A radial basis function implementation of the adaptive dynamic programming algorithm

Adaptive Dynamic Programming constitutes a potentially powerful approach to optimal control. An approximation to the Bellman cost functional is updated in real time. The technique is applicable to a broad class of nonlinear networks with unknown dynamics and is guaranteed to converge to the optimal control with stepwise stability. The goal of this paper is to describe an implementation of the Adaptive Dynamic Programming Algorithm in which a radial basis function is used to define the approximate cost functional, which is updated locally in the neighborhood of the state trajectory each time the system is run. An application of the algorithm to a nonlinear flight control problem with unknown aircraft dynamics is presented.