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.