| Issue |
ESAIM: COCV
Volume 21, Number 3, July-September 2015
|
|
|---|---|---|
| Page(s) | 876 - 899 | |
| DOI | https://doi.org/10.1051/cocv/2014054 | |
| Published online | 20 May 2015 | |
Hamilton–Jacobi equations for optimal control on junctions and networks∗,∗∗
1
University Paris Diderot, Sorbonne Paris Cité, Laboratoire
Jacques-Louis Lions, UMR 7598, UPMC, CNRS, 75205
Paris,
France
achdou@ljll.univ-paris-diderot.fr
2
IRMAR, Université de Rennes 1, Rennes, France
3
IRMAR, Université de Rennes 1, Rennes, France
nicoletta.tchou@univ-rennes1.fr
Received:
13
February
2014
Revised:
26
September
2014
We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a network. A notion of viscosity solution of Hamilton–Jacobi equations on the network has been proposed in earlier articles. Here, we propose a simple proof of a comparison principle based on arguments from the theory of optimal control. We also discuss stability of viscosity solutions.
Mathematics Subject Classification: 34H05 / 49J15
Key words: Optimal control / networks / Hamilton–Jacobi equations / viscosity solutions
© EDP Sciences, SMAI, 2015
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