一、题目：

Stochastic H2/H∞ control for Mean-Field Stochastic Differential Systems with (x, u, v)-dependent noise

二、主讲人：

孟庆欣

三、摘要：

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.

四、主讲人简介：

孟庆欣教授，浙江省杰出青年基金项目获得者、“南太湖本土高层次人才特殊支持计划”科技创新领军人才、浙江省高校中青年学科带头人、湖州市1112人才工程入选者、复旦大学物理系出站博士后。孟庆欣教授一直从事随机分析、随机控制、金融工程等方面的研究工作；主持国家自然科学基金项目多项，浙江省自然科学基金重点项目，浙江省杰出青年基金项目等。近年来先后在SIAM Journal On Control And Optimization、Automatica、System & Control Letters等国内外著名期刊上发表了多篇有关随机控制及其金融工程应用的学术论文，解决了随机控制理论中的两个重要公开问题，获得湖州师范学院第三届科研成果奖一等奖和湖州师范学院第五届“陆增镛教师奖”。

五、邀请人：

聂天洋 数学学院教授

六、时间：

10月28日（周五）9:30-10:30

七、地点：

腾讯会议

八、联系人：

聂天洋，联系方式：nietianyang@sdu.edu.cn

九、主办单位：

山东大学数学学院