Journal
APPLICABLE ANALYSIS
Volume 100, Issue 7, Pages 1397-1413Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00036811.2019.1643012
Keywords
D; N; Hao; Hamilton-Jacobi equations; viscosity solutions; optimal control; junctions
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This paper focuses on optimal control problems on junctions using the viscosity solution approach. Compared to previous studies, the paper works on a less restrictive set of assumptions and shows that the value function is a unique viscosity solution of an associated Hamilton-Jacobi equation. The viscosity solution method is used to establish a necessary and sufficient condition for optimal control in a class of optimal control problems.
This paper focuses on the viscosity solution approach to optimal control problems on junctions. Compared to Achdou et al. [Hamilton-Jacobi equations for optimal control on junctions and networks: ESAIM Control Optim. ESAIM Control Optim Calc Var. 2015;21(3):876-899] and Khang [Hamilton-Jacobi equations for optimal control on networks with entry or exit costs. ESAIM Control Optim Calc Var. 2018. (In press). EDP Sciences. ], we work on a less restrictive set of assumptions. We show that the value function is a unique viscosity solution of an associated Hamilton-Jacobi equation, and present some further properties of it. In addition, the viscosity solution method is used to establish a necessary and sufficient condition for an optimal control in a class of optimal control problems.
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