Stochastic perturbation method for optimal control problems governed by PDEs with small uncertainties

主讲人：孙同军

摘要：In this talk, we investigate the first-order and second-order perturbation approximation schemes for optimal control problems governed by elliptic/parabolic PDEs with small uncertainties. First, we propose the finite dimensional noise assumption for the random coefficient, and expand the state and co-state variables up to a certain order with respect to a small parameter by using the perturbation technique. Then, we insert all the expansions into the known deterministic parametric optimality system, and obtain the first-order and second-order optimality systems. These two systems are discretized by the finite element method to establish the first-order and second-order approximate schemes. Further, a priori / posteriori error estimates are derived for the state, co-state and control variables of the first-order and second-order approximation, respectively. Finally, some numerical experiments are presented to verify the theoretical results.

主讲人简介：孙同军，山东大学数学学院教授、博士生导师。主要从事计算数学专业的教学和科研工作。 中国工业与应用数学学会不确定性量化专委会委员、金融科技与算法专委会委员，中国计算物理学会计算石油地质专委会委员，山东数学会计算数学专委会委员。担任国家和多个省份自然科学基金、教育部学位中心的通讯评审专家，计算数学领域内多个国际知名期刊的审稿人，美国数学会Mathematical Reviews评论人。曾在日本、加拿大和英国的多所大学留学和访问。 研究方向：偏微分方程数值解法的理论及应用。近几年，在带有随机项系数的偏微分方程最优控制问题的数值方法等方面获得了一些研究成果。主持了国家、教育部和山东省的自然科学基金项目6项。 作为主要成员参加了国家和省部级的自然科学基金项目10余项。已在国内外学术刊物上发表论文50余篇，其中SCI期刊论文30余篇。

邀请人：明炬

时间：2023年5月16日（星期二）16:00-17:30