New differentiated consensus problem with topology cost constraints

A new differentiated consensus problem is studied. The problem is, given a system with multiple classes, consensus is targeted for each class and the consensus values can be different among the classes. Specifically, differentiated consensus is studied in a distributed stochastic network of nodes (or agents), where tasks assigned with different priorities are serviced. The network is assumed to have a switching topology and involves noises, delays in measurements, and topology cost constraints. The goal is to reach a balanced load (i.e., consensus) across the network and, at the same time, to satisfy the topology cost constraint, both for each priority class. A new control protocol is proposed, with which the network resources are allocated in a randomized way with a probability assigned to each priority class. It is shown that the control protocol meets the topology cost constraint and can be used to reach an approximate consensus for each of the priority classes in the network.