Adaptive fuzzy modelling and control for discrete-time nonlinear uncertain systems

This paper presents an adaptive fuzzy modelling and control scheme for discrete-time nonlinear uncertain systems. The proposed adaptive scheme includes two parts: on-line fuzzy modelling using Takagi-Sugeno (T-S) fuzzy systems and model reference adaptive control design. The T-S fuzzy model has a self-organizing structure, i.e. the fuzzy rules can be added, replaced or deleted automatically via on-line clustering and the consequence parameters of the T-S model can be recursively updated by recursive least square estimation (RLSE) method, which allows it to identify complex nonlinear uncertain systems on-line. The adaptive controller is based on the T-S fuzzy model employed as a dynamic model of the plant. The controller can adaptively generate control signals while the structure and parameters of the T-S model are-updated on-line. The effectiveness of our approach is verified by its applications in the identification of a second-order nonlinear uncertain system and the tracking control of a single robot arm.