Overview
- Authors:
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Uwe Helmke
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Department of Mathematics, University of Würzburg, Würzburg, Germany
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John B. Moore
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Department of Systems Engineering and Cooperative Research Centre for Robust and Adaptive Systems, Research School of Information Sciences and Engineering, Australian National University, Canberra, Australia
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Table of contents (9 chapters)
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Front Matter
Pages i-xiii
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- Uwe Helmke, John B. Moore
Pages 1-42
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- Uwe Helmke, John B. Moore
Pages 43-80
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- Uwe Helmke, John B. Moore
Pages 81-100
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- Uwe Helmke, John B. Moore
Pages 101-124
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- Uwe Helmke, John B. Moore
Pages 125-161
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- Uwe Helmke, John B. Moore
Pages 163-200
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- Uwe Helmke, John B. Moore
Pages 201-227
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- Uwe Helmke, John B. Moore
Pages 229-267
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- Uwe Helmke, John B. Moore
Pages 269-309
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Back Matter
Pages 311-403
About this book
This work is aimed at mathematics and engineering graduate students and researchers in the areas of optimization, dynamical systems, control sys tems, signal processing, and linear algebra. The motivation for the results developed here arises from advanced engineering applications and the emer gence of highly parallel computing machines for tackling such applications. The problems solved are those of linear algebra and linear systems the ory, and include such topics as diagonalizing a symmetric matrix, singular value decomposition, balanced realizations, linear programming, sensitivity minimization, and eigenvalue assignment by feedback control. The tools are those, not only of linear algebra and systems theory, but also of differential geometry. The problems are solved via dynamical sys tems implementation, either in continuous time or discrete time , which is ideally suited to distributed parallel processing. The problems tackled are indirectly or directly concerned with dynamical systems themselves, so there is feedback in that dynamical systems are used to understand and optimize dynamical systems. One key to the new research results has been the recent discovery of rather deep existence and uniqueness results for the solution of certain matrix least squares optimization problems in geomet ric invariant theory. These problems, as well as many other optimization problems arising in linear algebra and systems theory, do not always admit solutions which can be found by algebraic methods.
Authors and Affiliations
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Department of Mathematics, University of Würzburg, Würzburg, Germany
Uwe Helmke
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Department of Systems Engineering and Cooperative Research Centre for Robust and Adaptive Systems, Research School of Information Sciences and Engineering, Australian National University, Canberra, Australia
John B. Moore
