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数学学院、所2019年系列学术活动(第196场):张旭 教授 四川大学

发表于: 2019-11-06 16:14  点击:

报告题目:Operator-valued, backward stochastic Riccati equations and application

报 告 人:张旭教授 四川大学

报告时间:2019年11月7日上午  10:00-11:00

报告地点:数学楼第二报告厅

报告摘要:

We introduce an operator-valued, backward stochastic Riccati equation for a general stochastic linear quadratic control problem in infinite dimensions.Generally speaking, the well-posedness of this equation is a challenging problem. Indeed, in the infinite dimensional setting, there exists no satisfactory stochastic integration/evolution equation theory (in the literatures) which can be employed to treat the well-posedness of such a quadratically nonlinear equation. To overcome this difficulty, we adapt our transposition solution method, which was developed in our previous works but for operator-valued, backward stochastic (linear) Lyapunov equations. Under some assumptions, we establish the equivalence between the existence of optimal feedback operator for infinite dimensional stochastic linear quadratic control problems with random coefficients and the solvability of the corresponding operator-valued, backward stochastic Riccati equations.

报告人简介:

张旭教授,现四川大学教授,国家杰出青年基金获得者,中国科学院“百人计划”入选者,教育部“长江学者”特聘教授。张旭教授的主要研究领域为数学控制论,及相关的偏微分方程与随机分析。曾获国家自然科学二等奖,他先后分别担任其研究领域中两份主要国际期刊《SIAM J. Control Optim.》和《ESAIM Control Optim. Calc. Var.》的编委和副主编,及《Acta Appl. Math.》、《J. Math. Anal. Appl.》、《Sci. Rep.》(Nature子刊),《中国科学:数学》(中文版及英文版)等刊编委和《Math. Control Relat. Fields》的主编。