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Optimal H-infinity state feedback for systems with symmetric and Hurwitz state matrix

Lidström, Carolina LU and Rantzer, Anders LU (2016) American Control Conference, 2016 In American Control Conference (ACC), 2016 p.3366-3371
Abstract
We address H-infinity state feedback and give a simple form for an optimal control law applicable to linear time invariant systems with symmetric and Hurwitz state matrix. More specifically, the control law as well as the minimal value of the norm can be expressed in the matrices of the system's state space representation, given separate cost on state and control input. Thus, the control law is transparent, easy to synthesize and scalable. If the plant possesses a compatible sparsity pattern, it is also distributed. Examples of such sparsity patterns are included. Furthermore, if the state matrix is diagonal and the control input matrix is a node-link incidence matrix, the open-loop system's property of internal positivity is preserved by... (More)
We address H-infinity state feedback and give a simple form for an optimal control law applicable to linear time invariant systems with symmetric and Hurwitz state matrix. More specifically, the control law as well as the minimal value of the norm can be expressed in the matrices of the system's state space representation, given separate cost on state and control input. Thus, the control law is transparent, easy to synthesize and scalable. If the plant possesses a compatible sparsity pattern, it is also distributed. Examples of such sparsity patterns are included. Furthermore, if the state matrix is diagonal and the control input matrix is a node-link incidence matrix, the open-loop system's property of internal positivity is preserved by the control law. Finally, we give an extension of the optimal control law that incorporate coordination among subsystems. Examples demonstrate the simplicity in synthesis and performance of the optimal control law. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Distributed Control, Linear Systems, H-infinity control
in
American Control Conference (ACC), 2016
pages
6 pages
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
conference name
American Control Conference, 2016
external identifiers
  • scopus:84992108759
ISBN
978-1-4673-8682-1
978-1-4673-8683-8
DOI
10.1109/ACC.2016.7525437
language
English
LU publication?
yes
id
15403740-baf4-4f8b-9426-7f1302dde3e1
date added to LUP
2016-11-30 09:52:03
date last changed
2017-02-13 10:42:44
@inproceedings{15403740-baf4-4f8b-9426-7f1302dde3e1,
  abstract     = {We address H-infinity state feedback and give a simple form for an optimal control law applicable to linear time invariant systems with symmetric and Hurwitz state matrix. More specifically, the control law as well as the minimal value of the norm can be expressed in the matrices of the system's state space representation, given separate cost on state and control input. Thus, the control law is transparent, easy to synthesize and scalable. If the plant possesses a compatible sparsity pattern, it is also distributed. Examples of such sparsity patterns are included. Furthermore, if the state matrix is diagonal and the control input matrix is a node-link incidence matrix, the open-loop system's property of internal positivity is preserved by the control law. Finally, we give an extension of the optimal control law that incorporate coordination among subsystems. Examples demonstrate the simplicity in synthesis and performance of the optimal control law.},
  author       = {Lidström, Carolina and Rantzer, Anders},
  booktitle    = {American Control Conference (ACC), 2016},
  isbn         = {978-1-4673-8682-1},
  keyword      = {Distributed Control,Linear Systems,H-infinity control},
  language     = {eng},
  pages        = {3366--3371},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  title        = {Optimal H-infinity state feedback for systems with symmetric and Hurwitz state matrix},
  url          = {http://dx.doi.org/10.1109/ACC.2016.7525437},
  year         = {2016},
}