Distributed Consensus in Networks

Abstract

Consensus is a fundamental problem and plays an important role in many practical networked systems. This article gives a brief overview on distributed consensus in networks. The main focus is to present the most basic and fundamental results of consensus. Specifically, various definitions on consensus are introduced, such as average consensus, leader‐following consensus, and dynamic average consensus. Three main techniques for convergence analysis of consensus based on decoupling, infinite matrix products, and Lyapunov function are elaborated. Some design issues related to consensus are also discussed. Advanced topics on consensus, such as complicated agent dynamics, communication delays, quantization, event‐triggered mechanism, finite‐time convergence, and state constraints, are presented. The relation between consensus and other cooperative control problems is also established. Finally, future research directions are discussed.

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“…While there are many challenges in the process of research due to the diversity of complex networks, one most challenging issue in modern science and engineering networks is the control of complex networks [6], [7]. The traditional control theory is encountered more and more large-scale complex networks [8]- [12], where nodes are higher-dimensional dynamical systems and edges represent the interactions among them. For example, in the paper citation network, nodes and edges represent papers and reference relationships between papers [6].…”

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“…One theme in cooperative control is to assemble and coordinate individual physical devices into a coherent whole to perform a common task [1][2][3][4]. In particular, in the control community, containment control has become one interesting research direction because cooperative control usually poses geometrical constraints during agents' movements.…”

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“…where W ( ψ, φ) is a K function, and d 5 = δd 4 2 sup{ φ 2 }. Thus, from Theorem 4.18 in [123], the conclusion is obtained.…”

“…Therefore, from Theorem 11.4 in [123] and noticing that the closed loop system is linear, we can conclude that there exists a positive constant δ * such that for every 0 < δ < δ * , x converges to x * exponentially.…”

“…where K = diag{k i }. The system given by (3.10) attains a singular perturbed form given in Chapter 11 in [123]. The small parameter δ separates the dynamics into By analyzing the properties of the separated models, the properties of the whole system can be obtained.…”