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Hamilton–Jacobi equations for optimal control on junctions and networks

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 consid ere desprobì emes de contrôle optimal pour lesquels l'´ etat est contraint a rester sur un réseau. Une notion de solution de viscosité des equations de Hamilton-Jacobi associées a ´ eté 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 aussí etudiée .
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Yves Achdou, Salomé Oudet, Nicoletta Tchou. Hamilton–Jacobi equations for optimal control on junctions and networks. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2015, 21 (3), pp.876-899. ⟨10.1051/cocv/2014054⟩. ⟨hal-00847210v4⟩

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