Two coupled neural-networks-based solution of the Hamilton–Jacobi–Bellman equation

This work is aimed at looking into the determination of optimal neuro-feedback control for discrete time nonlinear systems. The basic idea consists in the use of two coupled neural networks to approximate the solution of the Hamilton–Jacobi–Bellman equation (HJB) and to obtain a robust feedback closed-loop control law. The used learning algorithm is a modified version of the backpropagation one. As an illustration, a numerical nonlinear discrete time example is considered. Simulation results show the effectiveness of the proposed method.