Multistage evolutionary optimization of fuzzy systems—application to optimal fuzzy control

We discuss the classic Bellman and Zadeh’s (1970) problem of multistage (multistep) optimal control of fuzzy dynamic system under fuzzy constraints imposed on controls applied and fuzzy goals imposed on states attained. The fuzzy decision, serving the purpose of a performance function, is assumed to be the intersection of the fuzzy constraints and fuzzy goals. An optimal sequence of controls is sought which maximizes the fuzzy decision over a fixed and specified planning horizon. The use of a genetic algorithm is shown to be a viable alternative to the traditionally employed solution techniques: Bellman and Zadeh’s (1970) dynamic programming [possibly augmented with Kacprzyk’s(1993a–c) interpolative reasoning], Kacprzyk’s (1978a, 1979) branch-and-bound, and Francelin and Gomide’s (1992, 1993)[cf. also Francelin, Gomide and Kacprzyk’s (1995)] neural-network-based approach.