Nearly Optimal Control Scheme Using Adaptive Dynamic Programming Based on Generalized Fuzzy Hyperbolic Model

An effective scheme is presented to design the nearly optimal control for continuous-time (C-T) nonlinear systems. The generalized fuzzy hyperbolic model (GFHM) is used to approximate the solution of the Hamilton-Jacobi-Bellman (HJB) equation (i.e., the value function) for the first time. Further, the approximate solution is utilized to obtain the nearly optimal control. The value function is estimated by only using single GFHM, which captures the mapping between the state and value function. First, we illustrate the design process for the nearly optimal control involving nonlinear systems. Then stability conditions and conservatism analysis are given, and the approximate errors are proven to be uniformly ultimately bounded (UUB). Finally, a numerical example illustrates the effectiveness of our method and an example compared with the adaptive method based on dual neural-network models is used to demonstrate the advantages of our method.