Reduced-order solution of the weakly coupled matrix difference Riccati equation

Xuemin Shen; Zoran Gajic; Muhammad T. Qureshi

doi:10.23919/acc.1991.4791838

Reduced-order solution of the weakly coupled matrix difference Riccati equation

Xuemin Shen, Zoran Gajic, Muhammad T. Qureshi

Institute for Quantitative Biomedicine (IQB)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

A method of obtaining the solution of the weakly coupled matrix difference Riccati equation by solving two reduced-order linear difference equations is presented. The order reduction is achieved by using a decoupling transformation applied to the Hamiltonian matrix of a weakly coupled discrete linear-quadratic control problem. Since the decoupling transformation can be obtained, up to an arbitrary degree of accuracy at very low cost, this approach produces an efficient numerical method for solving the weakly coupled difference Riccati equation.

Original language	English (US)
Title of host publication	Proceedings of the American Control Conference
Publisher	Publ by American Automatic Control Council
Pages	2437-2438
Number of pages	2
ISBN (Print)	0879425652, 9780879425654
DOIs	https://doi.org/10.23919/acc.1991.4791838
State	Published - 1991
Event	Proceedings of the 1991 American Control Conference - Boston, MA, USA Duration: Jun 26 1991 → Jun 28 1991

Publication series

Name	Proceedings of the American Control Conference
Volume	3
ISSN (Print)	0743-1619

Other

Other	Proceedings of the 1991 American Control Conference
City	Boston, MA, USA
Period	6/26/91 → 6/28/91

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

Access to Document

10.23919/acc.1991.4791838

Cite this

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title = "Reduced-order solution of the weakly coupled matrix difference Riccati equation",

abstract = "A method of obtaining the solution of the weakly coupled matrix difference Riccati equation by solving two reduced-order linear difference equations is presented. The order reduction is achieved by using a decoupling transformation applied to the Hamiltonian matrix of a weakly coupled discrete linear-quadratic control problem. Since the decoupling transformation can be obtained, up to an arbitrary degree of accuracy at very low cost, this approach produces an efficient numerical method for solving the weakly coupled difference Riccati equation.",

author = "Xuemin Shen and Zoran Gajic and Qureshi, {Muhammad T.}",

year = "1991",

doi = "10.23919/acc.1991.4791838",

language = "English (US)",

isbn = "0879425652",

series = "Proceedings of the American Control Conference",

publisher = "Publ by American Automatic Control Council",

pages = "2437--2438",

booktitle = "Proceedings of the American Control Conference",

note = "Proceedings of the 1991 American Control Conference ; Conference date: 26-06-1991 Through 28-06-1991",

}

Shen, X, Gajic, Z & Qureshi, MT 1991, Reduced-order solution of the weakly coupled matrix difference Riccati equation. in Proceedings of the American Control Conference. Proceedings of the American Control Conference, vol. 3, Publ by American Automatic Control Council, pp. 2437-2438, Proceedings of the 1991 American Control Conference, Boston, MA, USA, 6/26/91. https://doi.org/10.23919/acc.1991.4791838

Reduced-order solution of the weakly coupled matrix difference Riccati equation. / Shen, Xuemin; Gajic, Zoran; Qureshi, Muhammad T.
Proceedings of the American Control Conference. Publ by American Automatic Control Council, 1991. p. 2437-2438 (Proceedings of the American Control Conference; Vol. 3).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Gajic, Zoran

AU - Qureshi, Muhammad T.

PY - 1991

Y1 - 1991

N2 - A method of obtaining the solution of the weakly coupled matrix difference Riccati equation by solving two reduced-order linear difference equations is presented. The order reduction is achieved by using a decoupling transformation applied to the Hamiltonian matrix of a weakly coupled discrete linear-quadratic control problem. Since the decoupling transformation can be obtained, up to an arbitrary degree of accuracy at very low cost, this approach produces an efficient numerical method for solving the weakly coupled difference Riccati equation.

AB - A method of obtaining the solution of the weakly coupled matrix difference Riccati equation by solving two reduced-order linear difference equations is presented. The order reduction is achieved by using a decoupling transformation applied to the Hamiltonian matrix of a weakly coupled discrete linear-quadratic control problem. Since the decoupling transformation can be obtained, up to an arbitrary degree of accuracy at very low cost, this approach produces an efficient numerical method for solving the weakly coupled difference Riccati equation.

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T3 - Proceedings of the American Control Conference

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BT - Proceedings of the American Control Conference

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T2 - Proceedings of the 1991 American Control Conference

Y2 - 26 June 1991 through 28 June 1991

ER -

Reduced-order solution of the weakly coupled matrix difference Riccati equation

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