Trajectories of the ε-perturbed optimal control problem in R² converge subsequentially to the network Γ, and in the Eikonal case the value functions converge to the value function of the corresponding network optimal control problem.
Hamilton-Jacobi equations on networks as limits of singularly perturbed problems in optimal control: dimension reduction
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Approximation of an optimal control problem on a network with a perturbed problem in the whole space
Trajectories of the ε-perturbed optimal control problem in R² converge subsequentially to the network Γ, and in the Eikonal case the value functions converge to the value function of the corresponding network optimal control problem.