On Second-Order Necessary Conditions in Optimal Control of Problems with Mixed Final Point Constraints
Résumé
We investigate the second-order necessary opti-mality conditions for weak local minima for the Mayer optimal control problem with an arbitrary control constraint U ⊂ R m and final-point constraints given by equalities and inequalities. In the difference with the previous literature, we do not impose structural assumptions on U and use an inverse mapping theorem on a metric space to derive a variational inequality. The separation theorem leads in a straightforward way to the second-order necessary optimality conditions.
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