Nonlinear Dynamics

, Volume 96, Issue 2, pp 1317–1333 | Cite as

Finite-time consensus of high-order heterogeneous multi-agent systems with mismatched disturbances and nonlinear dynamics

  • Shang ShiEmail author
  • Hongyan Feng
  • Wenhui Liu
  • Guangming Zhuang
Original Paper


In this study, we investigate the finite-time consensus problem for a general class of high-order nonlinear heterogeneous multi-agent systems, for which not only the unknown nonlinear dynamics, mismatched disturbances but also the system orders are not required to be identical. We propose two families of consensus algorithms, and the output consensus can be achieved with them in a finite time even with nonlinear dynamics and mismatched disturbances. The Lipschitz-like condition generally required in the literature is removed in this paper. The integral sliding-mode control technique is used to construct the first family of consensus algorithms, which may cause chattering problem for the existence of high-frequency switching terms. To overcome the chattering phenomenon, a new variable-gain finite-time observer is developed to construct the second family of continuous algorithms based on a different assumption. It is shown that some existing consensus protocols can be broadened in several directions through the framework of this study; moreover, the output feedback finite-time consensus can also be solved.


Finite-time consensus Heterogeneous multi-agent systems Finite-time consensus Mismatched disturbances 



This work was supported in part by the National Natural Science Foundation of China under Grant 61703249, 61773191, 61803208, the Natural Science Foundation of Jiangsu Province under Grant BK20180726, the Natural Science Research Project of Jiangsu Higher Education Institutions under Grant 18KJB120005, the Natural Science Foundation of Shandong Province for Outstanding Young Talents in Provincial Universities under Grant ZR2016JL025.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of AutomationNanjing University of Science and TechnologyNanjingPeople’s Republic of China
  2. 2.School of Electrical and Automation EngineeringNanjing Normal UniversityNanjingPeople’s Republic of China
  3. 3.School of Mathematical SciencesLiaocheng UniversityLiaochengPeople’s Republic of China

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