A geometrically based criterion to avoid infimum gaps in optimal control

[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.

[发布日期] 2020-11-15

[关键词] Optimal control;Infimum gap;Necessary conditions;Set separation