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Volume 12 Issue 2
Feb.  2025

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2025  >  12(2): 347-355
X. Chen, Y. Wang, and  Y. Song,  “Unifying fixed time and prescribed time control for strict-feedback nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 2, pp. 347–355, Feb. 2025. doi: 10.1109/JAS.2024.124401
Citation: X. Chen, Y. Wang, and  Y. Song,  “Unifying fixed time and prescribed time control for strict-feedback nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 2, pp. 347–355, Feb. 2025. doi: 10.1109/JAS.2024.124401
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Unifying Fixed Time and Prescribed Time Control for Strict-Feedback Nonlinear Systems

doi: 10.1109/JAS.2024.124401
Funds:  This work was supported in part by the National Key Research and Development Program of China (2023YFA1011803), the National Natural Science Foundation of China (62273064, 61991400/61991403, 61933012, 62250710167, 62203078), Natural Science Foundation of Chongqing (CSTB2023NSCQ-MSX0588), the Central University Project (2023CDJKYJH047), and the Innovation Support Program for International Students Returning to China (cx2022016)
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    Abstract
  • This paper investigates the prescribed-time tracking control problem for a class of multi-input multi-output (MIMO) nonlinear strict-feedback systems subject to non-vanishing uncertainties. The inherent unmatched and non-vanishing uncertainties make the prescribed-time control problem become much more nontrivial. The solution to address the challenges mentioned above involves incorporating a prescribed-time filter, as opposed to a finite-time filter, and formulating a prescribed-time Lyapunov stability lemma (Lemma 5). The prescribed-time Lyapunov stability lemma is based on time axis shifting time-varying yet bounded gain, which establishes a novel link between the fixed-time and prescribed-time control method. This allows the restriction condition that the time-varying gain function must satisfy as imposed in most exist prescribed-time control works to be removed. Under the proposed control method, the desire trajectory is ensured to closely track the output of the system in prescribed time. The effectiveness of the theoretical results are verified through numerical simulation.

     

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    Highlights

    • In this work, a prescribed-time filter is proposed to allow the upper bound of the convergence time for the estimation error to be provided precisely in advance. This diverges from the finite/fixed-time filter as imposed in most existing finite-time control works, where the converge time of the estimation error can not be given precisely
    • The proposed prescribed-time control algorithm enables the control gains not to escape to infinity and the system to operate on the whole time interval but not only on the finite time interval, distinguishing itself from most existing prescribed-time control methodologies based on time-varying gains. This is achieved by establishing an important lemma, which allows an integration of the advantages of both time axis shifting finite-gain based method and fixed-time method. In addition, in contrast to most existing practical prescribed-time works where only a cautious upper bound for the actual settling time can be given, the proposed method can provide precise actual settling times and achieve higher tracking accuracy
    • In the proposed method, the issue of ``differential explosion" arising from the repeated differentiations of virtual control inputs, is effectively circumvented through the incorporation of the prescribed-time filter. In addition, unlike the the DSC based adaptive prescribed-time control algorithm where only semi-global boundedness is guaranteed, the global boundedness is achieved under the proposed control method

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