Nonlinear modeling of uncertain dynamical systems using fuzzy set concepts

In this paper we propose a new modeling approach for uncertain nonlinear dynamical systems using fuzzy set theory. The main idea of the proposed modeling approach is to interpret an uncertain dynamical system as a dynamic fuzzy system and provide its fuzzy model. The latter is described by a new fuzzy differential equation. Procedures to take into account system uncertainty in the new fuzzy model are described. To construct the fuzzy model, no a priori information on the uncertain system parameters is required except that their constraint set is assumed to be known and compact. Furthermore, the proposed fuzzy modeling approach does not impose restrictive assumptions on the structure of uncertainty (heretofore required by most traditional control design approaches). This fact makes it possible to design robust controllers for a wide range of practical systems. In addition, it sets the groundwork for systematic design of fuzzy controllers.