勷勤数学•专家报告

题      目：Stochastic Linear-Quadratic Optimal Control with Partial Observation

报  告  人：孙景瑞  副教授  (邀请人：杨舟)

                                  南方科技大学

时      间：9月7日  16：00-17：00

地     点：数科院西楼二楼会议室

报告人简介:

       孙景瑞，南方科技大学副教授。孙景瑞博士毕业于中国科学技术大学，曾先后在香港理工大学、新加坡国立大学、中佛罗里达大学从事科研教学工作，于2019年加盟南方科技大学数学系。孙景瑞博士的研究兴趣主要聚焦于随机控制及相关问题，已在Springer出版专著2部，在SICON、AAP、JDE、SPA、ESAIM: COCV等期刊发表学术论文20余篇。孙博士曾独立获得SIAM颁发的 "SIAG/CST Best SICON Paper Prize"（最佳SICON论文奖），主持（曾主持）多项科研基金，包括国自然优秀青年科学基金项目、国自然面上项目、国自然青年科学基金等。

摘      要：

       In this talk, we study a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the observation system, which in turn is influenced by the control process. The variation method fails in this case due to the interaction of the control and the observation process. To overcome the difficulty, we use the orthogonal decomposition of the state process to write the cost functional as the sum of two parts: one is a functional of the control and the filtering process, and the other part is independent of the choice of the control. The first part possesses a mathematical structure similar to the full information problem. By completing the square, we demonstrate that the open-loop optimal control is given by a feedback representation via the filtering process.

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