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Consensus on intervals of communication delay

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Abstract

This paper brings out a structured methodology for identifying intervals of communication time-delay where consensus in directed networks of multiple agents with high-order integrator dynamics is achieved. It is built upon the stability analysis of a transformed consensus problem which preserves all the nonzero eigenvalues of the Laplacian matrix of the associated communication topology graph. It is shown that networks of agents with first-order integrator dynamics can be brought to consensus independently of communication delay, on the other hand, for agents with second-order integrator dynamics, the consensus is achieved independently of communication delay only if certain conditions are satisfied. Conversely, if such conditions are not satisfied, it is shown how to compute the intervals of communication delay where multiple agents with second-order or higher-order can be brought to consensus. The paper is ended by showing an interesting example of a network of agents with second-order integrator dynamics which is consensable on the first time-delay interval, but as the time-delay increases, it loses consensability on the second time-delay interval, then it becomes consensable again on the third time-delay interval, and finally it does not achieve consensus any more on the fourth time-delay interval. This example shows the importance of analyzing consensus with time-delay in different intervals.

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Authors and Affiliations

  1. Graduate Program in Electrical Engineering, Federal University of Minas Gerais, Belo Horizonte, 31270-901, Brazil

    Heitor J. Savino

  2. Institute of Computing, Federal University of Alagoas, Maceio, 57072-900, Brazil

    Heitor J. Savino

  3. Department of Electronic Engineering, Federal University of Minas Gerais, Belo Horizonte, 31270-901, Brazil

    Fernando O. Souza & Luciano C. A. Pimenta

Authors
  1. Heitor J. Savino
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  2. Fernando O. Souza
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  3. Luciano C. A. Pimenta
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Corresponding author

Correspondence to Heitor J. Savino.

Additional information

This work was supported by the Brazilian agencies CNPq, CAPES, and FAPEMIG.

Recommended by Associate Editor Min Wu

Heitor J. Savino received the B. Sc. degree in mechatronic engineering from Amazonas State University, Brazil in 2011, received the M. Sc. degree in electrical engineering from Federal University of Amazonas, Brazil in 2012, and received the Ph.D. degree from Federal University of Minas Gerais, Brazil in 2016. From 2015 to 2016, he was a member of Interactive Robotics Group at Massachusetts Institute of Technology conducting research on multiple robotic manipulators. He is currently a professor at Federal University of Alagoas while conducting postdoctoral research at Federal University of Minas Gerais, Brazil.

His research interests include multi-agent systems, systems with time-delays, nonlinear systems, hybrid systems and robotics.

Fernando O. Souza received the B. Sc. degree in control and automation engineering from Pontifical Catholic University of Minas Gerais, Brazil in 2003, received the M. Sc. and Ph.D. degrees in electrical engineering at Federal University of Minas Gerais, Brazil in 2005 and 2008, respectively. He is presently an adjunct professor at Department of Electronic Engineering, Federal University of Minas Gerais, Brazil.

His research interests inchcde consensus of multi-agent systems, time-delay systems, and robust control.

Luciano C. A. Pimenta received the B. Sc., M. Sc. and Ph.D. degrees in electrical engineering from Federal University of Minas Gerais, Brazil in 2003, 2005 and 2009, respectively. From April 2007 to June 2008, he was a visiting Ph.D. student at the General Robotics, Automation, Sensing and Perception Laboratory at University of Pennsylvania, USA. He is currently an assistant professor with Department of Electronic Engineering at Federal University of Minas Gerais, Brazil.

His research interests include robotics, multi-robot systems and control theory.

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Savino, H.J., Souza, F.O. & Pimenta, L.C.A. Consensus on intervals of communication delay. Int. J. Autom. Comput. 15, 13–24 (2018). https://doi.org/10.1007/s11633-017-1095-6

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  • DOI: https://doi.org/10.1007/s11633-017-1095-6

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