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Dynamic Programming and Time-Varying Delay Systems

Lincoln, Bo LU (2003) In PhD Theses TFRT-1067.
Abstract
This thesis is divided into two separate parts. The first part is about Dynamic Programming for non-trivial optimal control problems. The second part introduces some useful tools for analysis of stability and performance of systems with time-varying 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 non-trivial optimal control problems. The second part introduces some useful tools for analysis of stability and performance of systems with time-varying 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 time-varying 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 continuous-time and discrete-time linear systems. The main contribution of the toolbox is to make well known theory easily applicable for analysis of real-time systems. (Less)
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author
supervisor
opponent
  • Professor Kumar, P. R., University of Illinois,Urbana-Champaign, IL, USA
organization
publishing date
type
Thesis
publication status
published
subject
keywords
control engineering, Automatiska system, robotteknik, reglerteknik, robotics, Automation, Stability analysis, Time-varying delays, Dynamic programming, Switched linear systems
in
PhD Theses
volume
TFRT-1067
pages
146 pages
publisher
Department of Automatic Control, Lund Institute of Technology (LTH)
defense location
Room M:B (the M-building), Lund Institute of Technology
defense date
2003-05-17 10:15
ISSN
0280-5316
language
English
LU publication?
yes
id
f051ab12-0052-413c-ae90-9d98e57534db (old id 465806)
date added to LUP
2007-09-10 12:45:31
date last changed
2018-08-17 19:05:49
@phdthesis{f051ab12-0052-413c-ae90-9d98e57534db,
  abstract     = {This thesis is divided into two separate parts. The first part is about Dynamic Programming for non-trivial optimal control problems. The second part introduces some useful tools for analysis of stability and performance of systems with time-varying 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 time-varying 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 continuous-time and discrete-time linear systems. The main contribution of the toolbox is to make well known theory easily applicable for analysis of real-time systems.},
  author       = {Lincoln, Bo},
  issn         = {0280-5316},
  keyword      = {control engineering,Automatiska system,robotteknik,reglerteknik,robotics,Automation,Stability analysis,Time-varying 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 Time-Varying Delay Systems},
  volume       = {TFRT-1067},
  year         = {2003},
}