Consensus in Multi‐Agent Systems

Abstract

Many cooperative behaviors of multi‐agent teams emerge from local interactions among the agents, where an agent interacts with a few “adjacent” teammates, but has no information about the remaining agents. For instance, the self‐organization of many biological populations –including swarms of insects, flocks of birds, and schools of fish –are based on such local interaction rules: the motion and decisions of an individual agent are determined by the behavior of its nearest neighbors in the population. A special case of multi‐agent coordination is consensus , that is, the agreement of agents on some quantity of interest or, more generally, the full or partial synchronization of their state trajectories. Establishing consensus is a “benchmark” problem in multi‐agent systems study, which allows to reveal the main principles of multi‐agent coordination and, in particular, the role of the system's interaction graph (or topology). Consensus lies in the heart of many natural phenomena (e.g., synchronous oscillation of neural cells, which maintains a stable heart rhythm) and engineering designs (e.g., attitude synchronization of satellites). In this article, we give a brief review of distributed consensus algorithms, focusing on the basic ideas and relevant mathematical theory, in particular, graph‐theoretic methods.

A tutorial on modeling and analysis of dynamic social networks. Part I

“…Many results, regarding consensus algorithms over time-varying graphs, have been obtained in [56,100,101,[103][104][105][106][107][108] and extended to general dynamic agents [56,57,[109][110][111]. More advanced results on nonlinear consensus algorithms [105,112,113] allow to examine the nonlinear Abelson model ( 11) under different assumptions on the coupling function g(•).…”

Differential inequalities in multi-agent coordination and opinion dynamics modeling

“…Distributed algorithms for multi-agent coordination have various applications to science and engineering, including control of robotic formations, scheduling of sensor networks, optimization and filtering, modeling biological and social systems. The relevant results are discussed in the works (Ren and Beard, 2008;Mesbahi and Egerstedt, 2010;Ren and Cao, 2011;Savkin et al, 2015;Proskurnikov and Cao, 2016a;Bullo, 2016;Proskurnikov and Tempo, 2017) and references therein. A "benchmark" problem in multi-agent control is to establish consensus (that is, agreement on some quantity of interest) among the agents interacting over a gen-eral graph.…”

A Review of Consensus-based Multi-agent UAV Implementations

“…In this section, we will briefly recap the most significant results regarding consensus theory. Some relevant surveys for a more comprehensive analysis can be found in the literature [2,5,6].…”