Min–max consensus of multi-agent systems in random networks

Abstract

This paper focuses on the study of the min–max consensus problem for multi-agent systems in random networks. A min–max consensus algorithm is proposed, which incorporates the weighted average of the agent’s state, the maximum value of its neighbors’ states, and the minimum value of its neighbors’ states. The interaction network is composed of a directed random network where edges exist with probability and are independent of each other. Then, the convergence of the min–max consensus algorithm is investigated utilizing max-plus algebra, min-plus algebra, and stochastic analysis theory. Sufficient and necessary conditions are given to ensure that the multi-agent systems achieve min–max consensus almost surely and in mean-square, respectively. Finally, some numerical simulations are conducted to confirm the effectiveness of the proposed consensus algorithm.