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Main Title: Sensitivity of Computational Control Problems
Author(s): Higham, Nicholas J.
Konstantinov, Mihail
Mehrmann, Volker
Petkov, Petko
Type: Research Paper
Abstract: It is well-known that many factors contribute to the accurate and efficient numerical solution of mathematical problems such as those arising in computational control system design. In simple terms these are the arithmetic of the machine on which the calculations are carried out, sensitivity (or conditioning) of the mathematical model to small changes of the data and the numerical stability of the algorithms. It happens quite often that these concepts are confused. We define these concepts and demonstrate some of the subtleties that often lead to confusion. In particular we demonstrate with several examples what may happen when a problem is modularized, i.e., split into subproblems for which computational modules are available. For three classical problems in computational control, pole placement, linear quadratic control and optimal $H_\infty$ control, we then discuss the conditioning of the problems and point out sources of difficulties. We give some ill-conditioned examples for which even numerically stable methods fail. We also stress the need for condition and error estimators that supplement the numerical algorithm and inform the user about potential or actual difficulties, and we explain what can be done to avoid these difficulties.
Subject(s): sensitivity and conditioning
numerical stability
machine arithmetic
pole placement
linear quadratic control
algebraic Riccati equation
H∞ control
Issue Date: 12-Mar-2003
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65F15 Eigenvalues, eigenvectors
93B40 Computational methods
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2003, 05
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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