My brilliant PhD student David Ohlin recently submitted a paper featuring an optimal control problem formulation with linear costs and network topology-motivated constraints. Interestingly, the problem has an explicit solution, which can be efficiently computed through linear programming.
A wide range of network routing and flow problems fit the formulation, including the shortest path problem as the simplest example. However, we can also capture more complex dynamic versions of such problems, where internal nodal dynamics, dissipation and diffusion across the network affects the optimal solution.
Check out the preprint here: https://arxiv.org/pdf/2311.03019.pdf
It was submitted to ECC 2024 in Stockholm.
Emma Tegling 