On Infinite Horizon Optimal Control Problems with a Feed Forward Neural Network Scheme

Abstract

In this paper, a class of infinite-horizon nonlinear optimal control problems is considered. The main idea is to convert the infinite horizon problem to an equivalent finite-horizon optimal control problem. According to the Pontryagin minimum principle for optimal control problems and by constructing an error function, we define an unconstrained minimization problem. In the optimization problem, we use trial solutions for the state, costate and control functions where these trial solutions are constructed by using two-layer perceptron. We then minimize the error function where weights and biases associated with all neurons are unknown. Substituting the optimal values of the weights and biases into the trial solutions, we obtain the optimal solution of the original problem. We also use a dynamic optimization scheme to learning process and discuss the stability and convergence properties of it. Some examples are given to show the efficiency of the method.