A direct approach to second order conditions for mixed equality constraints

In this paper we consider an optimal control problem posed over piecewise continuous controls and involving state-control (mixed) equality constraints. We provide an explicit derivation of second order necessary conditions simpler than others available in the literature, yielding a clear understanding of how to define a set of “differentially admissible variations” where a certain quadratic form is nonnegative. © 2006 Elsevier Inc. All rights reserved