Analysis and approximation of an impulse control problem on an infinite time interval

Consideration is given to the infinite-horizon problem of control whose dynamics involves ordinary control v, impulsive control u, and its derivative u over dot. A new reparametrization of the problem as introduced which adds one more variable to the state space. The new system can be studied Ising the techniques created for the problems of optimal control and involving only the controls front L-infinity. Its valve function coincides with that of the original problem. This correspondence also enables one to develop an approximation algorithm which is based on the principle of discrete programming and ensures in the original problem the convergence to the value function.