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

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.
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https://hal.inria.fr/hal-00702246
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Submitted on : Tuesday, January 22, 2013 - 4:10:35 PM
Last modification on : Friday, April 19, 2019 - 3:24:33 PM
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Joseph Frederic Bonnans, Laurent Pfeiffer, Oana Silvia Serea. Sensitivity analysis for relaxed optimal control problems with final-state constraints. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2013, 89, pp.55-80. ⟨10.1016/j.na.2013.04.013⟩. ⟨hal-00702246v2⟩

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