CCS2021 Satellite Symposium

Data-based Diagnosis of Networked Dynamical Systems

Coherence and Concentration in Tightly Connected Networks

Achieving coordinated behavior - engineered or emergent - on networked systems has attracted widespread interest in several fields.
This interest has led to remarkable advances in developing a theoretical understanding of the conditions under which agents within a network can reach an agreement (consensus) or develop coordinated behavior, such as synchronization.
However, much less understood is the phenomenon of network coherence.
Network coherence generally refers to nodesâ€™ ability in a network to have a similar dynamic response despite heterogeneity in their behavior.
In this talk, we present a general framework to analyze and quantify the level of network coherence that a system exhibits by relating coherence with a low-rank property.
More precisely, for a networked system with linear dynamics and coupling, we show that the system transfer matrix converges to a rank-one transfer matrix representing the coherent behavior as the network connectivity grows.
Interestingly, the non-zero eigenvalue of such a rank-one matrix is given by the harmonic mean of individual nodal dynamics, and we refer to it as the coherent dynamics.
Our analysis unveils the frequency-dependent nature of coherence and a non-trivial interplay between dynamics and network topology.
We further illustrate how this framework can be leveraged for obtaining accurate reduced-order models of coherent generators and tuning grid forming inverters to shape the (coherent) frequency response in power grids.

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