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Adaptive Fractional-order Unscented Kalman Filters for Nonlinear Fractional-order Systems

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  • Control Theory and Applications
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Abstract

In this paper, the Grüwald-Letnikov method is used to discretize a continuous-time nonlinear fractional-order system with unknown parameters and fractional-order, and an adaptive fractional-order unscented Kalman filter is proposed. Taking the unknown fractional-order and parameters as the augmented states, the augmented state equation is established to solve the problem on the unknown fractional-order and parameters. In order to improve the accuracy of state estimation, an adaptive fractional-order unscented Kalman filter is designed to deal with the nonlinear functions by using the unscented transformation. Meanwhile, the problem on state estimation for the estimated system with a non-differentiable nonlinear functions is also solved. Finally, the effectiveness of the proposed algorithm is verified by two simulation examples.

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Funding

This work was supported by the Liaoning Revitalization Talents Program Grant XLYC1807229, Liaoning Provincial Department of Education Project under LJC202010, Liaoning University Science Research Fund LDGY2019020, and China Postdoctoral Science Foundation Funded Project under Grant 2019M651206.

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Liaoning University, Liaoning, Shenyang, 110036, China

    Yue Miao, Zhe Gao & Chuang Yang

  2. College of Light Industry, Liaoning University, Liaoning, Shenyang, 110036, China

    Zhe Gao

Authors
  1. Yue Miao
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  2. Zhe Gao
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  3. Chuang Yang
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Corresponding author

Correspondence to Zhe Gao.

Additional information

Yue Miao received her B.S. degree in mathematics and applied mathematics from Tangshan Normal University, Tangshan, China, in 2019. She is currently working towards an M.S. degree in the School of Mathematics and Statistics, Liaoning University, China. Her research field is state estimation of fractional-order systems.

Zhe Gao received his M.S. degree in Control science and Engineering from the Northeastern University, Shenyang, China, in 2006, and a Ph.D. degree in Control science and Engineering from Beijing Institute of Technology, Beijing, China, in 2012. He is currently a Professor with Department of electrical engineering and automation, College of Light Industry, Liaoning University, Shenyang, China. His current research interests include analysis and design of fractional-order systems.

Chuang Yang received her B.S. degree in mathematics and applied mathematics from Qiqihar University, Qiqihar, China, in 2018. She is currently working towards an M.S. degree in the School of Mathematics and Statistics, Liaoning University, China. Her research field is state estimation of fractional-order systems.

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Miao, Y., Gao, Z. & Yang, C. Adaptive Fractional-order Unscented Kalman Filters for Nonlinear Fractional-order Systems. Int. J. Control Autom. Syst. 20, 1283–1293 (2022). https://doi.org/10.1007/s12555-021-0163-4

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  • DOI: https://doi.org/10.1007/s12555-021-0163-4

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