M. Akkouchi, A. Bounabat, and M. Goebel Mohamed Akkouchi, Abdellah Bounabat, and Manfred Goebel

Abstract

     We study in this paper a control problem associated to a semilinear second order ordinary differential equation with pointwise state constraints. The control acts as a coefficient of the state equation. For this problem, we prove the existence of optimal controls and obtain a necessary optimality condition. This condition looks somehow like Pontryagin's maximum principle. We end this work by giving  illustrative examples where we apply our results.