Consensus in multi-agent systems subject to input saturation and time-varying delays

Abstract

This paper deals with the problem of consensus in multi-agent systems. The consensus is investigated considering directed networks composed by identical agents described by linear models of arbitrary order, subject to input saturation and non-uniform time-varying delays. The main results are sufficient conditions for consensus analysis and design of distributed consensus protocols for multi-agent systems. In addition, because the saturation might prevent the multi-agent system to attain consensus on some set of initial conditions, it is also proposed a strategy to calculate a region in which the consensus is guaranteed. The results follow from the Lyapunov–Krasovskii theory and are formulated in the linear matrix inequalities (LMIs) framework. Finally, we present examples to illustrate the effectiveness of the proposed method in contrast with similar approaches existing in the literature.

Keywords:

• Consensus
• Lyapunov–Krasovskii
• linear matrix inequalities
• multi-agent systems
• input saturation
• time-varying delay

Acknowledgments

We thank Professor Valter J. S. Leite (Centro Federal de Educação Tecnológica de Minas Gerais) for the insightful technical discussion during the development of this work.

Disclosure statement

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

Notes

1 We used the inequality $2{\mathit{a}}^T\mathit{b}\le {\mathit{a}}^{T}X\mathit{a}+{\mathit{b}}^T{X}^{-1}\mathit{b}$ where $\mathit{a}$, $\mathit{b}\in {\mathbb{R}}^{m(n-1)}$ and $X>0\in {\mathbb{R}}^{m(n-1)\times m(n-1)}$.

Additional information

Funding

This work was in part supported by the project INCT (National Institute of Science and Technology) under the grant CNPq (Brazilian National Research Council) 465755/2014-3, FAPESP (São Paulo Research Foundation), Brazil 2014/50851-0. This work was also supported in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil (Finance Code 88887.136349/2017-00, and 001), and CNPq, Brazil (grant number 311063/2017-9, 429819/2018-8, and 311574/2017-3), and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), Brazil (Grant TEC-APQ-00543-17). Thales C. Silva holds a scholarship from CAPES, and Fernando O. Souza and Luciano C. A. Pimenta hold a scholarship from CNPq.

Notes on contributors

Thales C. Silva

Thales C. Silva received his BS degree in Electrical Engineering from Universidade Federal do Tocantins, in 2017 and his MSc degree in Electrical Engineering from Universidade Federal de Minas Gerais, Brazil in 2019. Now he is pursuing a PhD degree at the Universidade Federal de Minas Gerais, Brazil. His current research interests include time-delay systems, consensus of multi-agent systems and non-linear systems.

Fernando O. Souza

Fernando O. Souza obtained his BS degree in Control and Automation Engineering from the Pontifícia Universidade Católica de Minas Gerais, Brazil, in 2003. He received his MSc and PhD degrees in Electrical Engineering at the Universidade Federal de Minas Gerais, Brazil, in 2005 and 2008, respectively. He is presently an associate professor at the Department of Electronic Engineering, Universidade Federal de Minas Gerais, Brazil. His research interests are consensus of multi-agent systems, time-delay systems and robust control.

Luciano C. A. Pimenta

Luciano C. A. Pimenta received his BS, MSc and Ph.D. degrees in Electrical Engineering from the Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, Brazil, in 2003, 2005 and 2009, respectively. From April 2007 to June 2008, he was a visiting PhD student at the General Robotics, Automation, Sensing and Perception (GRASP) Laboratory at the University of Pennsylvania, Philadelphia, USA. He is currently an associate professor with the Department of Electronic Engineering at UFMG. His research interests include robotics, multi-robot systems and control theory.