This paper studies the regularity of the minimum time function, T.(•), for a control system with a closed target, taking the state equation in the form of a differential inclusion. Our first result is a sensitivity relation which guarantees the propagation of the proximal subdifferential of T along any optimal trajectory. Then, we obtain the local C2 regularity of the minimum time function along optimal trajectories by using such a relation to exclude the presence of conjugate times.
Cannarsa, P., Scarinci, T. (2015). Conjugate times and regularity of the minimum time function with differential inclusions. In P. Bettiol, P. Cannarsa, G. Colombo, M. Motta, F. Rampazzo (a cura di), Analysis and geometry in control theory and its applications (pp. 85-110). Springer International Publishing [10.1007/978-3-319-06917-3_4].
Conjugate times and regularity of the minimum time function with differential inclusions
CANNARSA, PIERMARCO;SCARINCI, TERESA
2015-01-01
Abstract
This paper studies the regularity of the minimum time function, T.(•), for a control system with a closed target, taking the state equation in the form of a differential inclusion. Our first result is a sensitivity relation which guarantees the propagation of the proximal subdifferential of T along any optimal trajectory. Then, we obtain the local C2 regularity of the minimum time function along optimal trajectories by using such a relation to exclude the presence of conjugate times.| File | Dimensione | Formato | |
|---|---|---|---|
|
Paper.pdf
solo utenti autorizzati
Licenza:
Copyright dell'editore
Dimensione
191.86 kB
Formato
Adobe PDF
|
191.86 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.
