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Sensitivity analysis for relaxed optimal control problems with final-state constraints

J. Frédéric Bonnans(frederic.bonnans***at***inria.fr)
Laurent Pfeiffer(laurent.pfeiffer***at***polytechnique.edu)
Oana Silvia Serea(oana-silvia.serea***at***univ-perp.fr)

Abstract: In this article, we compute a second-order expansion of the value function of a family of relaxed optimal control problems with final-state constraints, parameterized by a perturbation variable. The sensitivity analysis is performed for controls that we call R-strong solutions. They are optimal solutions with respect to the set of feasible controls with a uniform norm smaller than a given R and having an associated trajectory in a small neighborhood for the uniform norm. In this framework, relaxation enables us to consider a wide class of perturbations and therefore to derive sharp estimates of the value function.

Keywords: Optimal control, sensitivity analysis, relaxation, Young measures, Pontryagin's principle, strong solutions.

Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Citation: Published as the Inria research report No 7977 (May 2012).

Download: [PDF]

Entry Submitted: 05/29/2012
Entry Accepted: 05/29/2012
Entry Last Modified: 05/29/2012

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