A Unified Analytical Framework for Optimal Control Problems on Networks With Input Homogeneity

We consider optimal control problems on networks with input homogeneity and show a reduction to a universal set of reference problems without differential constraints, whose stationary points may be found analytically. Under suitable nondegeneracy conditions, the derivation shows that input homogeneity results in constant candidate optimal control inputs for the problems of maximizing the terminal response, minimizing the control effort, or minimizing the terminal time, and that these control inputs depend smoothly on the problem data. These predictions are validated using numerical analysis of problems of synchronization of coupled phase oscillators and spreading dynamics on time-varying networks.