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 language | English |
|---|---|
| Journal | Asian Journal of Control |
| DOIs | |
| Publication status | Accepted/In press - Jan 1 2018 |
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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 journal › Article
}
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.
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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 -