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Volume 9 Issue 6
Jun.  2022

IEEE/CAA Journal of Automatica Sinica

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Article Contents
H. F. Ye and  Y. D. Song,  “Adaptive control with guaranteed transient behavior and zero steady-state error for systems with time-varying parameters,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 6, pp. 1073–1082, Jun. 2022. doi: 10.1109/JAS.2022.105608
Citation: H. F. Ye and  Y. D. Song,  “Adaptive control with guaranteed transient behavior and zero steady-state error for systems with time-varying parameters,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 6, pp. 1073–1082, Jun. 2022. doi: 10.1109/JAS.2022.105608

Adaptive Control With Guaranteed Transient Behavior and Zero Steady-State Error for Systems With Time-Varying Parameters

doi: 10.1109/JAS.2022.105608
Funds:  This work was supported by the National Natural Science Foundation of China (61991400, 61991403, 61860206008, 61933012)
More Information
  • It is nontrivial to achieve global zero-error regulation for uncertain nonlinear systems. The underlying problem becomes even more challenging if mismatched uncertainties and unknown time-varying control gain are involved, yet certain performance specifications are also pursued. In this work, we present an adaptive control method, which, without the persistent excitation (PE) condition, is able to ensure global zero-error regulation with guaranteed output performance for parametric strict-feedback systems involving fast time-varying parameters in the feedback path and input path. The development of our control scheme benefits from generalized

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  • 1 Properties 1 and 2 of $ \psi(x) $ ensure that $ \psi_x $ is positive and invertible for all $ x \in \mathbb{R} $.
    2 For simplicity, arguments of functions are sometimes omitted if no confusion occurs.
    3 Note that when $ \theta(t) $ is an unknown constant and $ b(t)=1 $, this model is a simplified version of the one studied by [37], where the exponential regulation is proposed for a class of strict-feedback systems with known control gain and unknown constants θ.4 Here $ b(t) $ and $ \theta(t) $ are fast time-varying parameters and they are only piecewise continuous yet $ b(t) $ may undergo sudden changes. Therefore, some classical adaptive schemes [15], [19] are not available because those methods require the parameters be slow time-varying (i.e., here exists a parameter ϵ such that $ |\dot{\theta}(t)|<\epsilon $ and $ |\dot b(t)|<\epsilon $).
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    Highlights

    • This paper provides an adaptive PPC scheme for parameter-varying nonlinear systems
    • The proposed error transformation is new, resulting in a global solution independent of accurate initial error
    • Zero-error regulation is achieved for parameter-varying nonlinear systems in the absence of PE condition

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