Analysis of time-optimal problem in T-S fuzzy model via Lie algebra

Abstract

This paper investigates the geometric properties for time-optimal problem in Takagi-Sugeno (T-S) fuzzy model by using the Pontryagin maximum principle and Lie algebra. We will focus on the existence of time-optimal solution, singularity of switching function. These problems are considered because of rich geometry solution and the main important motivation for this paper is to study the Lie algebra formulation. The generalized rank condition for the existence of the optimal solution of accessible Lie algebra is derived. According to the necessary condition of optimality, time-optimal controller for the T-S fuzzy model is a bang-bang type with a finite number of switchings.