Adaptive tracking control of uncertain switched stochastic nonlinear systems

In this paper, a tracking control problem is investigated for a class of switched stochastic nonlinear uncertain systems with unknown dead-zone input. By using the common Lyapunov function method and backstepping technique, a common controller and an uniform adaptive mechanism are constructed, and a novel adaptive fuzzy control scheme is developed. It is proved that the proposed control method can guarantee that all the signals in the closed-loop system are bounded in probability and the tracking error is convergent to a neighborhood of the origin under arbitrary switching. Finally, simulation results are provided to show the effectiveness of the proposed control scheme.

[1]  James D. Keeler,et al.  Layered Neural Networks with Gaussian Hidden Units as Universal Approximations , 1990, Neural Computation.

[2]  Gang Tao,et al.  Adaptive Control of Plants with Unknown Dead-zones , 1992, 1992 American Control Conference.

[3]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control - design and stability analysis , 1994 .

[4]  H. Deng,et al.  Stochastic Nonlinear Stabilization|part I: a Backstepping Design Submitted to Systems and Control Letters , 1997 .

[5]  M. Krstić,et al.  Stochastic nonlinear stabilization—I: a backstepping design , 1997 .

[6]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[7]  Guomin Li,et al.  Robust nonlinear nominal-model following control to overcome deadzone nonlinearities , 2001, IEEE Trans. Ind. Electron..

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

[9]  Chen Bin,et al.  Fuzzy adaptive output feedback control for MIMO nonlinear systems , 2005, Fuzzy Sets Syst..

[10]  Daniel Liberzon,et al.  Common Lyapunov functions for families of commuting nonlinear systems , 2005, Syst. Control. Lett..

[11]  Chun-Yi Su,et al.  Adaptive tracking of nonlinear systems with non-symmetric dead-zone input , 2007, Autom..

[12]  Shaocheng Tong,et al.  Adaptive Fuzzy Output Tracking Control of MIMO Nonlinear Uncertain Systems , 2007, IEEE Transactions on Fuzzy Systems.

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

[14]  Junmin Li,et al.  Decentralized Output-Feedback Neural Control for Systems With Unknown Interconnections , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Yanjun Liu,et al.  Adaptive fuzzy controller design of nonlinear systems with unknown gain sign , 2009 .

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

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

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

[19]  Bing Chen,et al.  Direct adaptive neural control for stabilization of nonlinear time-delay systems , 2010, Science China Information Sciences.

[20]  Jun Zhao,et al.  Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings , 2010, Autom..

[21]  Xinping Guan,et al.  Brief paper: adaptive backstepping fault-tolerant control for unmatched non-linear systems against actuator dead-zone , 2010 .

[22]  Huaguang Zhang,et al.  Stabilization of Switched Nonlinear Systems With All Unstable Modes: Application to Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.

[23]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Backstepping Control for a Class of Stochastic Nonlinear Strict-Feedback Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[24]  Peng Shi,et al.  Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time , 2012, IEEE Transactions on Automatic Control.

[25]  Corentin Briat,et al.  Convex Dwell-Time Characterizations for Uncertain Linear Impulsive Systems , 2012, IEEE Transactions on Automatic Control.

[26]  Shengyuan Xu,et al.  Neural-Network-Based Decentralized Adaptive Output-Feedback Control for Large-Scale Stochastic Nonlinear Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[27]  Peng Shi,et al.  Stability of switched positive linear systems with average dwell time switching , 2012, Autom..

[28]  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.

[29]  Chong Lin,et al.  Adaptive neural tracking control for a class of perturbed pure-feedback nonlinear systems , 2013 .

[30]  Guang-Ren Duan,et al.  Global stabilization of switched stochastic nonlinear systems in strict-feedback form under arbitrary switchings , 2013, Autom..

[31]  Corentin Briat,et al.  Affine Characterizations of Minimal and Mode-Dependent Dwell-Times for Uncertain Linear Switched Systems , 2012, IEEE Transactions on Automatic Control.

[32]  Bing Chen,et al.  Adaptive neural tracking control for a class of stochastic nonlinear systems , 2014 .

[33]  Alireza Zakariazadeh,et al.  Real-time voltage control algorithm with switched capacitors in smart distribution system in presence of renewable generations , 2014 .

[34]  Jian Xiao,et al.  Stabilization of switched continuous-time systems with all modes unstable via dwell time switching , 2014, Autom..

[35]  Xiaolong Zheng,et al.  Adaptive neural tracking control for a class of switched uncertain nonlinear systems , 2015, Neurocomputing.

[36]  Bing Chen,et al.  Neural-Based Adaptive Output-Feedback Control for a Class of Nonstrict-Feedback Stochastic Nonlinear Systems , 2015, IEEE Transactions on Cybernetics.

[37]  李铁山.  Adaptive fuzzy backstepping control design for a class of pure-feedback switched nonlinear systems , 2015 .

[38]  Shaocheng Tong,et al.  Adaptive fuzzy output-feedback control for a class of nonlinear switched systems with unmodeled dynamics , 2015, Neurocomputing.

[39]  Shaocheng Tong,et al.  Adaptive NN Tracking Control of Uncertain Nonlinear Discrete-Time Systems With Nonaffine Dead-Zone Input , 2015, IEEE Transactions on Cybernetics.

[40]  Liang Liu,et al.  Adaptive tracking control for a class of uncertain switched nonlinear systems , 2015, Autom..