On Infinite-Horizon Optimal Control Problems

Abstract

In this paper, we consider infinite-horizon optimal control problems. First, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measure. The optimal measure is approximated by a finite combination of atomic measures and the approximate solution of the fist problem is find by the optimal solution of a finite-dimensional linear programming problem. The solution of this problem is used to find a piecewise constant control for the original one, and finally by using the approximate control signals we obtain the approximate trajectories.