Multistage control of a stochastic system in a fuzzy environment using a genetic algorithm

We consider the classic Bellman and Zadeh multistage control problem under fuzzy constraints imposed on applied controls and fuzzy goals imposed on attained states with a stochastic system under control that is assumed to be a Markov chain. An optimal sequence of controls is sought that maximizes the probability of attaining the fuzzy goal subject to the fuzzy constraints over a finite, fixed, and specified planning horizon. A genetic algorithm is shown to be a viable alternative to the traditionally employed Bellman and Zadeh dynamic programming. © 1998 John Wiley & Sons, Inc.