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.;
2020-01-01

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/176081
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