Optimal mean‐square consensus for heterogeneous multi‐agent system with probabilistic time delay

This paper studies the mean‐square consensus for heterogeneous multi‐agent systems with probabilistic time delay. Each agent in the system has an objective function and only knows its own objective function. Control protocols for the system both over the fixed and the switched weighted‐balanced topologies are designed. The consensus state of agents' position can make the sum of objective functions minimum. By adopting probability statistics, stochastic process, matrix theory and some stability method, sufficient conditions for the consensus protocol are given. Several simulations are presented to illustrate the potential correctness of the results.