Multi-consensus of second-order agents in discrete-time directed networks

Abstract

This paper deals with the multi-consensus problem in discrete-time directed networks with second-order agent dynamics. Necessary and sufficient conditions to ensure multi-equilibria consensus are obtained by utilising some concepts related to graph structures. It is shown that while the choice of control parameters directly affects the stability of the consensus problem, the equilibria states do not depend on them. Furthermore, the initial values of the states of the secondary layer subgraphs have no effect on the consensus equilibria of any agent in the network. A systematic method for choosing the control parameters is proposed and it is proved that this choice ensures multi-consensus of the network. Finally, illustrative examples are provided to better highlight the theoretical results.

Keywords:

• Multi-consensus
• second-order dynamics
• graph theory
• directed networks

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by The Scientific and Technological Research Council of Turkey (TUBITAK) [grant number 118E218].

Notes on contributors

Onur Cihan

Onur Cihan received the B.S. degrees in control engineering and electrical engineering from Istanbul Technical University, Turkey, in 2007. He received the M.S. and Ph.D. degrees in electrical and electronics engineering from Bogazici University, Istanbul, Turkey in 2009 and 2014, respectively. He was a postdoctoral researcher at Center for Systems Science, Yale University, New Haven, CT, before joining the Department of Electrical and Electronic Engineering, Marmara University, Istanbul, Turkey as an assistant professor. His research interests include mathematical systems theory, multi-agent systems, distributed control and data mining.

Mehmet Akar

Mehmet Akar received the B.S. and M.S. degrees in electrical engineering from Bilkent University, Ankara, Turkey, in 1994 and 1996, respectively, and the Ph.D. degree in electrical engineering from The Ohio State University, Columbus, OH, USA, in 1999. He was with Yale University, New Haven, CT, USA; with the Communication Sciences Institute, University of Southern California, Los Angeles, CA, USA; and with the National University of Ireland, Maynooth, Ireland. He is currently a full professor at the Department of Electrical and Electronics Engineering, Bogazici University, Istanbul, Turkey. His research interests include distributed/decentralized control, hybrid systems, and their applications in automotive and communication networks.