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Stochastic $$H_{2}/H_{\infty }$$ H 2 / H ∞ Control for Mean-Field Stochastic Differential Systems with (x, u, v)-Dependent Noise

Author

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  • Meijiao Wang

    (University of Shanghai for Science and Technology)

  • Qingxin Meng

    (Huzhou University)

  • Yang Shen

    (University of New South Wales)

  • Peng Shi

    (The University of Adelaide)

Abstract

This paper studies a continuous-time stochastic $$H_{2}/H_{\infty }$$ H 2 / H ∞ control problem for mean-field stochastic differential systems, with random initial value and diffusion coefficients depending explicitly on the state, control and disturbance as well as their expectations. A mean-field stochastic bounded real lemma is first established, characterizing the equivalence between $$H_{\infty }$$ H ∞ robust stability and the solvability of two indefinite differential Riccati equations. Based on this extremely useful result, an equivalent condition for the existence of $$H_{2}/H_{\infty }$$ H 2 / H ∞ controller is proposed by utilizing the solution of two sets of cross-coupled indefinite Riccati equations. Moreover, when an $$H_{2}/H_{\infty }$$ H 2 / H ∞ controller exists, both the optimal control input and the corresponding worst-case disturbance admit linear feedback representations of the state and its mathematical expectation.

Suggested Citation

  • Meijiao Wang & Qingxin Meng & Yang Shen & Peng Shi, 2023. "Stochastic $$H_{2}/H_{\infty }$$ H 2 / H ∞ Control for Mean-Field Stochastic Differential Systems with (x, u, v)-Dependent Noise," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1024-1060, June.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:3:d:10.1007_s10957-023-02220-5
    DOI: 10.1007/s10957-023-02220-5
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    References listed on IDEAS

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    1. Rodrigo da Ponte Caun & Edvaldo Assunção & Marcelo Carvalho Minhoto Teixeira, 2021. "H2/H∞ formulation of LQR controls based on LMI for continuous-time uncertain systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 52(3), pages 612-634, February.
    2. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
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