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A viability approach to Hamilton-Jacobi equations: application to concave highway traffic flux functions

Aubin, Jean-Pierre; Bayen, Alexandre M.; Saint-Pierre, Patrick (2005), A viability approach to Hamilton-Jacobi equations: application to concave highway traffic flux functions, 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. Proceedings, IEEE, p. 3519-3524. http://dx.doi.org/10.1109/CDC.2005.1582707

Type
Communication / Conférence
Date
2005
Conference title
44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05.
Conference date
2005-12
Conference city
Séville
Conference country
Espagne
Book title
44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. Proceedings
Publisher
IEEE
ISBN
0-7803-9567-0
Pages
3519-3524
Publication identifier
http://dx.doi.org/10.1109/CDC.2005.1582707
Metadata
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Author(s)
Aubin, Jean-Pierre
Bayen, Alexandre M.
Saint-Pierre, Patrick
Abstract (EN)
This paper presents a new approach which links the solution to a particular Hamilton-Jacobi partial differential equation to the solution of an optimal control problem provided by viability theory. It constructs the solution to this partial differential equation through its hypograph, which is defined as the capture basin of a target under an auxiliary dynamics that we define. The target itself represents the hypograph of a desired function. It is applied to concave Hamiltonian functions and has implications for the control of conservation laws with concave flux functions. It is a building block towards controlling conservation laws with concave flux functions, though at this stage, the link with boundary control of hyperbolic conservation laws cannot be made explicitly.
Subjects / Keywords
PDE

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