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Consensus conditions of multi-agent systems with unbalanced topology and stochastic disturbances. (Chinese. English summary) Zbl 1212.90072
Summary: Consensus conditions of multi-agent systems with general directed communication topology and Gaussian communication noises are investigated. Here, the topology includes not only balanced graphs but also unbalanced graphs, and the latter is the main concern of this paper. By using results for Markov chains, a communication class of network nodes is given. By considering the influence of the noises, the consensus conditions are provided: (1) for the case where the information received by some agents in the communication class is corrupted by noises, a sufficient and necessary condition for a mean square consensus is given. It is shown that this condition can also ensure an almost sure consensus. (2) For the case where no information received by the agents in the communication class is corrupted, but the information received by some agents outside of the communication class is corrupted, a sufficient condition for a mean square consensus is obtained, which is shown to be necessary in some sense. (3) For the case without noise, a sufficient and necessary condition for a consensus is presented.

MSC:
90B18 Communication networks in operations research
68M10 Network design and communication in computer systems
68M14 Distributed systems
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