Latent consensus protocol with weak background links and time-delay

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Abstract

Coordination in multiagent system with information influences and time-delay is considered. In particular, the case when consensus is not achieved for any vector of initial values was considered. Such a problem may arise in a multi-agent system with a weakly coupled structure, that is, when there are several leading agents or groups of agents. To achieve consensus, a latent consensus protocol with weak background links and time-delay was used. Using the Nyquist criterion applied by Tsypkin, a boundary value of time-delay was established, depending on the spectral properties of the Laplace matrix, and a condition for the independence of convergence from time-delay. With a decrease in the weights of background links, the boundary value of time-delay of the protocol under consideration approaches the one of the required protocol. It was found that in the case of convergence, the latent consensus protocol with background links converges to consensus for any vector of initial values, while the weights of background links can be arbitrarily small. Thus, the use of this protocol solves the above problem, and this study allows adapting other previously considered latent consensus protocols for multiagent systems with time-delay.

About the authors

Dmitriy Konstantinovich Khomutov

V.A. Trapeznikov Institute of Control Sciences of RAS

Email: homutov_dk@mail.ru
Moscow

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