Cluster-Delay Consensus for the Second-Order Nonlinear Multi-Agent Systems with Random Noises

Cluster-delay consensus in a noisy environment has been investigated for the second-order nonlinear multi-agent systems, which consist of a leader and several followers. A novel protocol with white noise is proposed for the followers of different groups tracking their leader gradually with distinct time delays, i.e., followers are divided into several groups according to the time-delays with the leader and each group approaches its own equilibrium state almost surely and exponentially. Based on the Lyapunov’s method for stability, matrix theory and stochastic differential equations, sufficient conditions are derived to achieve the cluster-delay consensus. Finally, simulation experiments are conducted to illustrate and validate our control algorithm.