Distributed Tracking of Network Size, Diameter, Radius, and Node Eccentricities in Open Multi-Agent Systems

We present a distributed algorithm enabling the dynamic tracking of diameter and radius (DR) of time-varying open networks (ON) together with nodes' eccentricities and network size (ES), called DR−ON−ES, which does not require the disclosure of nodes' identity nor any a priori information on the network. The convergence properties of DR−ON−ES are discussed within the framework of open multi-agent systems (OMASs): sufficient conditions are provided to ensure that the TPI of an OMAS executing DR−ON−ES is globally asymptotically open stable, meaning that all trajectories converge to within a neighborhood of the sought parameters. The parameters' estimations at equilibrium points are characterized in terms of mean expected value and mean squared error. As an ancillary result, we remark that DR−ON−ES exploits the OSTDMC Protocol – a novel distributed protocol formalized and analyzed in this manuscript – to achieve consensus on the time-varying maximum value of a set of signals fed locally to the agents of the network.