Observer-based adaptive fuzzy backstepping dynamic surface control design and stability analysis for MIMO stochastic nonlinear systems

In this paper, an adaptive fuzzy backstepping output feedback dynamic surface control (DSC) approach is developed for a class of multiinput and multioutput (MIMO) stochastic nonlinear systems with immeasurable states. Fuzzy logic systems are firstly utilized to approximate the unknown nonlinear functions, and then a fuzzy state observer is designed to estimate the immeasurable states. By combining adaptive backstepping technique and dynamic surface control (DSC) technique, an adaptive fuzzy output feedback backstepping DSC approach is developed. The proposed control method not only overcomes the problem of “explosion of complexity” inherent in the backstepping design methods, but also the problem of the immeasurable states. It is proved that all the signals of the closed-loop adaptive control stochastic system are semiglobally uniformly ultimately bounded (SUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.

[1]  Bing Chen,et al.  Direct adaptive fuzzy control for nonlinear systems with time-varying delays , 2010, Inf. Sci..

[2]  Yuanqing Xia,et al.  Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching , 2008, 2008 27th Chinese Control Conference.

[3]  Jin Bae Park,et al.  Neural-Network-Based Decentralized Adaptive Control for a Class of Large-Scale Nonlinear Systems With Unknown Time-Varying Delays , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  R. Khasminskii.  Stochastic Stability of Differential Equations , 1980 .

[5]  Shuzhi Sam Ge,et al.  Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays , 2008, Int. J. Control.

[6]  Peng Shi,et al.  Robust Output Feedback Tracking Control for Time-Delay Nonlinear Systems Using Neural Network , 2007, IEEE Transactions on Neural Networks.

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

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

[9]  Xin-Ping Guan,et al.  Adaptive Fuzzy Output-Feedback Controller Design for Nonlinear Time-Delay Systems With Unknown Control Direction , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[10]  Shaocheng Tong,et al.  Robust Adaptive Tracking Control for Nonlinear Systems Based on Bounds of Fuzzy Approximation Parameters , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[11]  Bing Chen,et al.  Adaptive Neural Control for a Class of Perturbed Strict-Feedback Nonlinear Time-Delay Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[13]  Junmi Li,et al.  Adaptive NN output-feedback stabilization for a class of stochastic nonlinear strict-feedback systems. , 2009, ISA transactions.

[14]  Bing Chen,et al.  Novel adaptive neural control design for nonlinear MIMO time-delay systems , 2009, Autom..

[15]  Yuanqing Xia,et al.  Adaptive Backstepping Controller Design for Stochastic Jump Systems , 2009, IEEE Transactions on Automatic Control.

[16]  Arthur Jutan,et al.  Almost disturbance decoupling of MIMO nonlinear systems and application to chemical processes , 2004, Autom..

[17]  Shaocheng Tong,et al.  Observer-based fuzzy adaptive control for strict-feedback nonlinear systems , 2009, Fuzzy Sets Syst..

[18]  Zhong-Ping Jiang,et al.  Stable neural controller design for unknown nonlinear systems using backstepping , 2000, IEEE Trans. Neural Networks Learn. Syst..

[19]  Licheng Jiao,et al.  Adaptive NN Backstepping Output-Feedback Control for Stochastic Nonlinear Strict-Feedback Systems With Time-Varying Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Miroslav Krstic,et al.  Output-feedback stochastic nonlinear stabilization , 1999, IEEE Trans. Autom. Control..

[21]  Bing Chen,et al.  Fuzzy-Approximation-Based Adaptive Control of Strict-Feedback Nonlinear Systems With Time Delays , 2010, IEEE Transactions on Fuzzy Systems.

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

[23]  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).

[24]  Shuzhi Sam Ge,et al.  Adaptive neural network control for strict-feedback nonlinear systems using backstepping design , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[25]  Zhong-Ping Jiang,et al.  Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems , 2007, Autom..

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

[27]  T. Başar,et al.  Adaptive controller design for tracking and disturbance attenuation in parametric strict-feedback nonlinear systems , 1998, IEEE Trans. Autom. Control..

[28]  M. Polycarpou,et al.  Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators , 1998 .

[29]  L. Jiao,et al.  Brief Paper: Output-feedback adaptive dynamic surface control of stochastic non-linear systems using neural network , 2010 .

[30]  Weisheng Chen,et al.  Adaptive NN output‐feedback decentralized stabilization for a class of large‐scale stochastic nonlinear strict‐feedback systems , 2011 .

[31]  Hai-Bo Ji,et al.  Adaptive output-feedback tracking of stochastic nonlinear systems , 2006, IEEE Trans. Autom. Control..

[32]  Dan Wang,et al.  Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form , 2005, IEEE Transactions on Neural Networks.

[33]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[34]  Gang Feng,et al.  Robust control for a class of uncertain nonlinear systems: adaptive fuzzy approach based on backstepping , 2005, Fuzzy Sets Syst..