Hamilton-Jacobi equations for optimal control on junctions and networks

Yves Achdou (1) , Salomé Oudet (2) , Nicoletta Tchou (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Optimal control; networks; Hamilton-Jacobi equations; viscosity solutions

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Yves Achdou, Salomé Oudet, Nicoletta Tchou. Hamilton-Jacobi equations for optimal control on junctions and networks. ESAIM: Control, Optimisation and Calculus of Variations, 2015, 21 (3), pp.876-899. ⟨10.1051/cocv/2014054⟩. ⟨hal-00847210v3⟩