Volume 25, 2019
|Number of page(s)||31|
|Published online||18 June 2019|
Hamilton-Jacobi equations for optimal control on networks with entry or exit costs
IRMAR, Université de Rennes 1,
* Corresponding author: email@example.com
Accepted: 8 January 2018
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].
Mathematics Subject Classification: 34H05 / 35F21 / 49L25 / 49J15 / 49L20 / 93C30
Key words: Optimal control / networks / Hamilton-Jacobi equation / viscosity solutions / uniqueness / switching cost
© The authors. Published by EDP Sciences, SMAI 2019
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