Interpolative reasoning in optimal fuzzy control

Abstract

Considers optimal fuzzy control meant as the determination of an optimal sequence of controls which best satisfies fuzzy constraints on the consecutive states. A fuzzy system under control is assumed. Control with a fixed and specified, implicitly specified and fuzzy termination time is discussed. For computational feasibility, a possibly small number of reference fuzzy states and controls is assumed. All the fuzzy controls and states occurring in the course of the algorithm are then approximated by these reference fuzzy controls and states. Optimal control policies relating optimal reference fuzzy controls to reference fuzzy states are represented as a fuzzy relation, which is used via the compositional rule of interference to derive an optimal control for a particular fuzzy state. To obtain meaningful results, this process requires a large number of overlapping reference fuzzy controls and states, which diminishes the computational efficiency of the algorithms used. Therefore, a smaller number of nonoverlapping fuzzy states and controls is assumed, and then an interpolative reasoning scheme is employed to determine an optimal fuzzy control. >