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Fusion of PDF compensation and gain-scheduled control for discrete stochastic systems with randomly occurring nonlinearities

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Abstract

A fusion control strategy, including probability density function (PDF) compensation and gain-scheduled control, is proposed for discrete-time stochastic systems with randomly occurring nonlinearities. Usually, it is difficult to drive the tracking error strictly to zero in a random environment. So the proposed method aims to stabilize the closed-loop system in the exponentially mean square sense and guarantee the distribution of output error as close to the expected PDF as possible. The parameters of the gain-scheduled controller are obtained by solving appropriate linear matrix inequalities, and the parameters of the PDF compensator are updated in real time according to the Kullback–Leibler divergence between the PDF of output error and the desired one. The proposed method has the characteristics of low conservativeness and easy to implement. The effectiveness of the proposed method is shown by two examples.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (61973023, 61573050) and Beijing Natural Science Foundation (4202052).

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Authors and Affiliations

  1. College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, 100029, China

    Lian Geng, Jing Wang & Jinglin Zhou

  2. School of Automation and Electrical Engineering, Shenyang Ligong University, Shenyang, 110159, Liaoning, China

    Yanzhu Zhang

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  1. Lian Geng
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  2. Jing Wang
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  3. Jinglin Zhou
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  4. Yanzhu Zhang
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Correspondence to Jing Wang or Jinglin Zhou.

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Geng, L., Wang, J., Zhou, J. et al. Fusion of PDF compensation and gain-scheduled control for discrete stochastic systems with randomly occurring nonlinearities. Nonlinear Dyn 101, 393–406 (2020). https://doi.org/10.1007/s11071-020-05773-6

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  • DOI: https://doi.org/10.1007/s11071-020-05773-6

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