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On the convergence of tracking differentiator with multiple stochastic disturbances

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Abstract

This paper investigates the convergence, noise-tolerance, and filtering performance of a tracking differentiator in the presence of multiple stochastic disturbances for the first time. We consider a general case wherein the input signal is corrupted by additive colored noise, and the tracking differentiator is disturbed by additive colored noise and white noise. The tracking differentiator is shown to track the input signal and its generalized derivatives in the mean square sense. Further, the almost sure convergence can be achieved when the stochastic noise affecting the input signal is vanishing. Herein, numerical simulations are performed to validate the theoretical results.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61903087, 62173348, 12161141013, 12131008, 62073144, 62333006) and Science and Technology Innovation Program of Hunan Province (Grant No. 2022RC1188).

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Authors and Affiliations

  1. School of Mathematics and Big Data, Foshan University, Foshan, 528000, China

    Zehao Wu

  2. School of Mathematics and Statistics, Central South University, Changsha, 410075, China

    Huacheng Zhou

  3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Baozhu Guo

  4. Systems Engineering Institute, South China University of Technology, Guangzhou, 510640, China

    Feiqi Deng

Authors
  1. Zehao Wu
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  2. Huacheng Zhou
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  3. Baozhu Guo
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  4. Feiqi Deng
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Corresponding author

Correspondence to Huacheng Zhou.

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Wu, Z., Zhou, H., Guo, B. et al. On the convergence of tracking differentiator with multiple stochastic disturbances. Sci. China Inf. Sci. 67, 122203 (2024). https://doi.org/10.1007/s11432-022-3815-4

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  • DOI: https://doi.org/10.1007/s11432-022-3815-4

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