Consensus Acceleration in a Class of Predictive Networks

A fastest consensus problem of topology fixed networks has been formulated as an optimal linear iteration problem and efficiently solved in the literature. Considering a kind of predictive mechanism, we show that the consensus evolution can be further accelerated while physically maintaining the network topology. The underlying mechanism is that an effective prediction is able to induce a network with a virtually denser topology. With this topology, an even faster consensus is expected to occur. The result is motivated by the predictive mechanism widely existing in natural systems.