A genetic algorithm for the multistage control of a fuzzy system in a fuzzy environment

Abstract

We discuss a prescriptive approach to multistage optimal fuzzy control of a fuzzy system, given by a fuzzy state transition equation. Fuzzy constraints and fuzzy goals at consecutive control stages are given, and their confluence, Bellman and Zadeh's fuzzy decision, is an explicit performance function to be optimized. First, we briefly survey previous basic solution methods of dynamic programming (Baldwin and Pilsworth, 1982) and branch-and-bound (Kacprzyk, 1979), which are plagued by low numerical efficiency, and then sketch Kacprzyk's (1993a--e, 1994a) approach based on possibilistic interpolative reasoning aimed at enhancing the numerical efficiency but requiring a solution of a simplified auxiliary problem, and then some "readjustment" of the solution obtained. We propose a genetic algorithm for solving the problem considered. Real coding and specially defined operations of crossover, mutation, etc. are employed. The approach yields good results, and is quite efficient numerically