- 控制理论和非线性滤波讨论班

Finite dimensional estimation algebra on arbitrary state dimension with nonmaximal rank: linear structure of Wong matrix

组织者

丘成栋

演讲者

焦小沛

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，本科毕业于上海交通大学致远学院，博士毕业于清华大学数学科学系。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。现研究方向包括有限维滤波理论，丘-丘滤波方法，物理信息神经网络以及生物信息学。研究兴趣主要集中于（1）利用李代数等几何工具进行偏微分方程求解与有限维滤波系统的分类；（2）设计基于物理信息神经网络的新型数值算法。