Optimal tracing of harmonic signals in linear systems with noise in measurements
type: Item
instance of: scholarly article
title: Optimal tracing of harmonic signals in linear systems with noise in measurements
zbMATH Open document ID: 0971.93036
author: A. S. Shiryaev
author: V. A. Yakubovich
published in: Doklady Mathematics
publication date: 2001-02-13T00:00:00Z
review text: Consider a vector linear differential equation \({d\over dt} x(t)= Ax(t)+ bu(t)+ f^0\phi_1(t)\) where \(y(t)\) is a linear combination of \(x(t)\) and \(\phi_2(t)\) while \(z(t)\) is a linear combination of \(x(t)\) and \(u(t)\). The external disturbances \(\phi_1(t)\), \(\phi_2(t)\) are assumed to be harmonic functions. The authors define a class \({\mathcal N}\) of (not necessarily linear) admissible regulators. An admissible regulator is called optimal if it provides a minimum of a certain mean square integral. Under reasonable assumptions it is shown that there exists an optimal universal regulator in \({\mathcal N}\) that is linear.
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 93B51
zbMATH DE Number: 1564340
zbMATH Keywords: harmonic disturbances
zbMATH Keywords: optimal universal regulator
reviewed by: Kenneth S. Miller
MaRDI profile type: Publication
Recommended article: Q3364386
Recommended article: Q4871424
Recommended article: Optimal linear filtering in systems with noise in observations dependent on signal and estimate
Recommended article: Nonlinear least squares estimation for harmonics in multiplicative and additive noise
Recommended article: Optimal measurement of dynamically distorted signals
Recommended article: Harmonic linearization in optimal control
Recommended article: Optimal Input Signals for Parameter Estimation
Recommended article: Optimal Data Detection and Signal Estimation in Systems With Input Noise
Recommended article: Optimal compensation of nonlinearities in the presence of noise
Recommended article: Optimal Estimation for Discrete-Time Linear Systems in the Presence of Multiplicative and Time-Correlated Additive Measurement Noises
description: scientific article; zbMATH DE number 1564340