日产精品一致六区搬运工数学科学学院
荔园杰出学者讲座第二十八期
讲座题目：Linear-Quadratic Optimal Control Problem for Mean-Field SDEs with Certain Random Coefficients
主讲人：雍炯敏 教授（中佛罗里达大学）
讲座时间：2024年6月24日上午10:30-11:30
讲座地点：日产精品一致六区搬运工粤海校区汇星楼一号教室
内容概述： Motivated by linear-quadratic optimal control problems for mean-field SDEs with regime switching, we formulate an LQ problem governed by a standard Brownian motion, with the coefficients of the state equation and the weighting matrices/vectors being adapted to the filtration generated by the Markov chain independent of the Brownian motion governing the state equation. Through such a problem, we are going to approach our LQ problem in the following aspects: (i) Classical completing the squares gives a sufficient condition for the open-loop solvability of the LQ problem. However, this method is relevant to the optimality system (or Pantryagin’s maximum principle), and therefore the optimal control could be anticipating which is not practical feasible. This leads to the following question: (ii) Does the optimal control admit a non-anticipating representation? Under certain conditions, we found a closed-loop representation of open-loop optimal control, which is non -anticipating. Then it is natural to ask whether such a representation is itself optimal within the class of closed-loop controls. This leads to the problem (iii) the closed-loop solvability of our LQ problem, a characterization of which results in the solvability of Riccati equation. Finally, both open-loop and closed-loop solvability will be implied by the unform convexity of the cost functional in the control.
主讲人简介：雍炯敏，1982年本科毕业于复旦大学数学系，1986年在美国普渡大学获得博士学位。1988年应聘复旦大学数学系副教授，1991年晋升教授，1993年评为博士生导师，1997年获国家“杰出青年基金”，2000年至2003年担任复旦大学原数学系主任。雍炯敏教授自2003年秋季起任美国中佛罗里达大学数学系教授至今。雍炯敏教授曾于1992年获得“中国青年科技奖”，1995年获得“全国优秀教师”奖，1999年荣获“上海市科技进步一等奖”，2001年获得“上海市科技精英”称号，2002年荣获“苏步青数学奖”，2001年、2005年获得全国百篇优博指导教师，2011年获得美国工业与应用数学会SIAG/CST SICON最佳论文奖，2014年应邀在国际数学家大会作45分钟报告。
欢迎师生参加！
邀请人：数学科学学院
数学科学学院
2024年06月20日
