Fuzzy optimal control applying dynamic programming

The authors propose a design method for new fuzzy feedback systems which contain the idea of optimal control. The fuzzy optimal control rules are selected when the state variables are apart from the goal, and they are switched to ordinary fuzzy proportional-derivative (PD) control rules automatically near the goal to solve the problem of stability and off-set. For optimal control, the phase plane is digitized and the optimal output of the controller is obtained by applying fuzzy dynamic programming which has linguistically explained goals and constraints to each state on the phase plane. Quasi-optimal feedback control rules are obtained by describing the optimal output of the controller for each state as fuzzy rules whose inputs are state variables. The effectiveness of the system designed with this method was verified by simulations, and it was found that the characteristics of the system are similar to that of fuzzy sliding mode control