Advanced

On H-infinity Control and Large-Scale Systems

Bergeling, Carolina LU (2019) In PhD Theses
Abstract
In this thesis, a class of linear time-invariant systems is identified for which a particular type of H-infinity optimal control problem can be solved explicitly. It follows that the synthesized controller can be given on a simple explicit form. More specifically, the controller can be written in terms of the matrices of the system’s state-space representation. The result has applications in the control of large-scale systems, as well as for the control of infinite-dimensional systems, with certain properties.

For the large-scale applications considered, the controller is both globally optimal as well as possesses a structure compatible with the information-structure of the system. This decentralized property of the controller is... (More)
In this thesis, a class of linear time-invariant systems is identified for which a particular type of H-infinity optimal control problem can be solved explicitly. It follows that the synthesized controller can be given on a simple explicit form. More specifically, the controller can be written in terms of the matrices of the system’s state-space representation. The result has applications in the control of large-scale systems, as well as for the control of infinite-dimensional systems, with certain properties.

For the large-scale applications considered, the controller is both globally optimal as well as possesses a structure compatible with the information-structure of the system. This decentralized property of the controller is obtained without any structural constraints or regularization techniques being part of the synthesis procedure. Instead, it is a result of its particular form. Examples of applications are electrical networks, temperature dynamics in buildings and water irrigation systems.

In the infinite-dimensional case, the explicitly stated controller solves the infinite-dimensional H-infinity synthesis problem directly without the need of approximation techniques. An important application is diffusion equations. Moreover, the presented results can be used for evaluation and benchmarking of general purpose algorithms for H-infinity control.

The systems considered in this thesis are shown to belong to a larger class of systems for which the H-infinity optimal control problem can be translated into a static problem at a single frequency. In certain cases, the static problem can be solved through a simple least-squares argument. This procedure is what renders the simple and explicit expression of the controller previously described. Moreover, the given approach is in contrast to conventional methods to the problem of H-infinity control, as they are in general performed numerically.
(Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Associate professor Gayme, Dennice, Department of Mechanical Engineering, Johns Hopkins University, Whiting School of Engineering
organization
publishing date
type
Thesis
publication status
published
subject
keywords
H-infinity Control, Decentralized Control, Large-Scale Systems, Infinite-Dimensional Systems
in
PhD Theses
pages
143 pages
publisher
Department of Automatic Control, Lund Institute of Technology, Lund University
defense location
M:B, M-huset, Lunds Tekniska Högskola
defense date
2019-06-05 10:15:00
ISSN
0280-5316
ISBN
978-91-7895-095-9
978-91-7895-096-6
project
Distributed Control and Verification
language
English
LU publication?
yes
id
5f06f32c-95e8-4742-a8cc-fe560717edc6
date added to LUP
2019-05-07 15:03:33
date last changed
2019-05-10 14:34:30
@phdthesis{5f06f32c-95e8-4742-a8cc-fe560717edc6,
  abstract     = {In this thesis, a class of linear time-invariant systems is identified for which a particular type of H-infinity optimal control problem can be solved explicitly. It follows that the synthesized controller can be given on a simple explicit form. More specifically, the controller can be written in terms of the matrices of the system’s state-space representation. The result has applications in the control of large-scale systems, as well as for the control of infinite-dimensional systems, with certain properties. <br/><br/>For the large-scale applications considered, the controller is both globally optimal as well as possesses a structure compatible with the information-structure of the system. This decentralized property of the controller is obtained without any structural constraints or regularization techniques being part of the synthesis procedure. Instead, it is a result of its particular form.  Examples of applications are electrical networks, temperature dynamics in buildings and water irrigation systems.<br/><br/>In the infinite-dimensional case, the explicitly stated controller solves the infinite-dimensional H-infinity synthesis problem directly without the need of approximation techniques. An important application is diffusion equations. Moreover, the presented results can be used for evaluation and benchmarking of general purpose algorithms for H-infinity control.<br/><br/>The systems considered in this thesis are shown to belong to a larger class of systems for which the H-infinity optimal control problem can be translated into a static problem at a single frequency. In certain cases, the static problem can be solved through a simple least-squares argument. This procedure is what renders the simple and explicit expression of the controller previously described. Moreover, the given approach is in contrast to conventional methods to the problem of H-infinity control, as they are in general performed numerically. <br/>},
  author       = {Bergeling, Carolina},
  isbn         = {978-91-7895-095-9},
  issn         = {0280-5316},
  language     = {eng},
  publisher    = {Department of Automatic Control, Lund Institute of Technology, Lund University},
  school       = {Lund University},
  series       = {PhD Theses},
  title        = {On H-infinity Control and Large-Scale Systems},
  url          = {https://lup.lub.lu.se/search/ws/files/63879983/CarolinaBergelingPhDThesisExcludedNonPublishedPapers.pdf},
  year         = {2019},
}