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arXiv · 1501.01503

Conjugate times and regularity of the minimum time function with differential inclusions

Piermarco Cannarsa·Teresa Scarinci
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Abstract

This paper studies the regularity of the minimum time function, $T(\cdot)$, 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.

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Piermarco Cannarsa, Teresa Scarinci. 2015-01-07. Conjugate times and regularity of the minimum time function with differential inclusions. https://arxiv.org/abs/1501.01503

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