Modelling and robust control of uncertain dynamical systems using fuzzy set theory

Abstract

New modelling and control approaches for uncertain nonlinear dynamical systems using fuzzy set theory are developed and proposed in this paper. The philosophy of the proposed modelling approach is to provide a new fuzzy-set based representation of uncertain systems so that robust control design is made feasible without resorting to model simplification or imposing restrictive conditions on system uncertainty (heretofore required by most traditional control design approaches). Based on the new generated fuzzy model representation of uncertain systems, a fuzzy control design approach is also proposed. The latter consists of extending design techniques of the sliding mode control method to fuzzy systems. Accordingly, new control design concepts using fuzzy sets are introduced. The stability analysis of the proposed fuzzy-model based control system is also provided in this paper. The benefits of the present study are illustrated through numerical simulations of the fuzzy modelling and control of a single-link robot arm with uncertain dynamics.