Communication constraints in the state agreement problem

The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems. Particular examples are systems comprised of multiple agents. When it comes to coordinately control a group of autonomous mobile agents in order to achieve a common task, communication constraints impose limits on the achievable control performance. In this paper we consider a widely studied problem in the robotics and control communities, called consensus or state agreement problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the agreement. Time-invariant communication networks that exhibit particular symmetries are shown to yield slow convergence if the amount of information exchanged does not scale with the number of agents. On the other hand, we show that, randomly time-varying communication networks allow very fast convergence rates. The last part of the paper is devoted to the study of time-invariant communication networks with logarithmic quantized data exchange among the agents. It is shown that, by adding quantized data links to the network, the control performance significantly improves with little growth of the required communication effort.