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Smooth, Singularity-Free, Finite-Time Tracking Control for Euler–Lagrange Systems

Author

Listed:
  • Nguyen Xuan-Mung

    (Faculty of Mechanical and Aerospace Engineering, Sejong University, Seoul 05006, Korea)

  • Mehdi Golestani

    (Department of Electrical Engineering, Iran University of Science and Technology, Tehran 16844, Iran)

Abstract

This paper investigates the problem of constrained finite-time tracking control of Euler–Lagrange systems subject to system uncertainties and external disturbances. Firstly, we introduce a nonsingular, fast, constrained terminal sliding manifold (NFCTSM) that contains a time-varying gain to deal with the output tracking error constraint. Therefore, the desired performance in steady-state and transience such as ultimate-tracking-error bound, maximum overshoot, and convergence speed are provided. Then, based on the proposed NFCTSM, a smooth adaptive finite-time control is designed such that the tracking errors converge to an arbitrary small region around the origin during a finite period of time. Moreover, the square of the upper bound of the lumped uncertainty is estimated by the adaptive law in order not to use the discontinuous signum function. The efficacy and usefulness of the proposed control methodology are demonstrated via simulation results and comparison with relevant works.

Suggested Citation

  • Nguyen Xuan-Mung & Mehdi Golestani, 2022. "Smooth, Singularity-Free, Finite-Time Tracking Control for Euler–Lagrange Systems," Mathematics, MDPI, vol. 10(20), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3850-:d:945162
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    References listed on IDEAS

    as
    1. Puwei Lu & Wenkai Huang & Junlong Xiao & Fobao Zhou & Wei Hu, 2021. "Adaptive Proportional Integral Robust Control of an Uncertain Robotic Manipulator Based on Deep Deterministic Policy Gradient," Mathematics, MDPI, vol. 9(17), pages 1-16, August.
    2. Jun Xia & Yujia Zhang & Chenguang Yang & Min Wang & Andy Annamalai, 2019. "An improved adaptive online neural control for robot manipulator systems using integral Barrier Lyapunov functions," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(3), pages 638-651, February.
    3. Li, Yingjie & Zhao, Dingxuan & Zhang, Zhongjun & Liu, Jingang, 2015. "An IDRA approach for modeling helicopter based on Lagrange dynamics," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 733-747.
    4. Rui Li & Liang Yang & Yong Chen & Guanyu Lai, 2022. "Adaptive Sliding Mode Control of Robot Manipulators with System Failures," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    5. Ngoc Phi Nguyen & Nguyen Xuan Mung & Le Nhu Ngoc Thanh Ha & Tuan Tu Huynh & Sung Kyung Hong, 2020. "Finite-Time Attitude Fault Tolerant Control of Quadcopter System via Neural Networks," Mathematics, MDPI, vol. 8(9), pages 1-17, September.
    6. Runze Chen & Zhenling Wang & Weiwei Che, 2022. "Adaptive Sliding Mode Attitude-Tracking Control of Spacecraft with Prescribed Time Performance," Mathematics, MDPI, vol. 10(3), pages 1-18, January.
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