Abstract
We consider an optimal control on networks in the spirit of the works of Achdou et al. [NoDEA Nonlinear Differ. Equ. Appl. 20 (2013) 413–445] and Imbert et al. [ESAIM: COCV 19 (2013) 129–166]. The main new feature is that there are entry (or exit) costs at the edges of the network leading to a possible discontinuous value function. We characterize the value function as the unique viscosity solution of a new Hamilton-Jacobi system. The uniqueness is a consequence of a comparison principle for which we give two different proofs, one with arguments from the theory of optimal control inspired by Achdou et al. [ESAIM: COCV 21 (2015) 876–899] and one based on partial differential equations techniques inspired by a recent work of Lions and Souganidis [Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 27 (2016) 535–545].
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
Reference24 articles.
1. Hamilton-Jacobi equations on networks
2. Hamilton–Jacobi equations constrained on networks
3. Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations: a guided visit
4. Barles G., An introduction to the theory of viscosity solutions for first-order Hamilton-Jacobi equations and applications, in Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications. Vol. 2074 of
Lecture Notes in Mathematics.
Springer,
Heidelberg
(2013) 49–109.
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