Abstract. We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a network. In our setting, the value function is continuous. We define a notion of constrained viscosity solution of Hamilton-Jacobi equations on the network and we study related comparison principles. Under suitable assumptions, we prove in particular that the value function is the unique constrained viscosity solution of the Hamilton-Jacobi equation on the network. Mathematics Subject Classification (2010). Primary 35R02, 35F21, 35Q93; Secondary 34H05, 49J15.
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Abstract. 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.Résumé. On considère des problèmes de contrôle optimal pour lesquels l'état est contraintà rester sur un réseau. Une notion de solution de viscosité deséquations de Hamilton-Jacobi associées aété proposée dans des travaux antérieurs. Ici, on propose une preuve simple d'un principe de comparaison. Cette preuve est basée sur des arguments de contrôle optimal. La stabilité des solutions de viscosité est aussiétudiée.1991 Mathematics Subject Classification. 34H05, 49J15.The dates will be set by the publisher.
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