Universal Fuzzy Integral Sliding-Mode Controllers Based on T–S Fuzzy Models

This paper addresses the universal fuzzy integral sliding-mode controllers' problem for continuous-time multi-input multi-output nonlinear systems based on Takagi-Sugeno (T-S) fuzzy models. By using the approximation capability of T-S fuzzy models, the nonlinear systems are expressed by uncertain T-S fuzzy models with norm-bounded approximation errors. A novel fuzzy dynamic integral sliding-mode control (DISMC) scheme is then developed for the nonlinear systems based on their T-S fuzzy approximation models. One of the key features of the new DISMC scheme is that the restrictive assumption that all local linear systems share a common input matrix, which is required in most existing fuzzy integral sliding-mode control (ISMC) approaches, is removed. Furthermore, the results of universal fuzzy ISMCs for two classes of nonlinear systems, along with constructive procedures to obtain the universal fuzzy ISMCs, are provided, respectively. Finally, the advantages and effectiveness of the proposed approaches are illustrated via a numerical example.

[1]  G. Feng,et al.  A Survey on Analysis and Design of Model-Based Fuzzy Control Systems , 2006, IEEE Transactions on Fuzzy Systems.

[2]  Antonella Ferrara,et al.  Integral Sliding Mode Control for Nonlinear Systems With Matched and Unmatched Perturbations , 2011, IEEE Transactions on Automatic Control.

[3]  Xiao-Jun Zeng,et al.  Fuzzy Systems Approach to Approximation and Stabilization of Conventional Affine Nonlinear Systems , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[4]  Rainer Palm,et al.  Robust control by fuzzy sliding mode , 1994, Autom..

[5]  Kazuo Tanaka,et al.  Stability and stabilizability of fuzzy-neural-linear control systems , 1995, IEEE Trans. Fuzzy Syst..

[6]  James Lam,et al.  Robust integral sliding mode control for uncertain stochastic systems with time-varying delay , 2005, Autom..

[7]  Jianbin Qiu,et al.  T–S-Fuzzy-Model-Based Approximation and Controller Design for General Nonlinear Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[8]  Han Ho Choi,et al.  LMI-Based Sliding Surface Design for Integral Sliding Mode Control of Mismatched Uncertain Systems , 2007, IEEE Transactions on Automatic Control.

[9]  Yuandan Lin,et al.  A Smooth Converse Lyapunov Theorem for Robust Stability , 1996 .

[10]  Xingyu Wang,et al.  Robust $H_{\infty}$ Control for Nonlinear Stochastic Systems: A Sliding-Mode Approach , 2008, IEEE Transactions on Automatic Control.

[11]  Gang Feng,et al.  Analysis and Synthesis of Fuzzy Control Systems , 2010 .

[12]  Xiao-Jun Zeng,et al.  Approximation theory of fuzzy systems-MIMO case , 1995, IEEE Trans. Fuzzy Syst..

[13]  Yugang Niu,et al.  Robust Fuzzy Design for Nonlinear Uncertain Stochastic Systems via Sliding-Mode Control , 2007, IEEE Transactions on Fuzzy Systems.

[14]  Zhijun Li,et al.  Adaptive Fuzzy Control for Synchronization of Nonlinear Teleoperators With Stochastic Time-Varying Communication Delays , 2011, IEEE Transactions on Fuzzy Systems.

[15]  Jianbin Qiu,et al.  Nonsynchronized-State Estimation of Multichannel Networked Nonlinear Systems With Multiple Packet Dropouts Via T–S Fuzzy-Affine Dynamic Models , 2011, IEEE Transactions on Fuzzy Systems.

[16]  Jianbin Qiu,et al.  Asynchronous Output-Feedback Control of Networked Nonlinear Systems With Multiple Packet Dropouts: T–S Fuzzy Affine Model-Based Approach , 2011, IEEE Transactions on Fuzzy Systems.

[17]  Guan Xin-ping.  Robust H_∞ Control for Nonlinear Systems , 2002 .

[18]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[19]  Bart De Schutter,et al.  Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models , 2010, Studies in Fuzziness and Soft Computing.

[20]  Zhiyu Xi,et al.  Piecewise Integral Sliding-Mode Control for T–S Fuzzy Systems , 2011, IEEE Transactions on Fuzzy Systems.

[21]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[22]  Zhijun Li,et al.  Adaptive fuzzy logic control of dynamic balance and motion for wheeled inverted pendulums , 2009, Fuzzy Sets Syst..

[23]  V. Utkin,et al.  Integral sliding mode in systems operating under uncertainty conditions , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[24]  Guang-Ren Duan,et al.  Trilateral Teleoperation of Adaptive Fuzzy Force/Motion Control for Nonlinear Teleoperators With Communication Random Delays , 2013, IEEE Transactions on Fuzzy Systems.

[25]  Jianbin Qiu,et al.  Universal fuzzy controllers based on generalized T-S fuzzy models , 2012, Fuzzy Sets Syst..

[26]  Jian-Xin Xu,et al.  Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems , 2004, IEEE Transactions on Automatic Control.

[27]  Gang Feng,et al.  Delay-Dependent $\hbox{H}_{\infty }$ Filter Design for Discrete-Time Fuzzy Systems With Time-Varying Delays , 2009, IEEE Transactions on Fuzzy Systems.

[28]  Eduardo Sontag,et al.  On characterizations of the input-to-state stability property , 1995 .

[29]  Jianbin Qiu,et al.  Universal Fuzzy Models and Universal Fuzzy Controllers for Stochastic Nonaffine Nonlinear Systems , 2013, IEEE Transactions on Fuzzy Systems.

[30]  Liao Fucheng.  Robust H_∞ control for uncertain systems with time-varying delay , 2006 .

[31]  Wolfgang Hahn,et al.  Stability of Motion , 1967 .

[32]  Zonghai Li.  Adaptive fuzzy output feedback motion/force control for wheeled inverted pendulums , 2011 .

[33]  Giorgio Bartolini,et al.  A survey of applications of second-order sliding mode control to mechanical systems , 2003 .

[34]  M. Chen,et al.  Delay-Dependent H ∞ Filter Design for Discrete-Time Fuzzy Systems With Time-Varying Delays Meng Chen, Gang Feng, Fellow, IEEE ,H aibo Ma, and Ge Chen , 2009 .

[35]  R. Palm,et al.  Sliding mode fuzzy control , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[36]  Jianbin Qiu,et al.  A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay , 2009, IEEE Transactions on Fuzzy Systems.