Dynamic Programming and Time-Varying Delay Systems
(2003) In PhD Thesis 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/465806
- author
- Lincoln, Bo LU
- supervisor
- opponent
-
- Professor Kumar, P. R., University of Illinois,Urbana-Champaign, IL, USA
- organization
- publishing date
- 2003
- 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 Thesis 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 10:15:00
- ISSN
- 0280-5316
- 0280-5316
- language
- English
- LU publication?
- yes
- additional info
- Article: Paper 1: Lincoln, B. and B. Bernhardsson "LQR optimization of linear system switching." IEEE Transactions on Automatic Control, vol 47, pp. 1701-1705, October 2002. Article: Paper 2: Lincoln, B. and A. Rantzer "Relaxing Dynamic Programming." Submitted to IEEE Transactions on Automatic Control, 2003. Article: Paper 3: Kao, C-Y. and B. Lincoln "Simple Stability Criteria for Systems with Time-Varying Delays." Submitted to Automatica, 2003. Article: Paper 4: Lincoln, B. and A. Cervin: "Jitterbug: A tool for analysis of real-time control performance." In Proceedings of the 41st IEEE Conference on Decision and Control, pp. 1319-1324, December 2002.
- id
- f051ab12-0052-413c-ae90-9d98e57534db (old id 465806)
- date added to LUP
- 2016-04-01 16:26:15
- date last changed
- 2019-05-23 15:52:33
@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}}, keywords = {{control engineering; Automatiska system; robotteknik; reglerteknik; robotics; Automation; Stability analysis; Time-varying delays; Dynamic programming; Switched linear systems}}, language = {{eng}}, publisher = {{Department of Automatic Control, Lund Institute of Technology (LTH)}}, school = {{Lund University}}, series = {{PhD Thesis TFRT-1067}}, title = {{Dynamic Programming and Time-Varying Delay Systems}}, url = {{https://lup.lub.lu.se/search/files/4672800/8571915.pdf}}, year = {{2003}}, }