Speaker: Meng Qingxin, Professor, Fudan University

Date: October 28, 2022

Time: 09:30-10:30

Location: Tencent Meeting

Sponsor: School of Mathematics, Shandong University

Abstract:

This paper is concerned with stochastic $H_{2}/H_{\infty}$ control problem for continuous-time stochastic differential systems with the diffusion coefficients depending explicitly on the state, control and disturbance as well as their expectations. A stochastic bounded real lemma of mean-field type is proved, which characterizes the equivalence between the $H_{\infty}$ robust stability and the solvability of two coupled indefinite differential Riccati equations. This extremely critical result enables us to obtain sufficient and necessary conditions for the existence of $H_{2}/H_{\infty}$ control for the underlying systems by virtue of the solvability of two sets of cross-coupled indefinite Riccati differential equations. Moreover, in the case that $H_{2}/H_{\infty}$ control exists, the worst case disturbance and the optimal control input admit a linear feedback forms of the state and its mathematical expectation, via the solutions to the two sets of coupled Riccati differential equations.

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https://view.sdu.edu.cn/info/1020/170927.htm