H2 guaranteed cost fuzzy control design for discrete-time nonlinear systems with parameter uncertainty

  • Authors:
  • Huai-Ning Wu;Kai-Yuan Cai

  • Affiliations:
  • School of Automation Science and Electrical Engineering, Beihang University (Beijing University of Aeronautics and Astronautics), Beijing 100083, PR China;School of Automation Science and Electrical Engineering, Beihang University (Beijing University of Aeronautics and Astronautics), Beijing 100083, PR China

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2006

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Abstract

This paper presents a design method of H"2 guaranteed cost (GC) fuzzy controllers for discrete-time nonlinear systems with parameter uncertainties. The Takagi and Sugeno (T-S) fuzzy model with parameter uncertainties is employed to represent an uncertain discrete-time nonlinear system. A sufficient condition for the existence of H"2 GC fuzzy controllers is presented in terms of linear matrix inequalities (LMIs). The resulting fuzzy controllers not only guarantee that the closed-loop fuzzy system is quadratically stable, but also provide a guaranteed cost on the H"2 performance index. Furthermore, an optimal H"2 GC fuzzy controller in the sense of minimizing a bound on the guaranteed cost is provided by means of an LMI optimization procedure. Finally, it is also demonstrated, through numerical simulations on the backing up control of a truck-trailer, that the proposed design method is effective.