The Covariance Extension Equation: A Riccati-Type Approach to Analytic Interpolation

被引：3

作者：

Cui, Yufang ^{[1
]}

Lindquist, Anders ^{[1
,2
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Automat, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2022年 / 67卷 / 11期

关键词：

Interpolation; Mathematical models; Robust control; Kalman filters; Covariance matrices; White noise; Signal processing; Analytic interpolation; moment problems; model reduction; robust control; spectral estimation; sensitivity shaping; NEVANLINNA-PICK INTERPOLATION; CONVEX-OPTIMIZATION APPROACH; SPECTRAL ESTIMATION; IDENTIFICATION; REALIZATION; ENTROPY;

D O I：

10.1109/TAC.2021.3122367

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Analytic interpolation problems with rationality and derivative constraints are ubiquitous in systems and control. This article provides a new method for such problems, both in the scalar and matrix case, based on a nonstandard Riccati-type equation. The rank of the solution matrix is the same as the degree of the interpolant, thus providing a natural approach to model reduction. A homotopy continuation method is presented and applied to some problems in modeling and robust control. We also address a question on the positive degree of a covariance sequence originally posed by Kalman.

引用

页码：5825 / 5840

页数：16

共 47 条

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