BIMSA > Seminar on Control Theory and Nonlinear Filtering Explicit Solution of the Generalized Kolmogorov Equation in Brockett-Mitter Program
Explicit Solution of the Generalized Kolmogorov Equation in Brockett-Mitter Program
Organizer
Shing Toung Yau
Speaker
Minli Feng
Time
Monday, July 3, 2023 3:00 PM - 3:30 PM
Venue
数学系理科楼A-304
Abstract
Ever since the technique of the Kalman-Bucy filter was popularized, there has been an intense interest in finding new classes of finite-dimensional recursive filters. In the late 1970s the concept of the estimation algebra of a filtering system was introduced. In 1990, Tam, Wong, and Yau presented a rigorous proof of the Brocket-Mitter program which allows one to construct finite-dimensional recursive filters from finite-dimensional estimation algebras. Later Yau wrote down explicitly a system of ordinary differential equations and generalized Kolmogorov equation to which the robust DMZ equation can be reduced. Thus there remains three fundamental problems in Brockett-Mitter program, first of which is the problem of finding explicit solution to the generalized Kolmogorov equation. We will share these results in the presentation.