Sufficient Minimum Condition in Singular Control for Systems with Parameters

Abstract

Here we study problems of singular optimal control for which the index of performance, the differential constraints and the final conditions contain parameters. We determinate the trajectory of the neighboring extremal for the initial point perturbed and perturbed final manifold. This allows to obtain the second variation in the singular case. The sufficient conditions of minimum are a consequence of the non-negativity condition for the second variation. As application, we analyze the optimality of the singular control for an affine differential system.