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

Abstract

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 non-degeneracy 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.

Schrödinger Meets Kuramoto via Feynman-Kac: Minimum Effort Distribution Steering for Noisy Nonuniform Kuramoto Oscillators

“…An interesting observation follows: (12) becomes the same forward FPK operator as in (10a) only if Υ equals identity. Consequently, the Algorithm COMPUTEFACTORSSBP proposed in [21, Sec.…”

“…Related literature and novelty of this work: While there exists a significant literature on the dynamics and control of Kuramoto oscillators in general [6]- [12], the stochastic control of Kuramoto oscillators remains under-investigated. Ref.…”