Optimal control design for nonlinear systems: Adaptive dynamic programming based on fuzzy critic estimator

In this paper, an optimal control design approach based on fuzzy critic estimator (FCE) is presented for nonlinear continuous-time systems. The main idea of our study is to approximate the solution (i.e., value function) of the Hamilton-Jacobi-Bellman (HJB) equation by making use of FCE as an estimator/approximator, which is utilized to obtain the optimal control. The value function is estimated by FHM, which captures the mapping between the state and value function. Firstly, we illustrate the design process of the optimal control involving nonlinear systems. Secondly, we analyze the stability conditions and prove the approximate error is uniformly ultimately bounded (UUB). Finally, a numerical example is given to illustrate the effectiveness and advantages of our approach.