Fuzzy dynamic programming

This paper develops a fuzzy dynamic programming technique with fuzzy state variables and decision variables. Fuzzy discretization is initially applied to the state and control spaces generating fuzzy cellular spaces. State transition is achieved by a fuzzy cell to cell mapping. The target state cell membership is subsequently computed by premiss matching. The paths that lead to a target cell which is the image of many different state cell combinations have different costs with different memberships. A cost functional is representing the time spent and the fuzzy distance of the present fuzzy state cell to a fuzzy desired state. Paths having minimum costs are thereafter selected. The developed methodology is applied to a ballistic missile tracking problem and results are discussed from the efficiency of the new fuzzy optimal control technique point of view