This article has an erratum: [erratum]
Volume 21, Number 3, July-September 2015
|Page(s)||876 - 899|
|Published online||20 May 2015|
University Paris Diderot, Sorbonne Paris Cité, Laboratoire
Jacques-Louis Lions, UMR 7598, UPMC, CNRS, 75205
2 IRMAR, Université de Rennes 1, Rennes, France
3 IRMAR, Université de Rennes 1, Rennes, France
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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