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Finite dimensional estimation algebra on arbitrary state dimension with nonmaximal rank: linear structure of Wong matrix
Finite dimensional estimation algebra on arbitrary state dimension with nonmaximal rank: linear structure of Wong matrix
组织者
演讲者
时间
2023年01月31日 21:30 至 22:00
地点
Online
摘要
Ever since Brockett, Clark and Mitter introduced estimation algebra method, it becomes powerful tool to classify the finite dimensional filtering system. In this paper, we investigate finite dimensional estimation algebra with non-maximal rank. Structure of Omega will be focused on which is critical for known classification of estimation algebra. In this paper, we first consider general estimation algebra with non-maximal rank and determine the linear structure of submatrix of Omega by using rank condition and quality of Euler operator. In the second part, we proceed to consider case of linear rank n-1 and prove the linear structure of Omega. Finally, we give the structure of nonlinear filters which implies the drift term must be a quadratic function plus a gradient of smooth function.
演讲者介绍
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。