Abstract
Strong feasibility (a.k.a. strict feasibility) of the dual problem of a given linear matrix inequality (LMI) is an important property to guarantee the existence of an optimal solution of the LMI problem. In particular, the LMI problem may not have any optimal solutions if the dual is not strongly feasible. This implies that the computed solutions by SDP solvers may be meaningless and useless for designing the controllers of H∞ output feedback control problems. The facial reduction is a tool to analyze and reduce such non-strongly feasible problems. We introduce the strong feasibility of the dual and facial reduction and provide the necessary and sufficient condition on the strong feasibility. Furthermore, we reveal that the condition is closely related to invariant zeros in the plant.
| Original language | English |
|---|---|
| Title of host publication | SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 47-53 |
| Number of pages | 7 |
| ISBN (Electronic) | 9784907764586 |
| DOIs | |
| Publication status | Published - Apr 2 2018 |
| Event | 2018 SICE International Symposium on Control Systems, SICE ISCS 2018 - Tokyo, Japan Duration: Mar 9 2018 → Mar 11 2018 |
Publication series
| Name | SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems |
|---|---|
| Volume | 2018-January |
Other
| Other | 2018 SICE International Symposium on Control Systems, SICE ISCS 2018 |
|---|---|
| Country | Japan |
| City | Tokyo |
| Period | 3/9/18 → 3/11/18 |
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All Science Journal Classification (ASJC) codes
- Process Chemistry and Technology
- Energy Engineering and Power Technology
- Electrical and Electronic Engineering
- Control and Optimization
Cite this
Strong feasibility of the dual problem of linear matrix inequality for H∞ output feedback control problem. / Waki, Hayato; Sebe, Noboru.
SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems. Institute of Electrical and Electronics Engineers Inc., 2018. p. 47-53 (SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems; Vol. 2018-January).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Strong feasibility of the dual problem of linear matrix inequality for H∞ output feedback control problem
AU - Waki, Hayato
AU - Sebe, Noboru
PY - 2018/4/2
Y1 - 2018/4/2
N2 - Strong feasibility (a.k.a. strict feasibility) of the dual problem of a given linear matrix inequality (LMI) is an important property to guarantee the existence of an optimal solution of the LMI problem. In particular, the LMI problem may not have any optimal solutions if the dual is not strongly feasible. This implies that the computed solutions by SDP solvers may be meaningless and useless for designing the controllers of H∞ output feedback control problems. The facial reduction is a tool to analyze and reduce such non-strongly feasible problems. We introduce the strong feasibility of the dual and facial reduction and provide the necessary and sufficient condition on the strong feasibility. Furthermore, we reveal that the condition is closely related to invariant zeros in the plant.
AB - Strong feasibility (a.k.a. strict feasibility) of the dual problem of a given linear matrix inequality (LMI) is an important property to guarantee the existence of an optimal solution of the LMI problem. In particular, the LMI problem may not have any optimal solutions if the dual is not strongly feasible. This implies that the computed solutions by SDP solvers may be meaningless and useless for designing the controllers of H∞ output feedback control problems. The facial reduction is a tool to analyze and reduce such non-strongly feasible problems. We introduce the strong feasibility of the dual and facial reduction and provide the necessary and sufficient condition on the strong feasibility. Furthermore, we reveal that the condition is closely related to invariant zeros in the plant.
UR - http://www.scopus.com/inward/record.url?scp=85049335246&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85049335246&partnerID=8YFLogxK
U2 - 10.23919/SICEISCS.2018.8330155
DO - 10.23919/SICEISCS.2018.8330155
M3 - Conference contribution
T3 - SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems
SP - 47
EP - 53
BT - SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems
PB - Institute of Electrical and Electronics Engineers Inc.
ER -