Adaptive group consensus in uncertain networked Euler–Lagrange systems under directed topology

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• 作者：Jun Liu ; Jinchen Ji ; Jin Zhou ; Lan Xiang ; Liyun Zhao
• 关键词：Group consensus ; Networked Euler–Lagrange systems ; Parametric uncertainties ; Adaptive control ; Input ; to ; state stable
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：82
• 期：3
• 页码：1145-1157
• 全文大小：913 KB
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• 作者单位：Jun Liu (1) (2)
  Jinchen Ji (3)
  Jin Zhou (1)
  Lan Xiang (4)
  Liyun Zhao (1) (5)
  
  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, People’s Republic of China
  2. Department of Mathematics, Jining University, Qufu, 273155, Shandong, People’s Republic of China
  3. Faculty of Engineering and IT, University of Technology Sydney, PO Box 123, Broadway, Sydney, NSW, 2007, Australia
  4. Department of Physics, School of Science, Shanghai University, Shanghai, 200444, People’s Republic of China
  5. School of Mathematics, Physics and Biological Engineering, Inner Mongolia University of Science and Technology, Baotou, 014010, People’s Republic of China
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

This paper investigates the adaptive group consensus of networked Euler–Lagrange systems with parametric uncertainties under directed topology graph. A novel decomposition approach is developed by using both algebraic graph theory and matrix theory. Three distributed adaptive group consensus protocols are proposed for the cases of topology graphs with acyclic partition and balanced couple, respectively. Some necessary and sufficient conditions for solving group consensus problems are established. It is shown that for the case of directed acyclic graphs, the group consensus can always be guaranteed by the structure of acyclic interaction topology. In particular, an explicit expression of group consensus states can be obtained using the proposed integral protocol, which can be used to develop a unified approach yielding the desired group consensus. For the case of directed balanced couple graphs, a simple algebraic criterion for ensuring group consensus is presented in terms of the eigenvalue computation of Laplacian matrix and thus can be easily applied in practice. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed control methodologies. Keywords Group consensus Networked Euler–Lagrange systems Parametric uncertainties Adaptive control Input-to-state stable