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

Pao-Tsun Lin, Chi-Hsu Wang, Tsu-Tian Lee
2009 IEEE transactions on fuzzy systems  
This paper investigates a geometric property of timeoptimal 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 timeoptimal solution reveals the controllability of T-S fuzzy model that can be found by the generalized rank condition. The
more » ... ank 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.
doi:10.1109/tfuzz.2008.924321 fatcat:j2e6jfj7fvd7rpp6mg3dhxy6ie