Adaptive practical synchronisation of Lagrangian networks with a directed graph via pinning control

Mihua Ma; Jianping Cai; Jin Zhou

Adaptive practical synchronisation of Lagrangian networks with a directed graph via pinning control

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Author(s): Mihua Ma ^{1, 2} ; Jianping Cai ¹ ; Jin Zhou ²
- Affiliations: 1: School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, People's Republic of China ;
  2: Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, People's Republic of China
Source: Volume 9, Issue 14, 17 September 2015, p. 2157 – 2164
DOI: 10.1049/iet-cta.2015.0056 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 30/04/2014, Accepted 05/05/2015, Revised 02/05/2015, Published 17/06/2015

This study investigates the practical synchronisation of networked Lagrangian systems with a directed graph by pinning adaptive control. Some simple yet general algebraic criteria are proposed based on practical stability theory on dynamical systems, and the proposed criteria ensure that all the robotic agents described by Lagrangian dynamics can achieve desired practical synchronisation. The main features of the present investigation include, an efficient pinning adaptive strategy is implemented by applying local linear feedback injections to a small fraction of agents, which means that the presented control strategy does not require the prerequisite knowledge of system models. Moreover, an allowable attraction region is explicitly given by Lagrangian dynamics parameter and the controlled network structure, and so it is very convenient to application in practice. Besides, this study addresses the fundamental problems in the pinning control of networked Lagrangian systems: what kind of agents and how many agents should be pinned? As a direct application of the theoretical results, practical synchronisation of eight two-link revolute manipulators is discussed in detail. Numerical experiments verify the effectiveness of the proposed control technique.

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Adaptive practical synchronisation of Lagrangian networks with a directed graph via pinning control

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