Singular solutions in optimal control: second order conditions and a shooting algorithm

Maria Soledad Aronna 1, 2
1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
Abstract : In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final state are considered. We investigate singular solutions for this class of problems. First, we obtain second order necessary and sufficient conditions for weak optimality. Afterwards, we propose a shooting algorithm and show that the sufficient condition above-mentioned is also sufficient for the local quadratic convergence of the algorithm.
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Maria Soledad Aronna. Singular solutions in optimal control: second order conditions and a shooting algorithm. [Research Report] RR-7764, INRIA. 2011, pp.33. ⟨inria-00631564v2⟩

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