Consensus control of multi-agent system with constraint - the scalar case

This paper describes a new distributed algorithm for the consensus control of a group of agents connected via a communication network where the states of the agents lie within individually-defined constraints. It considers the case where the state of each agent is a scalar in an undirected network with no communication delays and uses the edge weights as the working variables to enforce satisfaction of the constraints. The convergence and consensus of the states under reasonably mild assumptions are provided. The proposed algorithm has the advantage that it preserves many of the desirable properties of the standard unconstrained consensus algorithm: the consensus value is independent of the sequence of network changes; the average of the states remains a constant for all time steps; and the states of the agents, when all constraints are identical, follow the same trajectories as the standard consensus algorithm. Several examples are provided to illustrate the results.