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An innovative parameter estimation for fractional-order systems in the presence of outliers

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Abstract

This paper investigates the problem of parameter estimation for fractional-order linear systems when output signal is polluted by noise and outliers. Different from conventional filtering and semi-definite programming methods, the outliers detection problem is formulated as a matrix decomposition problem based on a novel nuclear norm method, which can not only make exact detection of outliers, but also estimate measurement noise at the same time. Then, a new parameter estimation approach is developed via a modified fractional-order gradient method with variable initial value mechanism and fractional-order parameter update law. With the adoption of recovered output signal, the proposed approach can obtain much better estimation performance, whose effectiveness and superiority are verified by strict mathematical analysis and detailed numerical examples.

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Acknowledgements

The authors are grateful to the associate editor and reviewers for their constructive comments based on which the presentation of this paper has been greatly improved. The work described in this paper was fully supported by the National Natural Science Foundation of China (No. 61573332, No. 61601431), the Fundamental Research Funds for the Central Universities (No. WK2100100028), the Anhui Provincial Natural Science Foundation (No.1708085QF141) and the General Financial Grant from the China Postdoctoral Science Foundation (No. 2016M602032).

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Authors and Affiliations

  1. Department of Automation, University of Science and Technology of China, Hefei, 230026, China

    Rongzhi Cui, Yiheng Wei, Yuquan Chen, Songsong Cheng & Yong Wang

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  1. Rongzhi Cui
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  2. Yiheng Wei
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  3. Yuquan Chen
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  4. Songsong Cheng
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  5. Yong Wang
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Correspondence to Yong Wang.

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Cui, R., Wei, Y., Chen, Y. et al. An innovative parameter estimation for fractional-order systems in the presence of outliers. Nonlinear Dyn 89, 453–463 (2017). https://doi.org/10.1007/s11071-017-3464-7

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