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Seminar on Control Theory and Nonlinear Filtering
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
Organizer
Speaker
Time
Tuesday, January 31, 2023 9:30 PM - 10:00 PM
Venue
Online
Abstract
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.
Speaker Intro
Jiao Xiaopei graduated with a bachelor's degree from the Zhi Yuan College of Shanghai Jiao Tong University (Physics Department) in 2017 and obtained his PhD from the Department of Mathematical Sciences at Tsinghua University in 2022, under the guidance of Professor Stephen Shing-Toung Yau (IEEE Fellow, former tenured professor at the University of Illinois at Chicago). He has conducted postdoctoral research at the Beijing Institute of Mathematica Science and Application and at the University of Twente in the Netherlands (under the guidance of Professor Johannes Schmidt-Hieber, Fellow of the Institute of Mathematical Statistics). His current research interests include control theory, numerical partial differential equations, and bioinformatics.