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

by Ci Chen

Institution: Dublin City University
Year: 2015
Keywords: Control theory; Control; Riccati equations
Record ID: 1181637
Full text PDF: http://doras.dcu.ie/20260/


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.