Hamilton-Jacobi equations for optimal control on junctions and networks. (English) Zbl 1318.49049
ESAIM, Control Optim. Calc. Var. 21, No. 3, 876-899 (2015); erratum ibid. 22, No. 2, 539-542 (2016).
Summary: 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.
MSC:
| 49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
| 49J15 | Existence theories for optimal control problems involving ordinary differential equations |
| 34H05 | Control problems involving ordinary differential equations |
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