Discrete-Time Fuzzy Sliding Mode Control of Nonlinear Systems

This paper addresses the control problem of nonlinear systems based on the Takagi-Sugeno (T-S) fuzzy model. T-S model was adopted for fuzzy modeling of the nonlinear system. The global T-S fuzzy model of nonlinear systems was transformed into linear uncertain system model. So the stability problem of nonlinear systems becomes the robust stabilization problem of linear uncertain systems. Discrete-time sliding mode control approach was employed to guarantee robust stability of linear uncertain systems. The stable sliding surface was designed by using linear matrix inequalities to reduce the influence of mismatched uncertainties. The sufficient condition for the existence of stable sliding surface in terms of LMI was derived and the sliding mode control law was presented also, which guaranteed the global stability of the systems

[1]  Han Ho Choi.  On the existence of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties , 1999, Autom..

[2]  Jin Bae Park,et al.  Robust fuzzy control of nonlinear systems with parametric uncertainties , 2001, IEEE Trans. Fuzzy Syst..

[3]  Weibing Gao,et al.  Discrete-time variable structure control systems , 1995, IEEE Trans. Ind. Electron..

[4]  Han Ho Choi,et al.  An LMI-based switching surface design method for a class of mismatched uncertain systems , 2003, IEEE Trans. Autom. Control..

[5]  Kazuo Tanaka,et al.  Stability analysis and design of fuzzy control systems , 1992 .

[6]  F.H.F. Leung,et al.  Fuzzy model based controller for an inverted pendulum , 1996 .

[7]  Kazuo Tanaka,et al.  A unified approach to controlling chaos via an LMI-based fuzzy control system design , 1998 .

[8]  Jin Bae Park,et al.  Intelligent digitally re-designed PAM fuzzy controller for nonlinear systems , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[9]  Sang Woo Kim,et al.  A New Sliding Surface Design Method of Linear Systems with Mismatched Uncertainties , 2005, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[10]  Hugh F. Durrant-Whyte,et al.  Fuzzy moving sliding mode control with application to robotic manipulators , 1999, Autom..

[11]  Han Ho Choi,et al.  A new method for variable structure control system design: A linear matrix inequality approach , 1997, Autom..

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

[13]  Kazuo Tanaka,et al.  A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer , 1994, IEEE Trans. Fuzzy Syst..

[14]  Kiriakos Kiriakidis,et al.  Fuzzy model-based control of complex plants , 1998, IEEE Trans. Fuzzy Syst..

[15]  Seung-Bok Choi,et al.  A time-varying sliding surface for fast and robust tracking control of second-order uncertain systems , 1994, Autom..

[16]  Kazuo Tanaka,et al.  An approach to fuzzy control of nonlinear systems: stability and design issues , 1996, IEEE Trans. Fuzzy Syst..

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

[18]  Kazuo Tanaka,et al.  Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs , 1998, IEEE Trans. Fuzzy Syst..

[19]  Christopher Edwards.  A practical method for the design of sliding mode controllers using linear matrix inequalities , 2004, Autom..