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.
A geometrically based criterion to avoid infimum gaps in optimal control
Palladino M.
;Rampazzo F.
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 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.File | Dimensione | Formato | |
---|---|---|---|
Palladino-Rampazzo-JDEfinal.pdf
accesso aperto
Descrizione: Articolo principale
Tipologia:
Preprint (submitted version)
Licenza:
Accesso gratuito
Dimensione
482.69 kB
Formato
Adobe PDF
|
482.69 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.