The minimum time function T(·) of smooth control systems is known to be locally semiconcave provided Petrov’s controllability condition is satisfied. Moreover, such a regularity holds up to the boundary of the target under an inner ball assumption. We generalize this analysis to differential inclusions, replacing the above hypotheses with the continuity of T(·) near the target, and an inner ball property for the multifunction associated with the dynamics. In such a weakened setup, we prove that the hypograph of T(·) satisfies, locally, an exterior sphere condition. As is well known, this geometric property ensures most of the regularity results that hold for semiconcave functions, without assuming T(·) to be Lipschitz.

Cannarsa, P., & Nguyen, K. (2011). Exterior Sphere Condition and Time Optimal Control for Differential Inclusions. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 49(6), 2558-2576 [10.1137/110825078].

Exterior Sphere Condition and Time Optimal Control for Differential Inclusions

CANNARSA, PIERMARCO;
2011

Abstract

The minimum time function T(·) of smooth control systems is known to be locally semiconcave provided Petrov’s controllability condition is satisfied. Moreover, such a regularity holds up to the boundary of the target under an inner ball assumption. We generalize this analysis to differential inclusions, replacing the above hypotheses with the continuity of T(·) near the target, and an inner ball property for the multifunction associated with the dynamics. In such a weakened setup, we prove that the hypograph of T(·) satisfies, locally, an exterior sphere condition. As is well known, this geometric property ensures most of the regularity results that hold for semiconcave functions, without assuming T(·) to be Lipschitz.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
English
Con Impact Factor ISI
proximal normal vectors; exterior sphere condition; differential inclusions; time optimal control; semiconcave functions
Cannarsa, P., & Nguyen, K. (2011). Exterior Sphere Condition and Time Optimal Control for Differential Inclusions. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 49(6), 2558-2576 [10.1137/110825078].
Cannarsa, P; Nguyen, K
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
PMC-KTN_SICON.pdf

accesso aperto

Descrizione: articolo
Dimensione 259.18 kB
Formato Adobe PDF
259.18 kB Adobe PDF Visualizza/Apri

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/2108/102728
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 14
social impact