Sufficiency for Singular Controls with Equality Constraints

Javier F. Rosenblueth and Gerardo Sánchez Licea


Optimal control, Sufficient conditions for optimality, Weak minima, Singularity


In this paper we derive second order sufficient conditions for a weak minimum of a fixed-endpoint optimal control problem involving equality control constraints, without imposing the standard assumption of nonsingularity. The technique used corresponds to a generalization of the one introduced by Hestenes, in terms of directional convergent sequences of trajectories, originally posed for the problem of Bolza in the calculus of variations.

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