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Distributed adaptive output consensus control of second-order systems containing unknown non-linear control gains

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  • Gang Wang
  • Chaoli Wang
  • Qinghui Du
  • Xuan Cai

Abstract

In this paper, we address the output consensus problem of tracking a desired trajectory for a group of second-order agents on a directed graph with a fixed topology. Each agent is modelled by a second-order non-linear system with unknown non-linear dynamics and unknown non-linear control gains. Only a subset of the agents is given access to the desired trajectory information directly. A distributed adaptive consensus protocol driving all agents to track the desired trajectory is presented using the backstepping technique and approximation technique of Fourier series (FSs). The FS structure is taken not only for tracking the non-linear dynamics but also the unknown portion in the controller design procedure, which can avoid virtual controllers containing the uncertain terms. Stability analysis and parameter convergence of the proposed algorithm are conducted based on the Lyapunov theory and the algebraic graph theory. It is also demonstrated that arbitrary small tracking errors can be achieved by appropriately choosing design parameters. Though the proposed work is applicable for second-order non-linear systems containing unknown non-linear control gains, the proposed controller design can be easily extended to higher-order non-linear systems containing unknown non-linear control gains. Simulation results show the effectiveness of the proposed schemes.

Suggested Citation

  • Gang Wang & Chaoli Wang & Qinghui Du & Xuan Cai, 2016. "Distributed adaptive output consensus control of second-order systems containing unknown non-linear control gains," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(14), pages 3350-3363, October.
  • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:14:p:3350-3363
    DOI: 10.1080/00207721.2016.1139760
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    References listed on IDEAS

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    1. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, September.
    2. Editors, 2014. "International Journal of Systems Science," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(12), pages 1-1, December.
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    Cited by:

    1. Meiying Ou & Haibin Sun & Shengwei Gu & Yangyi Zhang, 2017. "Distributed finite-time trajectory tracking control for multiple nonholonomic mobile robots with uncertainties and external disturbances," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(15), pages 3233-3245, November.

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