Synchronization in multi-agent systems with switching topologies and non-homogeneous communication delays

We study the synchronization problem for n single state agents with linear continuous time dynamics. The agent states are required to synchronize and travel at a desired common speed. This problem arises naturally in the design of coordinated path-following algorithms problem [9] and in studies on the synchronization of Kuramoto oscillator networks [17]. When the desired speed is zero or there are no time delays, it has been shown in the literature that a so-called neighboring control rule makes the states synchronize asymptotically under some connectivity conditions on the union of the underlying communication graphs. We will show that when both the desired speed and the communication delay are non-zero, the behavior of the synchronization system changes significantly. We start by considering asymmetric networks and switching topologies with homogeneous time delays. We then address some issues related to the behavior of the synchronization system in the presence of heterogeneous time delays. We provide connectivity conditions under which the synchronization problem is solved and introduce synchronization laws that compensates for the effect of non-zero speed and time delays. Simulations illustrate the synchronization of three agents.