On Scalable Hinfinity Control
(2016) Abstract
 Many of the classical approaches to controller synthesis do not scale well for large and complex systems. This is mainly due to computational complexity and the lack of distributed structure in the resulting controllers. It is important that limitations on the information given and processed by sensors and actuators can be incorporated into the design procedure. However, such constraints may greatly complicate controller synthesis. In this thesis, the need for scalability is addressed and a scalable as well as optimal control law is presented. The criteria on optimality is measured in the Hinfinity norm, a norm that is fundamental in the theory of robust control and treats the objective of worstcase disturbance attenuation.
The... (More)  Many of the classical approaches to controller synthesis do not scale well for large and complex systems. This is mainly due to computational complexity and the lack of distributed structure in the resulting controllers. It is important that limitations on the information given and processed by sensors and actuators can be incorporated into the design procedure. However, such constraints may greatly complicate controller synthesis. In this thesis, the need for scalability is addressed and a scalable as well as optimal control law is presented. The criteria on optimality is measured in the Hinfinity norm, a norm that is fundamental in the theory of robust control and treats the objective of worstcase disturbance attenuation.
The optimal controller is a state feedback law applicable to linear and timeinvariant systems with some symmetry in their structure. More specifically, the system has to be stable and have a statespace representation with a symmetric state matrix. Furthermore, the state and control inputs have to be penalized separately. An analog result is given for infinitedimensional systems. In the infinitedimensional case, the criteria on the system are essentially as in the finitedimensional case, however, somewhat more involved.
Systems with the aforementioned property of symmetry have states that affect each other with equal rate coefficients. Such representations appear, for instance, in different types of transportation networks such as buffer systems. The heat equation is an infinitedimensional system for which the result is applicable. This equation can model heat conduction systems as well as other types of diffusion, such as chemical diffusion. Examples are included to demonstrate the simplicity in synthesis as well as the performance of the control law. (Less)
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http://lup.lub.lu.se/record/5166b395369c43e69750a40d4b433428
 author
 Lidström, Carolina ^{LU}
 supervisor

 Anders Rantzer ^{LU}
 Bo Bernhardsson ^{LU}
 organization
 publishing date
 20160616
 type
 Thesis
 publication status
 published
 pages
 66 pages
 publisher
 Department of Automatic Control, Lund Institute of Technology, Lund University
 language
 English
 LU publication?
 yes
 id
 5166b395369c43e69750a40d4b433428
 date added to LUP
 20160621 11:52:00
 date last changed
 20180312 16:39:30
@misc{5166b395369c43e69750a40d4b433428, abstract = {Many of the classical approaches to controller synthesis do not scale well for large and complex systems. This is mainly due to computational complexity and the lack of distributed structure in the resulting controllers. It is important that limitations on the information given and processed by sensors and actuators can be incorporated into the design procedure. However, such constraints may greatly complicate controller synthesis. In this thesis, the need for scalability is addressed and a scalable as well as optimal control law is presented. The criteria on optimality is measured in the Hinfinity norm, a norm that is fundamental in the theory of robust control and treats the objective of worstcase disturbance attenuation. <br/><br/>The optimal controller is a state feedback law applicable to linear and timeinvariant systems with some symmetry in their structure. More specifically, the system has to be stable and have a statespace representation with a symmetric state matrix. Furthermore, the state and control inputs have to be penalized separately. An analog result is given for infinitedimensional systems. In the infinitedimensional case, the criteria on the system are essentially as in the finitedimensional case, however, somewhat more involved. <br/><br/>Systems with the aforementioned property of symmetry have states that affect each other with equal rate coefficients. Such representations appear, for instance, in different types of transportation networks such as buffer systems. The heat equation is an infinitedimensional system for which the result is applicable. This equation can model heat conduction systems as well as other types of diffusion, such as chemical diffusion. Examples are included to demonstrate the simplicity in synthesis as well as the performance of the control law.}, author = {Lidström, Carolina}, language = {eng}, month = {06}, note = {Licentiate Thesis}, pages = {66}, publisher = {Department of Automatic Control, Lund Institute of Technology, Lund University}, title = {On Scalable Hinfinity Control}, year = {2016}, }