Synthesis of Nonlinear Control Strategies via Fuzzy Logic

In this paper an analytic formulation of a class of fuzzy logic control algorithms is presented. This formulation makes use of the idea that characterstic functions of fuzzy sets may be considered to be algebraic functions of their argument. Placing common constraints such as continuity and boundedness on these functions, and making use of a variation of the so called centroid of area defuzzification rule, results in an analytic formulation of the control law that (i) can be used to explain how fuzzy control algorithms function as they do, and (ii) makes formal analysis of fuzzy control systems, at least in principle, possible.