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Shaping control of stationary probability density function of nonlinear stochastic system via dimension augmentation method

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Abstract

For many engineering and industrial systems, the stationary probability density functions (SPDFs) of the key outputs are required to control and shape for targeting a pre-designed function. In this paper, the shaping control of SPDF of a nonlinear stochastic system via dimension augmentation method is reported. The nonlinear stochastic dynamic system is transformed into an augmented system with Hamiltonian structure by dimension augmenting. The target pre-designed SPDF is augmented accordingly. The Hamiltonian function H of the augmented system is determined by solving the Poisson bracket of Hamiltonian and target SPDF, which derives from the balance condition of the probability circulation flow. The analytical expression of shaping control is then obtained from the condition that the probability potential flow is zero. A two-dimensional nonlinear stochastic system is carried out as an example. Numerical results show that the proposed control strategy can accurately shape the stationary probability density functions.

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Funding

This work was supported by The State Grid Science and Technology Project (No. SGZJJXI0SYJS2101112).

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Authors and Affiliations

  1. Department of Mechanics, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou, 310027, China

    Hongwu Bai, Lei Xia & Ronghua Huan

  2. HTYS (Hangzhou) Information Technology Co., LTD., Hangzhou, 310000, China

    Hongwu Bai

  3. Xi’an Institute of Space Radio Technology, Xi’an, 710000, China

    Hongwu Bai

  4. State Grid Zhejiang Electric Power Co., LTD., Jiaxing Power Supply Company, Jiaxing, 314000, China

    Huajie Zhang, Mengshi Zhao & Yifan Guo

Authors
  1. Hongwu Bai
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  2. Lei Xia
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  3. Huajie Zhang
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  4. Mengshi Zhao
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  5. Yifan Guo
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  6. Ronghua Huan
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Contributions

Hongwu Bai contributed to investigation, methodology, and writing—original draft; Lei Xia contributed to validation, supervision and writing—review; Huajie Zhang contributed to writing—original draft; Mengshi Zhao contributed to investigation and software; Yifan Guo contributed to validation and writing—review; Ronghua Huan contributed to resources, supervision, and validation.

Corresponding authors

Correspondence to Lei Xia or Ronghua Huan.

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The authors declare no conflict of interest.

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Bai, H., Xia, L., Zhang, H. et al. Shaping control of stationary probability density function of nonlinear stochastic system via dimension augmentation method. Int. J. Dynam. Control 11, 2335–2341 (2023). https://doi.org/10.1007/s40435-023-01117-5

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  • DOI: https://doi.org/10.1007/s40435-023-01117-5

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