Synchronization of networked multibody systems using fundamental equation of mechanics  

作　　者：Jun LIU Jinchen JI Jin ZHOU 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,China [2]Department of Mathematics,Jining University,Qufu 273155,Shandong Province,China [3]Faculty of Engineering and Information Technology,University of Technology Sydney,NSW 2007,Australia [4]Shanghai Key Laboratory of Mechanics in Energy Engineering,Shanghai 200072,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2016年第5期555-572,共18页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.10972129 and 11272191);the Specialized Research Foundation for the Doctoral Program of Higher Education(No.200802800015);the Science and Technology Project of High Schools of Shandong Province(No.J15LJ07);the Shandong Provincial Natural Science Foundation(No.ZR2015FL026)

摘　　要：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.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.

关 键 词：fundamental equation of mechanics analytical dynamics synchronization networked multibody system gyrodynamics coordinate control 

分 类 号：O231[理学—运筹学与控制论]