A Consensus Protocol over Noisy Two‐Layered Networks with Cooperative and Antagonistic Interactions

This study is concerned with the consensus problems of multi‐agent systems with cooperative and antagonistic noisy interactions described by two‐layered network. That is, each agent is simultaneously influenced by the force of attraction and repulsion between each neighboring agents in cooperative and antagonistic layers. A distributed algorithm for achieving the consensus in a probabilistic sense is proposed and its sufficient conditions are clarified. The conditions tell us rigorous stopping rules which enable us to know the number of iterations that achieves consensus within a prespecified accuracy and probability. Some applications of consensus problems with cooperative and antagonistic interactions are shown through numerical examples.