On Hinfinity Control and LargeScale Systems
(2019) In PhD Theses Abstract
 In this thesis, a class of linear timeinvariant systems is identified for which a particular type of Hinfinity 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 statespace representation. The result has applications in the control of largescale systems, as well as for the control of infinitedimensional systems, with certain properties.
For the largescale applications considered, the controller is both globally optimal as well as possesses a structure compatible with the informationstructure of the system. This decentralized property of the controller is... (More)  In this thesis, a class of linear timeinvariant systems is identified for which a particular type of Hinfinity 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 statespace representation. The result has applications in the control of largescale systems, as well as for the control of infinitedimensional systems, with certain properties.
For the largescale applications considered, the controller is both globally optimal as well as possesses a structure compatible with the informationstructure 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 infinitedimensional case, the explicitly stated controller solves the infinitedimensional Hinfinity 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 Hinfinity control.
The systems considered in this thesis are shown to belong to a larger class of systems for which the Hinfinity 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 leastsquares 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 Hinfinity control, as they are in general performed numerically.
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Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5f06f32c95e84742a8ccfe560717edc6
 author
 Bergeling, Carolina ^{LU}
 supervisor

 Anders Rantzer ^{LU}
 Bo Bernhardsson ^{LU}
 Richard Pates ^{LU}
 opponent

 Associate professor Gayme, Dennice, Department of Mechanical Engineering, Johns Hopkins University, Whiting School of Engineering
 organization
 publishing date
 2019
 type
 Thesis
 publication status
 published
 subject
 keywords
 Hinfinity Control, Decentralized Control, LargeScale Systems, InfiniteDimensional Systems
 in
 PhD Theses
 pages
 143 pages
 publisher
 Department of Automatic Control, Lund Institute of Technology, Lund University
 defense location
 M:B, Mhuset, Lunds Tekniska Högskola
 defense date
 20190605 10:15:00
 ISSN
 02805316
 ISBN
 9789178950959
 9789178950966
 project
 Distributed Control and Verification
 language
 English
 LU publication?
 yes
 id
 5f06f32c95e84742a8ccfe560717edc6
 date added to LUP
 20190507 15:03:33
 date last changed
 20190510 14:34:30
@phdthesis{5f06f32c95e84742a8ccfe560717edc6, abstract = {{In this thesis, a class of linear timeinvariant systems is identified for which a particular type of Hinfinity 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 statespace representation. The result has applications in the control of largescale systems, as well as for the control of infinitedimensional systems, with certain properties. <br/><br/>For the largescale applications considered, the controller is both globally optimal as well as possesses a structure compatible with the informationstructure 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 infinitedimensional case, the explicitly stated controller solves the infinitedimensional Hinfinity 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 Hinfinity control.<br/><br/>The systems considered in this thesis are shown to belong to a larger class of systems for which the Hinfinity 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 leastsquares 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 Hinfinity control, as they are in general performed numerically. <br/>}}, author = {{Bergeling, Carolina}}, isbn = {{9789178950959}}, issn = {{02805316}}, keywords = {{Hinfinity Control; Decentralized Control; LargeScale Systems; InfiniteDimensional Systems}}, language = {{eng}}, publisher = {{Department of Automatic Control, Lund Institute of Technology, Lund University}}, school = {{Lund University}}, series = {{PhD Theses}}, title = {{On Hinfinity Control and LargeScale Systems}}, url = {{https://lup.lub.lu.se/search/files/63879983/CarolinaBergelingPhDThesisExcludedNonPublishedPapers.pdf}}, year = {{2019}}, }