Static group synchronization of second-order multi-agent systems via pinning control |
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| Authors: | Xiang-Gui Guo Hong-Jian Li Jun-Jie Zhao Wei-Wei Che |
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| Institution: | 1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;2. Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, Beijing 100083, China;3. Beijing Engineering Research Center of Industrial Spectrum Imaging, Beijing 100083, China;4. Institute of Complexity Science, Qingdao University, Qingdao 266071, China |
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| Abstract: | This paper investigates the expected static group synchronization problem of the second-order multi-agent systems via pinning control. For directed communication topology with spanning tree, based on Gershgorin disk theorem and the matrix property, a static pinning control protocol with fixed gains is first introduced and some sufficient and necessary static group synchronization criteria are also established. It is worth mentioning that a rigorous proof is also given that only one pinning node is needed to guarantee static group synchronization, which could be inferred that our protocol might be more economical and effective in large scale of multi-agent systems. Then, for weakly connected directed communication topology with nodes of zero in-degree, an adaptive pinning control applied to the node with zero in-degree is also proposed to achieve static group synchronization. Finally, the efficiency of the proposed protocols is verified by two simulation examples. |
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| Keywords: | Corresponding author at: School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing 100083 China |
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