Probabilistic consensus in Markovian multi-agent networks

This paper addresses the probabilistic consensus problem in a network of Markovian agents. The dynamics of each agent ismodeled as a finite-state Markov chain, with transition rates that are affected by the communication with the neighbors, so inducing an emulation effect. Consensus is reached when all the agent probability vectors converge to a common steady-state probability vector. The main result of the paper is the proof of consensus for communication networks described by either a complete graph or a star-topology graph. These results are also important in a network control perspective, as some parameters of the network model could be used as tuning knobs to steer the steady-state consensus wherever desired.