On the effects of communication failures in a multi-agent consensus network

This paper investigates the effects of either an edge or a node disconnection on a multi-agent consensus network, consisting of N agents that are modeled as simple scalar and discrete-time integrators. The communication among the agents is described by a weighted undirected graph. The first part of the paper addresses the case of an edge disconnection and summarizes the main results obtained in [29]. In particular, we show that if an edge disconnection does not affect the connectedness of the whole network, it does not even affect the final consensus value. Discernibility of the faulty network from the original one is investigated both in case the states of all the agents are available and in case only the states of a subset of the agents are available. Several equivalent conditions are derived and it is proved that the necessary and sufficient conditions for discernibility and for discernibility from the observation of a subset of agents are exactly the same and can be checked on the original state matrix and on its eigenvectors. The second part of the paper provides some original results about the effects of a node disconnection. In general, even when the connectedness of the remaining communication graph (namely the graph describing the interactions of the remainingN- 1 agents) is preserved, the network converges to a different consensus value. Also in this case, discernibility of the faulty network from the original one is investigated both in case the states of all the agents are available and in case only the states of a subset of the agents are available. Several equivalent conditions are provided to characterize both properties. Finally, a procedure to restore the original consensus value, after a node disconnection, is provided.

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