Synchronized Stop and Re-Start in Distributed Average Consensus for Control and Coordination Applications

In this work we develop and analyze a distributed iterative algorithm that enables the components of a distributed system, each with some initial value, to reach approximate average consensus on their initial values, after executing a finite number of iterations. The proposed algorithm has features that facilitate its use in control/coordination applications where timing constraints might prohibit the implementation of the asymptotic techniques that are used in most distributed average consensus protocols. More specifically, the proposed algorithm allows all the nodes to (i) simultaneously stop the average consensus process once the network has reached consensus, and (ii) restart the process again at any later time, presumably with different initial values. To provide this capability, the proposed algorithm uses a criterion that enables all the nodes to determine, in a distributed manner, when to terminate the operation because approximate average consensus has been reached, i.e., all nodes have obtained a value that is within a small distance from the average of their initial values. This criterion enables all the nodes in the system to terminate their operation (together, at the same time-step) after they have reached approximate consensus. Using another distributed protocol, the system can also restart the distributed calculation of a new average value at any later time, as long as any node initiates such a request.