INTERPOLATIVE REASONING FOE COMPUTATIONALLY EFFICIENT OPTIMAL FUZZY CONTROL

Fuzzy optimal control is considered. An optimal sequence of controls is sought best satisfying fuzzy constraints on the controls and fuzzy goals on the states (outputs), with a fuzzy system under control Control over a fixed and specified, implicitly specified, fuzzy, and infinite termination time is discussed. For computational efficiency a small number of reference fuzzy staters and controls is to be assumed by which fuzzy controls and stated are approximated. Optimal control policies reference fuzzy states are determined as a fuzzy relation used, via the compositional rule of inference, to derive an optimal control. Since this requires a large number of overlapping reference fuzzy controls and states implying a low computational efficiency, a small number of nonoverlapping reference fuzzy states and controls is assumed, and then interpolative reasoning is used to infer an optimal fuzzy control for a current fuzzy state.