Convergence and stability in consensus and coordination problems (a survey of basic results)

This paper is a survey of the basic results on coordination and consensus seeking in multiagent systems and on the stability of the corresponding algorithms. The first part of the paper is devoted to the consensus problem in the discrete time. The second part deals with more general problems of coordination in which every agent is characterized by 2d parameters in the Euclidean space of dimension d. These parameters are the coordinates and velocity components of the agents. We discuss procedures of determining the trajectories converging to a given course and obeying a prescribed geometric configuration of the agents (the agents are moving in formation). The dynamically adjusted speed of each agent is a function of the current parameters of this agent and its "neighbors." The information links between agents are determined by a communication digraph. To stabilize the system, linear feedback is used. The stability of motion is studied in terms that characterize the connectivity of the communication digraph.