Consensus tracking of perturbed open multi-agent systems with repelling antagonistic interactions

Abstract: An open multi-agent system (OMAS) comprises migrating agents which produce a flexible network structure that is naturally switching and size-varying. Meanwhile, agent migrations also make an OMAS more prone to environmental adversities. In this work, we deal with the consensus tracking problem of OMASs suffering these migration-induced adversities, including non-vanishing perturbations in the agent dynamics/state and the repelling antagonistic interactions among agents, over an intermittently disconnected signed digraph. The OMAS is interpreted into a perturbed $M<sup>3D$ system in which unstable subsystems are created when repelling interactions dominate the normal cooperative ones in the OMAS network regardless of its connectivity. To handle the destabilizing effects brought by the repelling interaction as well as the non-vanishing perturbations, we extend the stability theory for $M<sup>3D$ systems and apply it to the OMAS to show that practical consensus tracking can be achieved if the migration-induced switching satisfies the piecewise average dwell time and activation time ratio constraints. Particularly, we indicate that for vanishing perturbations and repelling interactions, asymptotic tracking can be expected under weaker switching constraints.