Conjugate times and regularity of the minimum time function with differential inclusionsReport as inadecuate




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1 DIPMAT - Dipartimento di Matematica Roma II 2 IMJ - Institut de Mathématiques de Jussieu

Abstract : This paper studies the regularity of the minimum time function, T ·, for a control system with a general 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.





Author: Piermarco Cannarsa - Teresa Scarinci -

Source: https://hal.archives-ouvertes.fr/



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