Hamilton–Jacobi equations for optimal control on multidimensional junctions with entry costs
Manh-Khang Dao, Boualem Djehiche · Nonlinear Differential Equations and Applications NoDEA · 2020
Abstract We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton–Jacobi equations (HJ), prove the comparison principle and that the value function of the optimal control problem is the unique viscosity solution of the HJ system. This is done under the usual strong controllability assumption and also under a weaker condition, coined ‘moderate controllability assumption’.