Second-order Analysis for Optimal Control Problems with Pure and Mixed State Constraints

Frédéric Bonnans 1, 2 Audrey Hermant 1, 2
1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CNRS - Centre National de la Recherche Scientifique : UMR7641, X - École polytechnique, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : This paper deals with the optimal control problem of an ordinary differential equation with several pure state constraints, of arbitrary orders, as well as mixed control-state constraints. We assume (i) the Hamiltonian to be strongly convex and the mixed constraints to be convex w.r.t. the control variable, and (ii) a linear independence condition of the active constraints at their respective order to hold. We give a complete analysis of the smoothness and junction conditions of the control and of the constraints multipliers. This allow us to obtain, when there are finitely many nontangential junction points, a theory of no-gap second-order optimality conditions and a characterization of the well-posedness of the shooting algorithm. These results generalize those obtained in the case of a scalar-valued state constraint and a scalar-valued control.
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Rapport
[Research Report] RR-6199, INRIA. 2007
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Frédéric Bonnans, Audrey Hermant. Second-order Analysis for Optimal Control Problems with Pure and Mixed State Constraints. [Research Report] RR-6199, INRIA. 2007. 〈inria-00148946v2〉

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