Beijing Institute of Mathematical Sciences and Applications

Shing Toung Yau

Xiao Pei Jiao

Tuesday, February 21, 2023 9:30 PM - 10:00 PM

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.

Xiaopei Jiao received his bachelor's degree from the Zhiyuan College of Shanghai Jiao Tong University and his Ph.D. from the Department of Mathematical Sciences at Tsinghua University. He subsequently worked as a postdoctoral researcher at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) and at the University of Twente in the Netherlands. His current research interests include finite-dimensional filtering theory, Yau-Yau filtering methods, physics-informed neural networks, and bioinformatics. His research focuses primarily on: (1) using geometric tools such as Lie algebras for solving partial differential equations and classifying nonlinear systems; (2) designing novel numerical algorithms based on physics-informed neural networks.