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

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.
Settore MAT/05 - Analisi Matematica
English
Rilevanza internazionale
Capitolo o saggio
Minimum time function; sensitivity relations; differential inclusions
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].
Cannarsa, P; Scarinci, T
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/170479
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