Communication constraints in coordinated consensus problems

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, communications constraints impose limits on the achievable control performance. Starting from an emerging problem, studied in the robotics and control communities, called consensus or state agreement problem, we characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the agreement. In particular we show that communication networks that exhibit particular symmetries yield slow convergence, if the amount of information exchanged does not scale with the number of agents. On the other hand, if we allow exchange of logarithmic quantized data, the control performance significantly improves with little growth of the required communication effort.