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Browsing by Author "Davis, L. D."

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    An Input Normal Form Homotopy for the L2 Optimal Model Order Reduction Problem
    Yuzhen, Ge; Collins, Emmanuel G.; Watson, Layne T.; Davis, L. D. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1993-06-01)
    In control system analysis and design, finding a reduced order model, optimal in the L-squared sense, to a given system model is a fundamental problem. The problem is very difficult without the global convergence of homotopy methods, and a homotopy based approach has been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. A homotopy algorithm based on the input normal form characterization of the reduced order model is developed here and is compared with the homotopy algorithms based on Hyland and Bernstein's optimal projection equations. The main conclusions are that the input normal form algorithm can be very efficient, but can also be very ill conditioned or even fail.
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    Minimal Parameter Homotopies for the L2 Optimal Model Order Reduction Problem
    Yuzhen, Ge; Collins, Emmanuel G.; Watson, Layne T.; Davis, L. D. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1992)
    The problem of finding a reduced order model, optimal in the L2 sense, to a given system model is a fundamental one in control system analysis and design. The problem is very difficult without the global convergence of homotopy methods, and a number of homotopy based approaches have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on several formulations are developed and compared here. The main conclusions are that dimensionality is inversely related to numerical well conditioning and algorithmic efficiency is inversely related to robustness of the algorithm.