Abstract
This study is concerned with the H{2} state-feedback controller synthesis problem under positivity constraint on the closed-loop system. This problem is believed to be a nonconvex problem in both continuous-and discrete-time system settings and hence remains to be the most challenging issue in positive system theory. For this hard problem, in the discrete-time system setting, the authors recently proposed a technique for the lower bound computation of the best achievable H{2} performance by a specific treatment of finite impulse responses (FIRs) of the closed-loop systems. The goal of this paper is to extend this idea to the continuous-time system setting. Even though there is no notion of FIR in (finite-dimensional) continuous-time system impulse responses, the truncation of the Taylor series expansion of the matrix exponential function in the impulse response paves the way for obtaining a semidefinite programming problem (SDP) for the lower bound computation. We show that, by increasing the truncation degree, we can construct a sequence of SDPs that generates a monotonically non-decreasing sequence of the lower bounds. By combining this lower bound computation technique with heuristic upper bound and suboptimal gain computation techniques, it becomes possible to draw definite conclusion on the quality of the computed suboptimal gains.
| Original language | English |
|---|---|
| Title of host publication | 2019 18th European Control Conference, ECC 2019 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 3797-3802 |
| Number of pages | 6 |
| ISBN (Electronic) | 9783907144008 |
| DOIs | |
| Publication status | Published - Jun 2019 |
| Externally published | Yes |
| Event | 18th European Control Conference, ECC 2019 - Naples, Italy Duration: Jun 25 2019 → Jun 28 2019 |
Publication series
| Name | 2019 18th European Control Conference, ECC 2019 |
|---|
Conference
| Conference | 18th European Control Conference, ECC 2019 |
|---|---|
| Country | Italy |
| City | Naples |
| Period | 6/25/19 → 6/28/19 |
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All Science Journal Classification (ASJC) codes
- Instrumentation
- Control and Optimization
Cite this
H2 state-feedback control for continuous-time systems under positivity constraint. / Ebihara, Yoshio; Colaneri, Patrizio; Geromel, Jose C.
2019 18th European Control Conference, ECC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 3797-3802 8796192 (2019 18th European Control Conference, ECC 2019).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - H2 state-feedback control for continuous-time systems under positivity constraint
AU - Ebihara, Yoshio
AU - Colaneri, Patrizio
AU - Geromel, Jose C.
PY - 2019/6
Y1 - 2019/6
N2 - This study is concerned with the H{2} state-feedback controller synthesis problem under positivity constraint on the closed-loop system. This problem is believed to be a nonconvex problem in both continuous-and discrete-time system settings and hence remains to be the most challenging issue in positive system theory. For this hard problem, in the discrete-time system setting, the authors recently proposed a technique for the lower bound computation of the best achievable H{2} performance by a specific treatment of finite impulse responses (FIRs) of the closed-loop systems. The goal of this paper is to extend this idea to the continuous-time system setting. Even though there is no notion of FIR in (finite-dimensional) continuous-time system impulse responses, the truncation of the Taylor series expansion of the matrix exponential function in the impulse response paves the way for obtaining a semidefinite programming problem (SDP) for the lower bound computation. We show that, by increasing the truncation degree, we can construct a sequence of SDPs that generates a monotonically non-decreasing sequence of the lower bounds. By combining this lower bound computation technique with heuristic upper bound and suboptimal gain computation techniques, it becomes possible to draw definite conclusion on the quality of the computed suboptimal gains.
AB - This study is concerned with the H{2} state-feedback controller synthesis problem under positivity constraint on the closed-loop system. This problem is believed to be a nonconvex problem in both continuous-and discrete-time system settings and hence remains to be the most challenging issue in positive system theory. For this hard problem, in the discrete-time system setting, the authors recently proposed a technique for the lower bound computation of the best achievable H{2} performance by a specific treatment of finite impulse responses (FIRs) of the closed-loop systems. The goal of this paper is to extend this idea to the continuous-time system setting. Even though there is no notion of FIR in (finite-dimensional) continuous-time system impulse responses, the truncation of the Taylor series expansion of the matrix exponential function in the impulse response paves the way for obtaining a semidefinite programming problem (SDP) for the lower bound computation. We show that, by increasing the truncation degree, we can construct a sequence of SDPs that generates a monotonically non-decreasing sequence of the lower bounds. By combining this lower bound computation technique with heuristic upper bound and suboptimal gain computation techniques, it becomes possible to draw definite conclusion on the quality of the computed suboptimal gains.
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UR - http://www.scopus.com/inward/citedby.url?scp=85071602393&partnerID=8YFLogxK
U2 - 10.23919/ECC.2019.8796192
DO - 10.23919/ECC.2019.8796192
M3 - Conference contribution
AN - SCOPUS:85071602393
T3 - 2019 18th European Control Conference, ECC 2019
SP - 3797
EP - 3802
BT - 2019 18th European Control Conference, ECC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
ER -