Modal Consensus of Single Integrators with Minimal 'Disagreement Interaction' via Distributed Endogenous Internal Model

In this letter, the problem of modal consensus of a network of agents is considered. We introduce the notion of 'disagreement interaction' and we propose a distributed control design strategy that minimizes such potentially detrimental interaction between the agents. The above concepts are then specialized to a multi-agent system consisting of single integrators. The proposed solution does not introduce additional dynamics to the system anywhere in the network. It is shown that the minimization of the disagreement interaction results in the feature that the agents exchange the information strictly necessary to induce an endogenous internal model, while limiting any other interaction, which is not instrumental for reaching consensus and which may possibly induce instability of the interconnected network even in the presence of individually asymptotically stable agents.