Fuzzy Optimal Control from Space Discretization to Machine Intelligence

The fuzzy optimal control with free target states is known to be difficult to obtain. This paper proposes a novel algorithm for solving fuzzy optimal control problems with free state terminal conditions and bounded controls. The algorithm makes use of the fuzzy generalized cell mapping (FGCM) method and Bellman’s principal of optimality. The cost function is defined as the expectation of fuzzy variables based on the Choquet integral of fuzzy set theory. A discrete form of fuzzy master equation is derived for the membership of the response. The transition matrix of the FGCM method is obtained as a function of controls and states. This allows to evaluate the transient responses of the controlled system. The proposed algorithm is applied to representative nonlinear systems with fuzzy uncertainties, leading to excellent control performance. It is noted that the optimal control is designed to minimize the fuzzy expected cost function. The results show that the optimal control is quite robust to the variability of fuzzy uncertainties in the system.