Abstract
ABSTRACT 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. <hal-01548133v2>], 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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