Browsing by Subject "Consensus problems"

Now showing 1 - 3 of 3

Open Access
A delayed consensus algorithm in networks of anticipatory agents
(IEEE, 2016) Atay, Fatihcan M.; Irofti, D.
We introduce and analyze a delayed consensus algorithm as a model for interacting agents using anticipation of their neighbors' states to improve convergence to consensus. We derive a necessary and sufficient condition for the system to reach consensus. Furthermore, we explicitly calculate the dominant characteristic root of the consensus problem as a measure of the speed of convergence. The results show that the anticipatory algorithm can improve the speed of consensus, especially in networks with poor connectivity. Hence, anticipation can improve performance in networks if the delay parameter is chosen judiciously, otherwise the system might diverge as agents try to anticipate too aggressively into the future.
Open Access
Effect of time delays on the convergence speed of consensus dynamics
(2020-01) Alhassan, Mohammed Kamil
We discuss consensus problems under time delays. The presence of time delays results in an inﬁnite-dimensional system rather than a system of ordinary differential equations. It has been shown that information transmission delays do not inﬂuence whether the system converges to a consensus value; however, further eﬀects of delays are unknown. We show that time delays in most graphs decreases the convergence speed; while somewhat surprisingly, they can improve convergence in certain special graphs. We discuss the structure of graphs for which such improvement is possible.
Open Access
On the Delay Margin for Consensus in Directed Networks of Anticipatory Agents
(Elsevier B.V., 2016) Irofti D.; Atay, F. M.
We consider a linear consensus problem involving a time delay that arises from predicting the future states of agents based on their past history. In case the agents are coupled in a connected and undirected network, the exact condition for consensus is that the delay be less than a constant threshold that is independent of the network topology or size. In directed networks, however, the situation is quite different. We show that the allowable maximum delay for consensus depends on the network topology in a nontrivial way. We study this delay margin in several network constellations, including various circulant networks with directed links. We show that the delay margin depends not only on the number of neighbors, but also on the directionality of connections with those neighbors. Furthermore, the delay margin improves as the circulant networks are rewired en route to a small-world configuration. © 2016