Partially affine control problems: second order conditions and a well-posed shooting algorithm

Maria Soledad Aronna (1, 2, 3)

1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 CIFASIS - Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas

This paper deals with optimal control problems for systems that are affine in one part of the control variables and nonlinear in the rest of the control variables. We have finitely many equality and inequality constraints on the initial and final states. First we obtain second order necessary and sufficient conditions for weak optimality. Afterwards, we propose a shooting algorithm, and we show that the sufficient condition above-mentioned is also sufficient for the injectivity of the shooting function at the solution.

Dans ce travail on étudie le problème de commande optimale avec un système affine dans une partie de la commande. On considé́re un nombre fini de contraintes d'é́galité́ et d'iné́galité́ sur les valeurs initiales et finales de l'é́tat. On commence par donner des conditions né́cessaire et suffisante du second ordre. Ensuite, on propose un algorithme de tir et on montre que la condition suffisante mentionné́e garantit que cet algorithme est bien posé́.

Mots clés: optimal control; Pontryagin Maximum Principle; singular control; shooting algorithm; second order optimality condition; control-affine system; SADCO

Domaines: Optimisation et contrôle [math.OC]

Maria Soledad Aronna. Partially affine control problems: second order conditions and a well-posed shooting algorithm. [Research Report] RR-7764, 2011, pp.27. ⟨inria-00631564v1⟩