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Hierarchical predefined-time control for time-varying formation tracking of multiple heterogeneous Euler–Lagrange agents

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Abstract

This paper investigates the time-varying formation tracking (TVFT) problem of multiple heterogeneous Euler–Lagrange agents (MHELAs) with predefined-time convergence ability under directed interaction topology, where both the parametric uncertainties and external disturbances are taken into account. A new predefined-time hierarchical control (PTHC) algorithm is designed to solve the aforementioned challenging problem. Specifically, the TBG-based distributed estimator algorithm utilizing the time base generator (TBG) is firstly designed to estimate the states of the virtual leader in a predefined time. Besides, based on the obtained estimators, the predefined-time controller is presented to accomplish the robust time-varying formation tracking of the MHELAs in the local control layer. By employing the Lyapunov and Lagrange stability theory, the sufficient conditions for achieving the desired performance of the MHELAs are derived. Eventually, numerical simulations are performed to illustrate that the aforementioned theoretical results for MHELAs are effective.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China under Grants 62073301 and 61803139, as well as the Fundamental Research Funds for National University, China University of Geosciences (Wuhan) under Grant 1910491B05.

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Authors and Affiliations

  1. School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan, 430074, China

    Kai-Lun Huang, Ming-Feng Ge, Chang-Duo Liang & Jiu-Wang Dong

  2. School of Mathematics, Hefei University of Technology, Hefei, 230009, China

    Xiao-Wen Zhao

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  1. Kai-Lun Huang
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Correspondence to Ming-Feng Ge.

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Huang, KL., Ge, MF., Liang, CD. et al. Hierarchical predefined-time control for time-varying formation tracking of multiple heterogeneous Euler–Lagrange agents. Nonlinear Dyn 105, 3255–3270 (2021). https://doi.org/10.1007/s11071-021-06792-7

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