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

M. Soledad Aronna(aronna***at***cmap.polytechnique.fr)

Abstract: 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.

Keywords: optimal control, Pontryagin Maximum Principle, singular control, shooting algorithm, second order optimality condition

Category 1: Infinite Dimensional Optimization

Citation: INRIA Research Report Nr. 7764

Download: [PDF]

Entry Submitted: 10/17/2011
Entry Accepted: 10/17/2011
Entry Last Modified: 10/17/2011

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