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Main Title: Robust numerical methods for robust control
Author(s): Benner, Peter
Byers, Ralph
Mehrmann, Volker
Xu, Hongguo
Type: Research Paper
Abstract: We present numerical methods for the solution of the optimal $H_{\infty}$ control problem. In particular, we investigate the iterative part often called the $\gamma$-iteration. We derive a method with better robustness in the presence of rounding errors than other existing methods. It remains robust in the presence of rounding errors even as $\gamma$ approaches its optimal value. For the computation of a suboptimal controller, we avoid solving algebraic Riccati equations with their problematic matrix inverses and matrix products by adapting recently suggested methods for the computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils. These methods are applicable even if the pencil has eigenvalues on the imaginary axis. We compare the new method with older methods and present several examples.
Subject(s): H∞ control
algebraic Riccati equation
CS decomposition
Lagrangian subspaces
Hamiltonian pencil
Issue Date: 27-Feb-2004
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 93B40 Computational methods
93B36 H∞-control
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2004, 06
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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