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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.
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: Optimization and Dynamical Systems
Authors: Uwe Helmke, John B. Moore
Series Title: Communications and Control Engineering
DOI: https://doi.org/10.1007/978-1-4471-3467-1
Publisher: Springer London
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag London 1994
Softcover ISBN: 978-1-4471-3469-5Published: 09 April 2014
eBook ISBN: 978-1-4471-3467-1Published: 06 December 2012
Series ISSN: 0178-5354
Series E-ISSN: 2197-7119
Edition Number: 1
Number of Pages: XIII, 403
Number of Illustrations: 2 b/w illustrations
Topics: Control and Systems Theory, Dynamical Systems and Ergodic Theory, Mathematical Modeling and Industrial Mathematics, Communications Engineering, Networks, Systems Theory, Control, Calculus of Variations and Optimal Control; Optimization