A Fresh Look on Network Synchronization

TL;DR

This paper explores network synchronization from a control theory perspective, revealing the equivalence with multi-agent consensus and proposing a flexible inner coupling matrix for improved synchronization performance.

Contribution

It introduces a novel control-theoretic approach to analyze and design network synchronization, establishing its fundamental equivalence with multi-agent consensus.

Findings

Synchronization region analyzed via inner coupling matrix.

Network synchronization and consensus are essentially equivalent.

Method demonstrated on a three-oscillator network example.

Abstract

This paper gives a fresh look at network synchronization. Here we no longer analyze it from the view of mathematics, such as graph theory, while we probe into one from control theory. First, we analyze the synchronization region using the inner coupling matrix, giving up the routine method of studying the network structure. The motivation comes from the inner coupling matrix that is not subject to any restrictions like network structure, such as distance and communication strength among nodes. It can be configured at will to meet the synchronization performance if only the states of the local dynamic are measurable or observable and the communication topology is connected. Thus, it is very useful for future practical engineering design. In addition, we have an amazing finding that the network synchronization and multi-agent system consensus problems are equivalence essentially. Afterwards a unified viewpoint, that is, the essence of multi-agent consensus control is the same as that of network synchronization, is present. Here, the equivalence relation is clearly proven and proposed. Therefore, we can synthesize the inner coupling matrix for network systems or the controller gain for multi-agent systems for each other. Finally, we also present a kind of method for addressing the nonlinear complex network system. Then the effectiveness of method is verified by taking the network of the three-oscillator universal probe as an example.