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.
File in questo prodotto:
File Dimensione Formato  
2020_JDE_269_Palladino.pdf

non disponibili

Dimensione 510.71 kB
Formato Adobe PDF
510.71 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/176081
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 5
social impact