nonlinear systems with unknown control coefficients , 2013, Int. J. Control.

[44]  M. Branicky Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[45]  Shaocheng Tong,et al.  A DSC Approach to Robust Adaptive NN Tracking Control for Strict-Feedback Nonlinear Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[46]  Kevin M. Passino,et al.  Decentralized adaptive control of nonlinear systems using radial basis neural networks , 1999, IEEE Trans. Autom. Control..

[47]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control , 1994 .

[48]  Abdesselem Boulkroune,et al.  Adaptive fuzzy tracking control for a class of MIMO nonaffine uncertain systems , 2012, Neurocomputing.