Synchronization of multi-agent systems with delayed control input information from neighbors

In this paper, we consider the synchronization of continuous multi-agent systems with integrator node dynamics. We comparatively study two control protocols, a standard local voting protocol, and a protocol that includes information about the control inputs of neighbors. It is shown that using control input information from neighbors improves performance in two aspects. First, the performance is improved with respect to a certain quadratic performance index defined herein and second, speed of convergence can be selected arbitrarily, independently of the graph topology. Realistically, control input information from neighbors can only be received after a time delay. It is therefore shown that the second protocol using time-delayed control input information from neighbors guarantees the synchronization of the multi-agent system for any nonnegative delay. Furthermore, it is shown that the convergence rate using time-delayed control inputs can still be selected with considerable freedom, and remains superior to the performance of the standard local voting protocol which depends on the graph topology. Some numerical examples and experiments are given to demonstrate the effectiveness of the new protocols.