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arXiv · 1705.03249

Variational Analysis for the Bilateral Minimal Time Function

Luong V. Nguyen
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Abstract

In this paper, we derive formulas for the Fr\'echet (singular) subdiferentials of the bilateral minimal time function $T:\mathbb{R}^n \times \mathbb{R}^n \to [0,+\infty]$ associated with a system governed by differential inclusions. As a consequence, we give a connection between the Fr\'echet normals to the sub-level sets of $T$ and to its epigraph. Finally, we show that the Fr\'echet normal cones to the sub-level set of $T$ at a point $(\alpha,\beta)$ and to epi($T$) at $((\alpha,\beta),T(\alpha,\beta))$ have the same dimension.

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Luong V. Nguyen. 2017-05-09. Variational Analysis for the Bilateral Minimal Time Function. https://arxiv.org/abs/1705.03249

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