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

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• 作者：J. Fr¨¦d¨¦ric Bonnans ; Laurent Pfeiffer ; Oana Silvia Serea
• 关键词：49J15 ; 49K40 ; 49Q12 ; 90C31
• 刊名：Nonlinear Analysis
• 出版年：2013
• 出版时间：September, 2013
• 年：2013
• 卷：89
• 期：Complete
• 页码：55-80
• 全文大小：536 K

文摘

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. In this framework, relaxation with Young measures enables us to consider a wide class of perturbations and therefore to derive sharp estimates of the value function. The sensitivity analysis is performed in a neighborhood of a local optimal solution of a reference problem. The local solution is assumed to be optimal with respect to the set of feasible relaxed controls having their support in a ball of a given radius and having an associated trajectory very close to the reference trajectory, for the -norm. We call such a solution a relaxed -strong solution.