Explicit Solutions for Root Optimization of a Polynomial Family with One Affine Constraint
Vincent D. Blondel(blondelmit.edu)
Abstract: Given a family of real or complex monic polynomials of fixed degree with one affine constraint on their coefficients, consider the problem of minimizing the root radius (largest modulus of the roots) or root abscissa (largest real part of the roots). We give constructive methods for efficiently computing the globally optimal value as well as an optimal polynomial when the optimal value is attained and an approximation when it is not. An optimal polynomial can always be chosen to have at most two distinct roots in the real case and just one distinct root in the complex case. Examples are presented illustrating the results, including several fixed-order controller optimal design problems.
Keywords: root optimization, fixed-order controller design, optimizing root abscissa and radius, minimum order controller design problem, feedback stabilization
Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )
Category 2: Global Optimization
Category 3: Applications -- Science and Engineering (Control Applications )
Citation: Submitted revised version.
Entry Submitted: 04/22/2011
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