A geometrically based criterion to avoid infimum gaps in optimal control

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Palladino, M.¹  Rampazzo, F.² 

[1] Gran Sasso Sci Inst GSSI, Via Crispi 7, I-67100 Laquila, Italy

[2] Univ Padua, Dept Math, Via Trieste 63, I-35121 Padua, Italy

关键词: Optimal control;    Infimum gap;    Necessary conditions;    Set separation;   

DOI  :  10.1016/j.jde.2020.06.066

来源: Elsevier

【 摘 要 】

In optimal control theory, infimum gap means a non-zero difference between the infimum values of a given minimum problem and an extended problem obtained by embedding the original family V of controls in a larger family W. For some embeddings - like standard convex relaxations or impulsive extensions - the normality of an extended minimizer has been shown to be sufficient for the avoidance of infimum gaps. A natural issue is then the search of a general hypothesis under which the criterium normality implies no gap holds true. We prove that this criterium is actually valid as soon as V is abundant in W, without any convexity assumption on the extended dynamics. Abundance, which was introduced by J. Warga in a convex context and was later generalized by B. Kaskosz, strengthens density, the latter being not sufficient for the mentioned criterium to hold true. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free