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Nonlinear discrete time optimal control based on Fuzzy Models

The approach of designing a discrete time optimal controller for a nonlinear system represented by a fuzzy model is presented in this paper. A fuzzy model with product inference engine, singleton fuzzifier, center average defuzzifier, and Gaussian membership functions is trained by the orthogonal least square (OLS) learning algorithm based on given input-output data pairs. An optimal control scheme is then formulated based on the fuzzy model. The numerical solution of the problem is achieved by use of a feasible-direction algorithm. To show the effectiveness of the proposed method, the simulation results of three nonlinear optimal control problems are presented. The results show that the performance of the proposed approach is quite similar to that of optimal control of the system represented by an explicit mathematical model, thus demonstrating the efficacy of the proposed scheme for optimal control of unknown nonlinear systems.