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Article Dans Une Revue Systems & Control Letters Année : 2020

Distance estimates to feasible controls for systems with final point constraints and second order necessary optimality conditions

Résumé

We prove an inverse mapping theorem on a metric space of controls that allows to "control" final points of trajectories of a nonlinear system. More precisely, our result provides local distance estimates of arbitrary controls from feasible ones. As an application we derive second-order necessary optimality conditions for L 1-local minima for the Mayer optimal control problem with a general control constraint U ⊂ R m , state constraints described by inequalities and final point constraints, possibly having empty interior. Thanks to this inverse mapping theorem we first get a second-order variational inequality as a necessary optimality condition. Then the separation theorem leads in a straightforward way to second-order necessary conditions.
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Dates et versions

hal-02955766 , version 1 (02-10-2020)

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H. Frankowska, N.P. P Osmolovskii. Distance estimates to feasible controls for systems with final point constraints and second order necessary optimality conditions. Systems & Control Letters, 2020, 144, pp.104770. ⟨10.1016/j.sysconle.2020.104770⟩. ⟨hal-02955766⟩
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