Fréchet Analysis and Sensitivity Relations for the Optimal Time Problem

Fréchet Analysis and Sensitivity Relations for the Optimal Time Problem

In this paper, we first present formulas for computing the Fr&#x00E9;chet subdifferentials and Fr&#x00E9;chet singular subdifferentials of the minimal time function <inline-formula> <tex-math notation="LaTeX">$\mathscr {T}$ </tex-math></inline-formula> for a...

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Bibliographic Details
Main Authors: Luong V. Nguyen, Nguyen T. Thu
Format: Article
Language:English
Published: IEEE 2020-01-01
Series:IEEE Access
Subjects:
Differential inclusions
Fréchet subdifferentials
minimum time function
sensitivity relations
Online Access:https://ieeexplore.ieee.org/document/9026975/
Description
Summary:In this paper, we first present formulas for computing the Fr&#x00E9;chet subdifferentials and Fr&#x00E9;chet singular subdifferentials of the minimal time function <inline-formula> <tex-math notation="LaTeX">$\mathscr {T}$ </tex-math></inline-formula> for a differential inclusion in <inline-formula> <tex-math notation="LaTeX">$\mathbb {R}^{n}$ </tex-math></inline-formula> with a general target <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>. These formulas are characterized in terms of Fr&#x00E9;chet normal cones to a sub-level set of <inline-formula> <tex-math notation="LaTeX">$\mathscr {T}$ </tex-math></inline-formula> and a level set of the minimized Hamiltonian associated with the differential inclusion. Our results extend, improve and complement to existing results. An application to sensitivity analysis for a class of time optimal control problems is also given.
ISSN:2169-3536

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