Fuzzy dynamic programming: interpolative reasoning for an efficient derivation of optimal control policies
Janusz Kacprzyk · Control and Cybernetics · 2013
We consider multistage optimal control of a fuzzy dy- namic 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 which is a standard techniques in the class of problems considered. We in- dicate its limitations, mainly related to its inherent curse of dimen- sionality. We propose to replace the source problem by its auxiliary counterpart with a small number of reference fuzzy states and ref- erence 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 in- terpolative reasoning approach to derive optimal fuzzy controls, not necessarily reference ones, for current fuzzy states, not necessarily reference ones.