Time-optimal control of T-S fuzzy models via lie algebra

  • Authors:

  • Pao-Tsun Lin;Chi-Hsu Wang;Tsu-Tian Lee

  • Affiliations:

  • Department of Electrical and Control Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C;Department of Electrical and Control Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C;Department of Electrical Engineering, National Taipei University of Technology, Taipei, Taiwan, R.O.C

  • Venue:
  • IEEE Transactions on Fuzzy Systems
  • Year:
  • 2009

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Abstract

This paper investigates a geometric property of time-optimal problem in the Takagi-Sugeno (T-S) fuzzy model via Lie algebra. We will focus on the existence of a time-optimal solution, singularity of switching function, and number of switching. These inherent problems are considered because of their rich geometric properties. The sufficient condition for the existence of a time-optimal solution reveals the controllability of T-S fuzzy model that can be found by the generalized rank condition. The time-optimal controller can be found as the bang-bang type with a finite number of switching by applying the maximum principle. In the study of the singularity problem, we will focus on the switching function whenever it vanishes over a finite time interval. Finally, we show that the bounded number of switching can be found if the TS model (also a nonlinear system) is solvable.