Dynamic Programming and TimeVarying Delay Systems
(2003) In PhD Theses TFRT1067. Abstract
 This thesis is divided into two separate parts. The first part is about Dynamic Programming for nontrivial optimal control problems. The second part introduces some useful tools for analysis of stability and performance of systems with timevarying delays.
The two papers presented in the first part attacks optimal control problems with finite but rapidly increasing search space. In the first paper we try it reduce the complexity of the optimization by exploiting the structure of a certain problem. The result, if found, is an optimal solution.
The second paper introduces a new general approach of relaxing the optimality constraint. The main contribution of the paper is an extension of the Bellman... (More)  This thesis is divided into two separate parts. The first part is about Dynamic Programming for nontrivial optimal control problems. The second part introduces some useful tools for analysis of stability and performance of systems with timevarying delays.
The two papers presented in the first part attacks optimal control problems with finite but rapidly increasing search space. In the first paper we try it reduce the complexity of the optimization by exploiting the structure of a certain problem. The result, if found, is an optimal solution.
The second paper introduces a new general approach of relaxing the optimality constraint. The main contribution of the paper is an extension of the Bellman equality to a double inequality. This inequality is a sufficient condition for a suboptimal solution to be within a certain distance to the optimal solution. The main approach of solving the inequality in the paper is value iteration, which is shown to work well in many different applications.
In the second part of the thesis, two analysis methods for systems with timevarying delays are presented in two papers. The first paper presents a set of simple graphical stability (and performance) criteria when the delays are bounded but otherwise unknown. All that is needed to verify stability is a Bode diagram of the closed loop system.
For more exact computations, the last paper presents a toolbox for Matlab called Jitterbug. It calculates quadratic costs and power spectral densities of interconnected continuoustime and discretetime linear systems. The main contribution of the toolbox is to make well known theory easily applicable for analysis of realtime systems. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/465806
 author
 Lincoln, Bo ^{LU}
 supervisor

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

 Professor Kumar, P. R., University of Illinois,UrbanaChampaign, IL, USA
 organization
 publishing date
 2003
 type
 Thesis
 publication status
 published
 subject
 keywords
 control engineering, Automatiska system, robotteknik, reglerteknik, robotics, Automation, Stability analysis, Timevarying delays, Dynamic programming, Switched linear systems
 in
 PhD Theses
 volume
 TFRT1067
 pages
 146 pages
 publisher
 Department of Automatic Control, Lund Institute of Technology (LTH)
 defense location
 Room M:B (the Mbuilding), Lund Institute of Technology
 defense date
 20030517 10:15
 ISSN
 02805316
 language
 English
 LU publication?
 yes
 id
 f051ab120052413cae909d98e57534db (old id 465806)
 date added to LUP
 20070910 12:45:31
 date last changed
 20180817 19:05:49
@phdthesis{f051ab120052413cae909d98e57534db, abstract = {This thesis is divided into two separate parts. The first part is about Dynamic Programming for nontrivial optimal control problems. The second part introduces some useful tools for analysis of stability and performance of systems with timevarying delays.<br/><br> <br/><br> The two papers presented in the first part attacks optimal control problems with finite but rapidly increasing search space. In the first paper we try it reduce the complexity of the optimization by exploiting the structure of a certain problem. The result, if found, is an optimal solution.<br/><br> <br/><br> The second paper introduces a new general approach of relaxing the optimality constraint. The main contribution of the paper is an extension of the Bellman equality to a double inequality. This inequality is a sufficient condition for a suboptimal solution to be within a certain distance to the optimal solution. The main approach of solving the inequality in the paper is value iteration, which is shown to work well in many different applications.<br/><br> <br/><br> In the second part of the thesis, two analysis methods for systems with timevarying delays are presented in two papers. The first paper presents a set of simple graphical stability (and performance) criteria when the delays are bounded but otherwise unknown. All that is needed to verify stability is a Bode diagram of the closed loop system.<br/><br> <br/><br> For more exact computations, the last paper presents a toolbox for Matlab called Jitterbug. It calculates quadratic costs and power spectral densities of interconnected continuoustime and discretetime linear systems. The main contribution of the toolbox is to make well known theory easily applicable for analysis of realtime systems.}, author = {Lincoln, Bo}, issn = {02805316}, keyword = {control engineering,Automatiska system,robotteknik,reglerteknik,robotics,Automation,Stability analysis,Timevarying delays,Dynamic programming,Switched linear systems}, language = {eng}, pages = {146}, publisher = {Department of Automatic Control, Lund Institute of Technology (LTH)}, school = {Lund University}, series = {PhD Theses}, title = {Dynamic Programming and TimeVarying Delay Systems}, volume = {TFRT1067}, year = {2003}, }