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

Meijiao Wang (), Qingxin Meng (), Yang Shen () and Peng Shi ()
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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

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 3, No 8, 1024-1060

Abstract: 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.

Keywords: $$H_{2}/H_{\infty }$$ H 2 / H ∞ control; Stochastic bounded real lemma; Mean-field; Indefinite Riccati differential equations; 49J53; 49K45; 60H99 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02220-5

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