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Mathematical Problems in Engineering
Volume 2018, Article ID 1957070, 11 pages
Research Article

Predefined-Time Consensus of Nonlinear First-Order Systems Using a Time Base Generator

1Centro de Investigación en Matemáticas (CIMAT), A.C., Computer Science Department, GTO, Mexico
2Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Zapopan, Mexico
3Intel Tecnología de México, Multi-Agent Autonomous Systems Lab, Intel Labs, Zapopan, Mexico

Correspondence should be addressed to Héctor M. Becerra; xm.tamic@arreceb.rotceh

Received 16 June 2018; Revised 11 September 2018; Accepted 17 September 2018; Published 9 October 2018

Academic Editor: Ju H. Park

Copyright © 2018 J. Armando Colunga et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a couple of consensus algorithms for multiagent systems in which agents have first-order nonlinear dynamics, reaching the consensus state at a predefined time independently of the initial conditions. The proposed consensus protocols are based on the so-called time base generators (TBGs), which are time-dependent functions used to build time-varying control laws. Predefined-time convergence to the consensus is proved for connected undirected communication topologies and directed topologies having a spanning tree. Furthermore, one of the proposed protocols is based on the super-twisting controller, providing robustness against disturbances while maintaining the predefined-time convergence property. The performance of the proposed methods is illustrated in simulations, and it is compared with finite-time, fixed-time, and predefined-time consensus protocols. It is shown that the proposed TBG protocols represent an advantage not only in the possibility to define a settling time but also in providing smoother and smaller control actions than existing finite-time, fixed-time, and predefined-time consensus.