H2 state-feedback control for continuous-time systems under positivity constraint

Yoshio Ebihara, Patrizio Colaneri, Jose C. Geromel

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

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 languageEnglish
Title of host publication2019 18th European Control Conference, ECC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3797-3802
Number of pages6
ISBN (Electronic)9783907144008
DOIs
Publication statusPublished - Jun 2019
Externally publishedYes
Event18th European Control Conference, ECC 2019 - Naples, Italy
Duration: Jun 25 2019Jun 28 2019

Publication series

Name2019 18th European Control Conference, ECC 2019

Conference

Conference18th European Control Conference, ECC 2019
CountryItaly
CityNaples
Period6/25/196/28/19

Fingerprint

Continuous time systems
State Feedback Control
Continuous-time Systems
Impulse Response
Impulse response
State feedback
feedback control
Positivity
Feedback control
impulses
Lower bound
Discrete-time Systems
Closed loop systems
Truncation
Closed-loop System
site data processors
Positive Systems
Matrix Exponential
Taylor Series Expansion
Taylor series

All Science Journal Classification (ASJC) codes

  • Instrumentation
  • Control and Optimization

Cite this

Ebihara, Y., Colaneri, P., & Geromel, J. C. (2019). H2 state-feedback control for continuous-time systems under positivity constraint. In 2019 18th European Control Conference, ECC 2019 (pp. 3797-3802). [8796192] (2019 18th European Control Conference, ECC 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ECC.2019.8796192

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 proceedingConference contribution

Ebihara, Y, Colaneri, P & Geromel, JC 2019, H2 state-feedback control for continuous-time systems under positivity constraint. in 2019 18th European Control Conference, ECC 2019., 8796192, 2019 18th European Control Conference, ECC 2019, Institute of Electrical and Electronics Engineers Inc., pp. 3797-3802, 18th European Control Conference, ECC 2019, Naples, Italy, 6/25/19. https://doi.org/10.23919/ECC.2019.8796192
Ebihara Y, Colaneri P, Geromel JC. H2 state-feedback control for continuous-time systems under positivity constraint. In 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). https://doi.org/10.23919/ECC.2019.8796192
Ebihara, Yoshio ; Colaneri, Patrizio ; Geromel, Jose C. / H2 state-feedback control for continuous-time systems under positivity constraint. 2019 18th European Control Conference, ECC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 3797-3802 (2019 18th European Control Conference, ECC 2019).
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