  Considering some predictive mechanisms, we show that ultrafast
average-consensus can be achieved in networks of interconnected agents. More
specifically, by predicting the dynamics of the network several steps ahead and
using this information in the design of the consensus protocol of each agent,
drastic improvements can be achieved in terms of the speed of consensus
convergence, without changing the topology of the network. Moreover, using
these predictive mechanisms, the range of sampling periods leading to consensus
convergence is greatly expanded compared with the routine consensus protocol.
This study provides a mathematical basis for the idea that some predictive
mechanisms exist in widely-spread biological swarms, flocks, and networks. From
the industrial engineering point of view, inclusion of an efficient predictive
mechanism allows for a significant increase in the speed of consensus
convergence and also a reduction of the communication energy required to
achieve a predefined consensus performance.
