Synchronization is an essential property of engineered and natural networked dynamical systems. The Kuramoto model of nonlinear synchronization has been widely studied in applications including entrainment of clock cells in brain networks and power system stability. Synchronization of Kuramoto networks has been found to be challenging in the presence of signed couplings between oscillators and when the network includes oscillators with heterogeneous natural frequencies. In this paper, we study the problem of minimum-set control input selection for synchronizing signed Kuramoto networks. We first derive sufficient conditions for synchronization in homogeneous as well as heterogeneous Kuramoto networks using a passivity-based framework. We then develop a submodular algorithm for selecting a minimum set of control inputs for a given Kuramoto network. We evaluate our approach through a numerical study on multiple classes of graphs, including undirected, directed, and cycle graphs.
This paper presents a distributed synchronization strategy for connected and automated vehicles in traffic networks. The strategy considers vehicles traveling from one intersection to the next as waves. The phase angle and frequency of each wave map to its position and velocity, respectively. The goal is to synchronize traffic such that intersecting traffic waves are out of phase at every intersection. This ensures the safe collective navigation of intersections. Vehicles share their phase angles through the V2X infrastructure, and synchronize these angles using the Kuramoto equation. This is …
The high-dimensional generalization of the one-dimensional Kuramoto paradigm has been an essential step in bringing about a more faithful depiction of the dynamics of real-world systems. Despite the multi-dimensional nature of the oscillators in these generalized models, the interacting schemes so far have been dominated by a scalar factor unanimously between any pair of oscillators that leads eventually to synchronization on all dimensions. As a natural extension of the scalar coupling befitting for the one-dimensional case, we take a tentative step in studying numerically and theoretically t…
