Delay-dependent rendezvous and flocking of large scale multi-agent systems with communication delays

We study the stability of multi-agent system (MAS) formations with delayed exchange of information between the agents. The agents are described by second order systems. They communicate via a symmetric connected communication topology with constant, heterogeneous, symmetric delays between any two neighboring agents. We consider two different tasks for the MAS: rendezvous, where all agents meet at an arbitrary point, and flocking, where all agents reach a given formation and move in a predefined direction. Therefore, we propose a decentralized control algorithm with position coupling gains k_ji. We prove that the MAS achieves rendezvous for any constant delay if the communication topology is connected and the coupling gain is sufficiently small. For larger gains, rendezvous and flocking are delay-dependent, i.e., they are reached for any delay smaller than a bound which depends on k_ji. Thereby, the controllers can be tuned in a totally decentralized fashion, i.e., only based on the communication delays to their neighbors and not considering the delays in the rest of the network. For the analysis, we use both frequency and time domain methods to prove delay-independent and delay-dependent rendezvous and flocking, respectively.