Geodesic
Hamilton–Jacobi equations for optimal control on junctions and networks
Achdou, Yves1  ; Oudet, Salomé2  ; Tchou, Nicoletta2 
1 University Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS, 75205 Paris, France
2 IRMAR, Université de Rennes 1, Rennes, France
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 876-899

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corrigé par Erratum to the article Hamilton–Jacobi equations for optimal control on junctions and networks

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.

Reçu le :
DOI : 10.1051/cocv/2014054
Classification : 34H05, 49J15
Keywords: Optimal control, networks, Hamilton–Jacobi equations, viscosity solutions

Achdou, Yves 1 ; Oudet, Salomé 2 ; Tchou, Nicoletta 2

1 University Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS, 75205 Paris, France
2 IRMAR, Université de Rennes 1, Rennes, France 
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     title = {Hamilton{\textendash}Jacobi equations for optimal control on junctions and networks},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {876--899},
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Achdou, Yves; Oudet, Salomé; Tchou, Nicoletta. Hamilton–Jacobi equations for optimal control on junctions and networks. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 876-899. doi: 10.1051/cocv/2014054

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