Design of a controller using successive approximation for singularly perturbed bilinear systems

Jae Won Chang, Beom Soo Kim, Myo Taeg Lim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

The infinite time optimum to regulate the problem of singularly perturbed bilinear systems with a quadratic performance criterion is obtained by a sequence of algebraic Lyapunov equations. The new approach is based on the successive approximation. In particular, the order reduction is achieved by using suitable state transformation so that the original Lyapunov equations are decomposed into the reduced-order local Lyapunov equations. In addition, the slow part of the solution and the fast part solution are now completely decoupled so that the numerical ill-conditioning is removed. The proposed algorithms not only solve optimal control problems in the singularly perturbed bilinear system but also reduce the computation time. This paper also includes an example to demonstrate the procedure.

Original languageEnglish
Title of host publicationIEEE Conference on Control Applications - Proceedings
Pages657-661
Number of pages5
Publication statusPublished - 2001 Dec 1
EventProceedings of the 2001 IEEE International Conference on Control Applications CCA '01 - Mexico City, Mexico
Duration: 2001 Sep 52001 Sep 7

Other

OtherProceedings of the 2001 IEEE International Conference on Control Applications CCA '01
CountryMexico
CityMexico City
Period01/9/501/9/7

Fingerprint

Controllers

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Chang, J. W., Kim, B. S., & Lim, M. T. (2001). Design of a controller using successive approximation for singularly perturbed bilinear systems. In IEEE Conference on Control Applications - Proceedings (pp. 657-661)

Design of a controller using successive approximation for singularly perturbed bilinear systems. / Chang, Jae Won; Kim, Beom Soo; Lim, Myo Taeg.

IEEE Conference on Control Applications - Proceedings. 2001. p. 657-661.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Chang, JW, Kim, BS & Lim, MT 2001, Design of a controller using successive approximation for singularly perturbed bilinear systems. in IEEE Conference on Control Applications - Proceedings. pp. 657-661, Proceedings of the 2001 IEEE International Conference on Control Applications CCA '01, Mexico City, Mexico, 01/9/5.
Chang JW, Kim BS, Lim MT. Design of a controller using successive approximation for singularly perturbed bilinear systems. In IEEE Conference on Control Applications - Proceedings. 2001. p. 657-661
Chang, Jae Won ; Kim, Beom Soo ; Lim, Myo Taeg. / Design of a controller using successive approximation for singularly perturbed bilinear systems. IEEE Conference on Control Applications - Proceedings. 2001. pp. 657-661
@inproceedings{dd23c440fe0d4778a372f60713d6d2b1,
title = "Design of a controller using successive approximation for singularly perturbed bilinear systems",
abstract = "The infinite time optimum to regulate the problem of singularly perturbed bilinear systems with a quadratic performance criterion is obtained by a sequence of algebraic Lyapunov equations. The new approach is based on the successive approximation. In particular, the order reduction is achieved by using suitable state transformation so that the original Lyapunov equations are decomposed into the reduced-order local Lyapunov equations. In addition, the slow part of the solution and the fast part solution are now completely decoupled so that the numerical ill-conditioning is removed. The proposed algorithms not only solve optimal control problems in the singularly perturbed bilinear system but also reduce the computation time. This paper also includes an example to demonstrate the procedure.",
author = "Chang, {Jae Won} and Kim, {Beom Soo} and Lim, {Myo Taeg}",
year = "2001",
month = "12",
day = "1",
language = "English",
pages = "657--661",
booktitle = "IEEE Conference on Control Applications - Proceedings",

}

TY - GEN

T1 - Design of a controller using successive approximation for singularly perturbed bilinear systems

AU - Chang, Jae Won

AU - Kim, Beom Soo

AU - Lim, Myo Taeg

PY - 2001/12/1

Y1 - 2001/12/1

N2 - The infinite time optimum to regulate the problem of singularly perturbed bilinear systems with a quadratic performance criterion is obtained by a sequence of algebraic Lyapunov equations. The new approach is based on the successive approximation. In particular, the order reduction is achieved by using suitable state transformation so that the original Lyapunov equations are decomposed into the reduced-order local Lyapunov equations. In addition, the slow part of the solution and the fast part solution are now completely decoupled so that the numerical ill-conditioning is removed. The proposed algorithms not only solve optimal control problems in the singularly perturbed bilinear system but also reduce the computation time. This paper also includes an example to demonstrate the procedure.

AB - The infinite time optimum to regulate the problem of singularly perturbed bilinear systems with a quadratic performance criterion is obtained by a sequence of algebraic Lyapunov equations. The new approach is based on the successive approximation. In particular, the order reduction is achieved by using suitable state transformation so that the original Lyapunov equations are decomposed into the reduced-order local Lyapunov equations. In addition, the slow part of the solution and the fast part solution are now completely decoupled so that the numerical ill-conditioning is removed. The proposed algorithms not only solve optimal control problems in the singularly perturbed bilinear system but also reduce the computation time. This paper also includes an example to demonstrate the procedure.

UR - http://www.scopus.com/inward/record.url?scp=0035692141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035692141&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0035692141

SP - 657

EP - 661

BT - IEEE Conference on Control Applications - Proceedings

ER -