Computing the Value Function for an Optimal Control Problem

A one-dimensional inflnite horizon deterministic singular optimal control problem with controls taking values in a closed cone in R leads to a dynamic programming equation of the form: 1 (x;v;v 0 );F 2 (x;v;v 0 ) = 0; 8x 2R; which is called the Hamilton Jacobi Bellman(HJB) equation that the value function must satisfy. In this paper we flnd explicitly the value function for an inflnite horizon deterministic optimal control problem.