Acta Mathematica Vietnamica
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OPTIMALITY CONDITIONS FOR CONTROLS ACTING AS COEFFICIENTS OF A NONLINEAR ORDINARY DIFFERENTIAL EQUATION OF SECOND ORDER
MOHAMED AKKOUCHI, ABDELLAH BOUNABAT, MANFRED GOEBELpp. 115-124
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.