Optimal policies in multistage fuzzy control information granulation and interpolative reasoning

Abstract

We consider multistage control of a fuzzy dynamic system under fuzzy constraints on controls and fuzzy goals on states. First, we present the standard solution by dynamic programming, indicate its limitations related to its inherent curse of dimensionality. We propose to use a granulation of the space of states and controls, and replace the source problem by its auxiliary counterpart with a small number of reference fuzzy states and reference fuzzy controls. After its solution by dynamic programming, we "adjust" the solution obtained by using Koczy and Hirota's interpolative reasoning technique.