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Applied Mathematics and Mechanics

, Volume 37, Issue 5, pp 555–572 | Cite as

Synchronization of networked multibody systems using fundamental equation of mechanics

  • Jun Liu
  • Jinchen Ji
  • Jin ZhouEmail author
Article

Abstract

From the analytical dynamics point of view, this paper develops an optimal control framework to synchronize networked multibody systems using the fundamental equation of mechanics. A novel robust control law derived from the framework is then used to achieve complete synchronization of networked identical or non-identical multibody systems formulated with Lagrangian dynamics. A distinctive feature of the developed control strategy is the introduction of network structures into the control requirement. The control law consists of two components, the first describing the architecture of the network and the second denoting an active feedback control strategy. A corresponding stability analysis is performed by the algebraic graph theory. A representative network composed of ten identical or non-identical gyroscopes is used as an illustrative example. Numerical simulation of the systems with three kinds of network structures, including global coupling, nearest-neighbour, and small-world networks, is given to demonstrate effectiveness of the proposed control methodology.

Key words

fundamental equation of mechanics analytical dynamics synchronization networked multibody system gyrodynamics coordinate control 

Chinese Library Classification

O316 O231.2 O232 

2010 Mathematics Subject Classification

70E55 70Q05 93C10 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina
  2. 2.Department of MathematicsJining UniversityQufuShandong Province, China
  3. 3.Faculty of Engineering and Information TechnologyUniversity of TechnologySydneyAustralia
  4. 4.Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghaiChina

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