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The use of operator factorization for linear control and estimation

Hagander, Per LU (1973) In Automatica 9(5). p.623-631
Abstract
The linear filtering, prediction and smoothing problems as well as the linear quadratic control problems can very generally be formulated as operator equations using basic linear algebra.

The equations are of Fredholm type II, and they are difficult to solve directly.

It is shown how the operator can be factorized into two Volterra operators using a matrix Riccati equation. Recursive solution of these triangular operator equations is then obtained by two initial value differential equations.

The proofs of smoothing and optimal control under known disturbances are in this way especially clear and simple.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Automatica
volume
9
issue
5
pages
623 - 631
publisher
Pergamon
external identifiers
  • scopus:49549160811
ISSN
0005-1098
DOI
10.1016/0005-1098(73)90047-2
language
English
LU publication?
yes
id
1d66bff4-6a1a-4cf2-847a-80e3e754a5f7
date added to LUP
2016-06-24 14:35:50
date last changed
2019-01-06 12:25:47
@article{1d66bff4-6a1a-4cf2-847a-80e3e754a5f7,
  abstract     = {The linear filtering, prediction and smoothing problems as well as the linear quadratic control problems can very generally be formulated as operator equations using basic linear algebra.<br/><br/>The equations are of Fredholm type II, and they are difficult to solve directly.<br/><br/>It is shown how the operator can be factorized into two Volterra operators using a matrix Riccati equation. Recursive solution of these triangular operator equations is then obtained by two initial value differential equations.<br/><br/>The proofs of smoothing and optimal control under known disturbances are in this way especially clear and simple.},
  author       = {Hagander, Per},
  issn         = {0005-1098},
  language     = {eng},
  number       = {5},
  pages        = {623--631},
  publisher    = {Pergamon},
  series       = {Automatica},
  title        = {The use of operator factorization for linear control and estimation},
  url          = {http://dx.doi.org/10.1016/0005-1098(73)90047-2},
  volume       = {9},
  year         = {1973},
}