Bridge Consensus: Ignoring Initial Inessentials

Abstract: In this paper, the problem of bridge consensus is presented and solved. Bridge consensus consists of a network of nodes, some of whom are participating and others are non-participating. The objective is for all the agents to reach average consensus of the participating nodes initial values in a distributed and scalable manner. To do this, the nodes must use the network connections of the non-participating nodes, which act as bridges for information and ignore the initial values of the non-participating nodes. The solution to this problem is made by merging the ideas from estimation theory and consensus theory. By considering the participating nodes has having equal information and the non-participating nodes as having no information, the nodes initial values are transformed into information space. Two consensus filters are run in parallel on the information state and information matrix. Conditions ensuring that the product of the inverse information matrix and the information state of each agent reaches average consensus of the participating agents' initial values is given.