Stable nonlinear controller design for a Takagi-Sugeno fuzzy model

Abstract

This paper proposes another adaptive control scheme for nonlinear systems using a Takagi-Sugeno fuzzy model. Takagi-Sugeno fuzzy models have been widely used to identify the structures and parameters of unknown or partially known plants, and to control nonlinear systems. This scheme shows a good approximation capability by the fuzzy blending of local dynamics. Since a Takagi-Sugeno fuzzy model is a nonlinear system in nature, and its parameters are not linearly parameterized, it is difficult to design an adaptive controller using conventional design methods for adaptive controllers which are derived from linearly parameterized systems. In this paper, the functional form of the local dynamics are assumed to be known, but the corresponding parameters are unknown. This additional information about system nonlinearity makes it possible to design an adaptive controller for a nonlinearly parameterized system. The control law is similar to that of a conventional adaptive control technique, while its parameter-update rule is based on the local search method. A parameter-update law is derived so that the time-derivative of the Lyapunov function is negative in the region of interest. Simulation results have shown that this adaptive controller is capable of a good performance.