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 C-2 regularity of the minimum time function along optimal trajectories by using such a relation to exclude the presence of conjugate times.

Conjugate Times and Regularity of the Minimum Time Function with Differential Inclusions

Scarinci, T
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 C-2 regularity of the minimum time function along optimal trajectories by using such a relation to exclude the presence of conjugate times.
978-3-319-06916-6
978-3-319-06917-3
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/151295
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