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| | Depeng Song1,Sen Chen1,Wenchao Xue2,et al.[en_title][J].Control Theory and Technology,2025,23(3):464~478.[Copy] |
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| On the stability condition of active disturbance rejection control with time-varying bandwidth observer |
| DepengSong1,SenChen1,WenchaoXue2,3,ZhiliangZhao1,4 |
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| (1 Electrical and Control Engineering, North University of China, Taiyuan 030051, Shanxi, China
4 School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, Shanxi, China;2 State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
3 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China) |
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| 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. |
| 关键词: Active disturbance rejection control · Time-varying bandwidth · Extended state observer · Closed-loop stability · Rate of change |
| DOI：https://doi.org/10.1007/s11768-025-00278-2 |
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| 基金项目:This work was supported partially by the National Natural Science Foundation (No. 62473344), the T-Flight Laboratory in ShanXi Provincial (No. GSFC2024NBKY05), the Natural Science Basic Research Program of Shaanxi (No. 2025JC-YBQN-035), and the National Natural Science Foundation of China (Grant No. 92471204). |
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| On the stability condition of active disturbance rejection control with time-varying bandwidth observer |
| Depeng Song1,Sen Chen1,Wenchao Xue2,3,Zhiliang Zhao1,4 |
| (1 Electrical and Control Engineering, North University of China, Taiyuan 030051, Shanxi, China
4 School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, Shanxi, China;2 State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
3 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China) |
| Abstract: |
| 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. |
| Key words: Active disturbance rejection control · Time-varying bandwidth · Extended state observer · Closed-loop stability · Rate of change |
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