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Fuzzy dynamic programming: interpolative reasoning for an efficient derivation of optimal control policies

Kacprzyk J.

Control and Cybernetics

2013

Vol. 42, no. 1

63--84

We consider multistage optimal control of a fuzzy dynamic system under fuzzy constraints on controls and fuzzy goals on states in the setting of Bellman and Zadeh (1970) and Kacprzyk (1983, 1997). First, we present the solution by dynamic programming chich is a standard techniques in the class of problems considered. We indicato its limitations, mainly related to its inherent curse of dimensionality. We propose to replace the source problem by its auxiliary counterpart with a small number of reference fuzzy states and reference fuzzy controls, solve it by dynamic programming to obtain optimal reference control policies relating optimal reference fuzzy controls to reference fuzzy states. Then, we show the use of an interpolative reasoning approach to derive optimal fuzzy controls, not necessarily reference ones, for current fuzzy states, not necessarily reference ones.