A consensus algorithm of third-order multi-agent systems with time delay in undirected networks based on partial neighbour information

For third-order multi-agent system with time delay based on fixed undirected networks, a theoretical condition is given first that ensures the system to asymptotically converge. Then, to simplify the communication complexity of the multi-agent consensus, a simple yet efficient algorithm is proposed termed the nearest neighbour principle (NNP). NNP leverages partial second-order and third-order neighbour information to largely reduce communication costs and thus contributing to the acceleration of convergence speed. Compared with classical third-order consensus algorithms, the simulation results show that NNP can not only urge the system to achieve consensus but also reduce its convergence time and communication cost.