Digital Fuzzy Set-Point Regulating Chaotic Systems: Intelligent Digital Redesign Approach

Abstract

This chapter concerns digital control of chaotic systems represented by Takagi-Sugeno fuzzy systems, using intelligent digital redesign (IDR) technique. The term IDR involves converting an existing analog fuzzy set-point regulator into an equivalent digital counterpart in the sense of state-matching. The IDR problem is viewed as a minimization problem of norm distances between nonlinearly interpolated linear operators to be matched. The main features of the present method are that its constructive condition with global rather than local state-matching, for concerned chaotic systems, is formulated in terms of linear matrix inequalities; the stability property is preserved by the proposed IDR algorithm. A few set-point regulation examples of chaotic systems are demonstrated to visualize the feasibility of the developed methodology, which implies the safe digital implementation of chaos control systems.