Dynamic min and max consensus and size estimation of anonymous multi-agent networks

In this paper we propose two distributed control protocols for discrete-time multi-agent systems (MAS), which solve the dynamic consensus problem on the max value. In this problem each agent is fed an exogenous reference signal and has the objective to estimate and track the instantaneous and time-varying value of the maximum among all the signals fed to the network by exploiting only local and anonymous interactions among the agents. The first protocol achieves bounded steady-state and tracking errors which can be traded-off for convergence time. The second protocol achieves zero steady-state error and requires knowledge of an upper bound to the diameter of the graph representing the network. Modified versions of both protocols are provided to solve the dual dynamic minconsensus problem. These protocols are then exploited to solve a distributed size estimation problem in a network of anonymous agents in a dynamic setting where the size of the network is time-varying during the execution of the estimation algorithm. Numerical simulations are provided in order to corroborate the characterization of the proposed protocols.