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Coordinated motion of Lagrangian systems with auxiliary oscillators under cooperative and cooperative–competitive interactions

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Abstract

The present paper investigates coordinated oscillatory motion of networked Lagrangian systems under diverse interactions. Based on two new auxiliary oscillator systems, we formulate two integral-sliding adaptive controllers to drive the systems to reach disparate coordination behaviors. Specially, in the case of cooperative network, where the correspondence between the agents is cooperating, the systems can achieve complete oscillatory synchronization if interactions network contains a spanning tree. In the case of weighted cooperative–competitive network, cluster oscillatory synchronization issue is solved for Lagrangian systems. Compared with the previous methods, three major advantages for introduction of auxiliary oscillator systems are that, firstly, Lagrangian systems reach the oscillatory synchronization with arbitrary amplitudes and initial phases instead of distributed stabilization or consensus; secondly, synchronization states are explicitly expressed under the integral-sliding controllers; thirdly, multi-partite synchronization is formed on the basis of the newly introduced cooperative–competitive interactions without the balanced couple condition. Finally, two numerical examples are provided to demonstrate effectiveness of the presented algorithms.

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Acknowledgements

This work is supported by the National Science Foundation of China (Grant No. 61663035), the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant Nos. 2019MS01001, 2019MS07002, 2018MS06017), and the Foundation of China Scholarship Council (Grant No. 201808155059).

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Authors and Affiliations

  1. School of Science, Inner Mongolia University of Science and Technology, Baotou, 014010, China

    Liyun Zhao, Wen Li, Fuhong Wei, Juan Wang & Hongbo Bo

  2. School of Mechanical and Mechatronic Engineering, University of Technology Sydney, Sydney, NSW, 2007, Australia

    Liyun Zhao

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  1. Liyun Zhao
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  2. Wen Li
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Correspondence to Liyun Zhao.

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Zhao, L., Li, W., Wei, F. et al. Coordinated motion of Lagrangian systems with auxiliary oscillators under cooperative and cooperative–competitive interactions. Nonlinear Dyn 100, 2415–2426 (2020). https://doi.org/10.1007/s11071-020-05609-3

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  • DOI: https://doi.org/10.1007/s11071-020-05609-3

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