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<p>With the growing adoption of artificial intelligence algorithms and neural networks, online learning and adaptive methods for updating the bandwidth have become increasingly prevalent. However, the conditions required to ensure closed-loop stability when employing a time-varying bandwidth, as well as the supporting mathematical foundations, remain insufficiently studied. This paper investigates the stability condition for active disturbance rejection control (ADRC) with a time-varying bandwidth extended state observer (ESO). A new stability condition is derived, which means that the upper bound of rate of change for ESO bandwidth should be restricted. Moreover, under the proposed condition, the closed-loop stability of ADRC with a time-varying bandwidth observer is rigorously proved for nonlinear uncertainties. In simulations, the necessity of the proposed condition is illustrated, demonstrating that the rate of change of ESO bandwidth is crucial for closed-loop stability.</p>

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On the stability condition of active disturbance rejection control with time-varying bandwidth observer

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Depeng Song,
  • Sen Chen,
  • Wenchao Xue,
  • Zhiliang Zhao

摘要

With the growing adoption of artificial intelligence algorithms and neural networks, online learning and adaptive methods for updating the bandwidth have become increasingly prevalent. However, the conditions required to ensure closed-loop stability when employing a time-varying bandwidth, as well as the supporting mathematical foundations, remain insufficiently studied. This paper investigates the stability condition for active disturbance rejection control (ADRC) with a time-varying bandwidth extended state observer (ESO). A new stability condition is derived, which means that the upper bound of rate of change for ESO bandwidth should be restricted. Moreover, under the proposed condition, the closed-loop stability of ADRC with a time-varying bandwidth observer is rigorously proved for nonlinear uncertainties. In simulations, the necessity of the proposed condition is illustrated, demonstrating that the rate of change of ESO bandwidth is crucial for closed-loop stability.