Discontinuous solutions of Hamilton–Jacobi equations on networks

P. J. Graber; C. Hermosilla; H. Zidani

doi:10.1016/j.jde.2017.08.040

Discontinuous solutions of Hamilton–Jacobi equations on networks

P. J. Graber
, C. Hermosilla
, H. Zidani

École Polytechnique

Baylor University
Universidad Técnica Federico Santa María

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

This paper studies optimal control problems on networks without controllability assumptions at the junctions. The Value Function associated with the control problem is characterized as the solution to a system of Hamilton–Jacobi equations with appropriate junction conditions. The novel feature of the result lies in that the controllability conditions are not needed and the characterization remains valid even when the Value Function is not continuous.

Original language	English
Pages (from-to)	8418-8466
Number of pages	49
Journal	Journal of Differential Equations
Volume	263
Issue number	12
DOIs	https://doi.org/10.1016/j.jde.2017.08.040
Publication status	Published - 15 Dec 2017

Keywords

Control problem on networks
Hamilton–Jacobi equations
State constraint problems
Stratified structure

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10.1016/j.jde.2017.08.040

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title = "Discontinuous solutions of Hamilton{\textendash}Jacobi equations on networks",

abstract = "This paper studies optimal control problems on networks without controllability assumptions at the junctions. The Value Function associated with the control problem is characterized as the solution to a system of Hamilton{\textendash}Jacobi equations with appropriate junction conditions. The novel feature of the result lies in that the controllability conditions are not needed and the characterization remains valid even when the Value Function is not continuous.",

keywords = "Control problem on networks, Hamilton{\textendash}Jacobi equations, State constraint problems, Stratified structure",

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AU - Graber, P. J.

AU - Hermosilla, C.

AU - Zidani, H.

PY - 2017/12/15

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N2 - This paper studies optimal control problems on networks without controllability assumptions at the junctions. The Value Function associated with the control problem is characterized as the solution to a system of Hamilton–Jacobi equations with appropriate junction conditions. The novel feature of the result lies in that the controllability conditions are not needed and the characterization remains valid even when the Value Function is not continuous.

AB - This paper studies optimal control problems on networks without controllability assumptions at the junctions. The Value Function associated with the control problem is characterized as the solution to a system of Hamilton–Jacobi equations with appropriate junction conditions. The novel feature of the result lies in that the controllability conditions are not needed and the characterization remains valid even when the Value Function is not continuous.

KW - Control problem on networks

KW - Hamilton–Jacobi equations

KW - State constraint problems

KW - Stratified structure

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VL - 263

SP - 8418

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

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ER -

Discontinuous solutions of Hamilton–Jacobi equations on networks

Abstract

Keywords

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