Consensus Tracking of Perturbed Open Multi-Agent Systems with Repelling Antagonistic Interactions

An open multi-agent system (OMAS) features migrating agents which produce a flexible network that is naturally switching and size-varying. Meanwhile, agent migrations also make an OMAS prone to environmental adversities. In this work, we investigate the consensus tracking problem of OMASs suffering migration-induced adversities, including non-vanishing agent dynamics/state perturbations and repelling antagonistic interactions among agents, over an intermittently disconnected signed digraph. The OMAS is interpreted into a perturbed multi-mode multi-dimensional ($M^3D$) system in which unstable subsystems are created when repelling interactions dominate the cooperative ones in the network regardless of its connectivity. To handle the destabilizing effect brought by repelling interactions and non-vanishing perturbations, we extend the stability theory for $M^3D$ systems and apply it to the OMAS to show that ultimately bounded consensus tracking can be achieved if the network switching satisfies the piecewise average dwell time and activation time ratio conditions. Particularly, for vanishing perturbations, asymptotic tracking can be ensured under weaker switching conditions.