Robust adaptive fuzzy controller for nonlinear system with unknown nonlinearities

Article type: Research Article

Authors: Park, Jang-Hyun | Park, Gwi-Tae

Affiliations: School of Electrical Engineering, Korea University, 1, 5-ka, Anam-dong, Seoul 136-701, South Korea. Tel.: +82 2 929 5185; Fax: +82 2 921 0544; E-mail: [email protected]

Abstract: This paper describes the design of the robust adaptive fuzzy controller for uncertain nonlinear dynamical systems with unknown nonlinearities. These unknown nonlinearities are approximated by the fuzzy system with a set of fuzzy IF-THEN rules whose parameters are adjusted on-line according to some adaptive laws for the purpose of controlling the output of the nonlinear system to track a given trajectory. The Lyapunov synthesis approach is used to develop a state-feedback adaptive control algorithm based on the adaptive fuzzy model. The key assumption is that the reconstruction errors satisfy certain bounding conditions. The control law consists of two terms. One is the certainty equivalent control and the other is the bounding control. A bounding parameter adaptive law is used to obtain this bounding control. The overall control system guarantees that the tracking error converges in the small neighborhood of zero and that all signals involved are uniformly bounded. The theoretical results are illustrated through a simulation example.

Journal: Journal of Intelligent & Fuzzy Systems, vol. 10, no. 2, pp. 87-98, 2001