Consensus dynamics, also known as agreement dynamics, is an area of research at the intersection of

systems theory Systems theory is the Transdisciplinarity, transdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or artificial. Every system has causal boundaries, is influenced by its context, de ...

and

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

. It studies how a group of agents—such as robots, sensors, or decision-makers—interacting over a network can reach a common decision or estimate through local rules and information exchange. This is known as the consensus problem in multi-agent systems, where the goal is to ensure that all agents eventually agree on a certain quantity, despite starting with potentially different initial values. Consensus dynamics has applications in areas such as physiological systems,

gene regulatory network A gene (or genetic) regulatory network (GRN) is a collection of molecular regulators that interact with each other and with other substances in the cell to govern the gene expression levels of mRNA and proteins which, in turn, determine the fu ...

s, large-scale energy systems, and coordinated control of autonomous vehicle fleets on land, in the air, or in space. The behavior of these systems is typically modeled using an unforced

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

governed by the network's interconnection topology and the agents' initial conditions. The consensus protocol, or agreement protocol, defines the rules of interaction that lead to convergence. Related coordination problems include the

rendezvous problem Rendezvous or rendez-vous may refer to: Arts and entertainment Film and television * The Rendezvous (1923 film), ''The Rendezvous'' (1923 film), a silent film adventure melodrama * Rendezvous (1930 film), ''Rendezvous'' (1930 film), a Ger ...

synchronization Synchronization is the coordination of events to operate a system in unison. For example, the Conductor (music), conductor of an orchestra keeps the orchestra synchronized or ''in time''. Systems that operate with all parts in synchrony are sa ...

, flocking, and formation control. These often rely on similar mathematical foundations and are studied under the broader umbrella of cooperative control. One computational approach to solving these problems is distributed constraint reasoning. Consensus models are also used in social and philosophical domains to analyze how groups reach agreement through debate or deliberation. For example, simulations can evaluate whether introducing a new argument shifts the outcome of a debate by providing an additional truth value.

References

* Ghapani, S.; Mei, J.; Ren, W.; Song, Y. (2016), "Fully distributed flocking with a moving leader for lagrange networks with parametric uncertainties", ''Automatica'', 67–76, doi:10.1016/j.automatica.2016.01.004 * {{DEFAULTSORT:Consensus Dynamics Multi-agent systems Network theory Control theory Graph theory Game theory Distributed computing Constraint programming

See also

References