Optimization and Dynamical Systems

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…

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