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Variational analysis and regularity of t...
Nguyen, Luong V....

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Variational analysis and regularity of the minimum time function for differential inclusions by Nguyen, Luong V. ( Author )
Lemonjar Open Access
Australian National University
07-09-2023
We study the time optimal control problem for differential inclusions with a general closed target. We first give the representation of the proximal horizontal subgradients of the minimum time function $\mathcal{T}$ and then, together with the representation of the proximal subgradients, we obtain some relationships between the normal cones to the sublevel of $\mathcal{T}$ and the normal cones to its epigraph. The relationships allow us to get the propagation of the proximal subdifferential as well as of the proximal horizontal subdifferential of $\mathcal{T}$ along optimal trajectories. Finally, we show, under suitable assumptions, that the epigraph of $\mathcal{T}$ is $\varphi$-convex near the target. This is the first nonlinear $\varphi$-convexity result valid in any dimension.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1502.04846
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