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.
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Acknowledgements
This research is partially supported by the European Commission (FP7-PEOPLE-2010-ITN, Grant Agreement no. 264735-SADCO), and by the INdAM National Group GNAMPA. This work was completed while the first author was visiting the Institut Henri Poincaré and Institut des Hautes Études Scientifiques on a senior CARMIN position. The authors are grateful to the anonymous referee for her/his useful comments.
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Cannarsa, P., Scarinci, T. (2015). Conjugate Times and Regularity of the Minimum Time Function with Differential Inclusions. In: Bettiol, P., Cannarsa, P., Colombo, G., Motta, M., Rampazzo, F. (eds) Analysis and Geometry in Control Theory and its Applications. Springer INdAM Series, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-319-06917-3_4
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DOI: https://doi.org/10.1007/978-3-319-06917-3_4
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