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Time-Optimal Control of T--S Fuzzy Models via Lie Algebra

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3 Author(s)
Pao-Tsun Lin ; Dept. of Electr. & Control Eng., Nat. Chiao Tung Univ., Hsinchu, Taiwan ; Chi-Hsu Wang ; Tsu-Tian Lee,

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 T-S model (also a nonlinear system) is solvable.

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Fuzzy Systems, IEEE Transactions on  (Volume:17 ,  Issue: 4 )