北京雁栖湖应用数学研究院

丘成栋

焦小沛

2023年02月21日 21:30 至 22:00

Online

Ever since Brockett, Clark and Mitter introduced the estimation algebra method, it becomes a powerful tool to classify the finite dimensional filtering system. In this paper, we investigate estimation algebra on state dimension $n$ and linear rank $n-1$, especially case of $n=4$. Mitter conjecture is always a key question on classification of estimation algebra. Weaker form of Mitter conjecture states observation functions in finite dimensional filters are affine functions. In this paper, we will focus on weaker form of Mitter conjecture. In the first part, it will be shown that a sufficient condition of weaker Mitter conjecture is partially constant structure of $Omega$. In the second part, partially constant structure of $Omega$ will be proven true and weaker Mitter conjecture hold for $n=4$ case.

焦小沛，于2017年本科毕业于上海交通大学致远学院（物理班），2022年博士毕业于清华大学数学科学系，师从丘成栋教授（IEEE fellow，前美国伊利诺伊大学芝加哥分校终身教授）。先后在北京雁栖湖应用数学研究院，荷兰特文特大学从事博士后工作（导师Johannes Schmidt-Hieber教授，国际数理统计学会会士）。现研究方向包括控制理论，数值偏微分方程，生物信息学。获得2025年国家青年科学基金[C类]资助。