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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

A delayed consensus algorithm in networks of anticipatory agents

Fatihcan M. Atay and Dina Irofti


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.

synchronization, prediction, anticipation

Related publications

2016 Repository Open Access
Fatihcan M. Atay and Dina Irofti

A delayed consensus algorithm in networks of anticipatory agents

In: 2016 European Control Conference (ECC) ; Aalborg, Denmark, June 29-July 1, 2016
[Piscataway, NJ] : IEEE, 2016. - pp. 1880-1885