Optimal Control of Second Order Systems with Infinite Time Horizon: Existence of Solutions

摘要

We investigate an optimal control problem described by a second-order ordinary differential equation on the interval ]0,∞[ and an integral cost functional. The study of this problem is based on a variational approach. In the first part of the paper, a theorem on the existence and uniqueness of a solution to the control system, corresponding to any admissible control, is derived. In the second part, some results on the continuous dependence of solutions on the controls and a theorem on the existence of classically optimal solution to the problem under consideration are given.