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On the robustness of the linear quadratic regulator via perturbation analysis of the Riccati equation

Chen, Ci (2015) On the robustness of the linear quadratic regulator via perturbation analysis of the Riccati equation. PhD thesis, Dublin City University.

Abstract
The linear quadratic regulator (LQR) has been shown to have very attractive stability robustness properties. However, some authors have shown that LQR may suffer from poor robustness when special perturbations in its state-space formulation were introduced. This thesis continues the study of the stability robustness of LQ regulators. To acquire good stability robustness, weight selection is first investigated. For general cost weighting matrices, a new lower bound on the minimum singular value of the return difference is proposed. New guaranteed stability margins are also presented. This gives a formal mathematical basis for guidelines for the designer to improve stability robustness. As the weight on the plant’s inputs approaches zero, the exact bound on the perturbations which ensures stability is compared with the guaranteed margins. It is shown that the stability robustness properties are preserved in a general sense. Then, a numerical analysis of the conditioning of the continuous-time algebraic Riccati equation (CARE) is presented. The condition numbers of the CARE are utilized to measure the sensitivity of LQR subject to parameter changes. It is shown that the condition numbers grow sig- nificantly when the weighting parameters on the system state and input matrices approach zero and infinity. This has application to the applied control situation because it can be used to detect hidden vulnerabilities in LQR systems.
Metadata
Item Type:Thesis (PhD)
Date of Award:March 2015
Refereed:No
Supervisor(s):Holohan, Anthony M.
Uncontrolled Keywords:Control; Riccati equations
Subjects:Engineering > Control theory
DCU Faculties and Centres:UNSPECIFIED
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 3.0 License. View License
Funders:School of Electronic Engineering
ID Code:20260
Deposited On:14 Apr 2015 10:51 by Anthony Holohan . Last Modified 19 Jul 2018 15:04
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