Reduction of H state feedback control problems for the MIMO servo systems

Hayato Waki, Noboru Sebe

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We deal with H state feedback control problem for the multi-input-multi-output (MIMO) servo system and discuss the advantages of the facial reduction (FR) to the resulting linear matrix inequality (LMI) problems. In fact, as far as our usual setting, the dual of the LMI problem is not strictly feasible because the generalized plant has always stable invariant zeros. Thus FR is available to such LMI problems, and we can reduce and simplify the original LMI problem to a smaller-size LMI problem. As a result, we observe that the numerical performance of the SDP solvers is improved. Also, as a by-product, we obtain the best performance index of the reduced LMI problem with a closed-form expression. This helps the H performance limitation analysis. Another contribution is to reveal that the resulting LMI problem obtained from H control problem has a finite optimal value, but no optimal solutions under an additional assumption. This is also confirmed in the numerical experiment of this paper. FR also plays an essential role in this analysis.

Original languageEnglish
JournalAsian Journal of Control
DOIs
Publication statusAccepted/In press - Jan 1 2018

Fingerprint

Servomechanisms
Linear matrix inequalities
State feedback
Feedback control
Byproducts

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

Cite this

Reduction of H state feedback control problems for the MIMO servo systems. / Waki, Hayato; Sebe, Noboru.

In: Asian Journal of Control, 01.01.2018.

Research output: Contribution to journalArticle

@article{0b5bde4751f3454cb2208f26585192e5,
title = "Reduction of H∞ state feedback control problems for the MIMO servo systems",
abstract = "We deal with H∞ state feedback control problem for the multi-input-multi-output (MIMO) servo system and discuss the advantages of the facial reduction (FR) to the resulting linear matrix inequality (LMI) problems. In fact, as far as our usual setting, the dual of the LMI problem is not strictly feasible because the generalized plant has always stable invariant zeros. Thus FR is available to such LMI problems, and we can reduce and simplify the original LMI problem to a smaller-size LMI problem. As a result, we observe that the numerical performance of the SDP solvers is improved. Also, as a by-product, we obtain the best performance index of the reduced LMI problem with a closed-form expression. This helps the H∞ performance limitation analysis. Another contribution is to reveal that the resulting LMI problem obtained from H∞ control problem has a finite optimal value, but no optimal solutions under an additional assumption. This is also confirmed in the numerical experiment of this paper. FR also plays an essential role in this analysis.",
author = "Hayato Waki and Noboru Sebe",
year = "2018",
month = "1",
day = "1",
doi = "10.1002/asjc.1985",
language = "English",
journal = "Asian Journal of Control",
issn = "1561-8625",
publisher = "National Taiwan University (IEEB)",

}

TY - JOUR

T1 - Reduction of H∞ state feedback control problems for the MIMO servo systems

AU - Waki, Hayato

AU - Sebe, Noboru

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We deal with H∞ state feedback control problem for the multi-input-multi-output (MIMO) servo system and discuss the advantages of the facial reduction (FR) to the resulting linear matrix inequality (LMI) problems. In fact, as far as our usual setting, the dual of the LMI problem is not strictly feasible because the generalized plant has always stable invariant zeros. Thus FR is available to such LMI problems, and we can reduce and simplify the original LMI problem to a smaller-size LMI problem. As a result, we observe that the numerical performance of the SDP solvers is improved. Also, as a by-product, we obtain the best performance index of the reduced LMI problem with a closed-form expression. This helps the H∞ performance limitation analysis. Another contribution is to reveal that the resulting LMI problem obtained from H∞ control problem has a finite optimal value, but no optimal solutions under an additional assumption. This is also confirmed in the numerical experiment of this paper. FR also plays an essential role in this analysis.

AB - We deal with H∞ state feedback control problem for the multi-input-multi-output (MIMO) servo system and discuss the advantages of the facial reduction (FR) to the resulting linear matrix inequality (LMI) problems. In fact, as far as our usual setting, the dual of the LMI problem is not strictly feasible because the generalized plant has always stable invariant zeros. Thus FR is available to such LMI problems, and we can reduce and simplify the original LMI problem to a smaller-size LMI problem. As a result, we observe that the numerical performance of the SDP solvers is improved. Also, as a by-product, we obtain the best performance index of the reduced LMI problem with a closed-form expression. This helps the H∞ performance limitation analysis. Another contribution is to reveal that the resulting LMI problem obtained from H∞ control problem has a finite optimal value, but no optimal solutions under an additional assumption. This is also confirmed in the numerical experiment of this paper. FR also plays an essential role in this analysis.

UR - http://www.scopus.com/inward/record.url?scp=85058052736&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85058052736&partnerID=8YFLogxK

U2 - 10.1002/asjc.1985

DO - 10.1002/asjc.1985

M3 - Article

AN - SCOPUS:85058052736

JO - Asian Journal of Control

JF - Asian Journal of Control

SN - 1561-8625

ER -