Nonlinear Dynamics

, Volume 85, Issue 1, pp 415–424 | Cite as

Flocking of networked Euler–Lagrange systems with uncertain parameters and time-delays under directed graphs

Original Paper
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Abstract

In this paper, the flocking problem for multiple nonlinear Euler–Lagrange systems is investigated with both parametric uncertainties and time-delays under directed communication graphs. With the help of a new coordinate transformation method, an adaptive controller, which is dependent on position and velocity measurements, is proposed to guarantee flocking. By frequency domain analysis, input–output stability analysis and the final value theorem, the synchronization of positions/velocities of all the agents is guaranteed, and in the meantime all agents ultimately track a designated velocity. It is shown that to ensure flocking the sufficient condition is closely relevant to a constant gain in the proposed controller and the nonzero eigenvalues of the Laplacian matrix whose moduli are less than one. Finally, one numerical simulation is presented to demonstrate the efficiency of the theoretical results.

Keywords

Flocking Networked nonlinear Euler–Lagrange systems  Time-delays Directed graph 
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Notes

Acknowledgments

The authors are grateful to the Editor, the Associate Editor and the reviewers for their valuable suggestions. This research was partially supported by the Research Grants Council, Hong Kong, through the General Research Fund under Grant 106140120, the HKU CRCG Seed Funding Programme for Basic Research 201411159037, the Natural Science Foundation of China under Grants 61374053 and 61473129, and the Program for New Century Excellent Talents in University from Chinese Ministry of Education under Grant NCET-12-0215.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringThe University of Hong KongPokfulamHong Kong
  2. 2.School of Automation, Image Processing and Intelligent Control Key Laboratory of Education Ministry of ChinaHuazhong University of Science and TechnologyWuhanChina

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