Abstract 

This paper is concerned with stochastic H₂/H_∞ 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_∞ 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 H₂/H_∞ 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 H₂/H_∞ 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. 

报告人简介：孟庆欣，湖州师范大学教授、浙江省杰青、浙江省高校中青年学科带头人、湖州市 1112 人才工程培养人选入选者、第五届“陆增镛教师奖”获得者。孟教授的研究领域为随机分析、随机控制、金融数学，主持国家自然科学基金项目4 项、浙江省自然科学基金项目 3 项、中国博士后基金资助项目 2 项，此外先后在SIAM Journal on Control and Optimization、Stochastic Processes and their Applications 、ESAIM Control Optim. Calc. Var.、Automatica、Applied Mathematics & Optimization等国内外著名期刊上发表学术论文 30 余篇。