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 of controls in a larger family. 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 is abundant in , 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.

A geometrically based criterion to avoid infimum gaps in optimal control

Palladino, M.;
2020

Abstract

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 of controls in a larger family. 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 is abundant in , 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.
Optimal control, Infimum gap, Necessary conditions, Set separation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12571/9521
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