Parametric optimization in control using the sum of roots for parametric polynomial spectral factorization

Authors:
Masaaki Kanno;Kazuhiro Yokoyama;Hirokazu Anai;Shinji Hara
Affiliations:
CREST, Japan Science and Technology Agency, Honcho, Kawaguchi-shi, Saitama, Japan;Rikkyo University, Toshima-ku, Tokyo, Japan;Fujitsu Laboratories Ltd, Nakahara-ku, Kawasaki, Japan;The University of Tokyo, Bunkyo-ku, Tokyo, Japan
Venue:
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Year:
2007

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Abstract

This paper proposes an algebraic approach for parametric optimization which can be utilized for various problems in signal processing and control.The approach exploits the relationship between the sum of roots and polynomial spectral factorization and solves parametric polynomial spectral factorization by means of the sum of roots and the theory of Gröbner basis. This enables us to express quantities such as the optimal cost in terms of parameters and the sum of roots.Furthermore an optimization method over parameters is suggested that makes use of the results from parametric polynomial spectral factorization and also employs quantifier elimination.The proposed approach is demonstrated on a numerical example of a particular control problem.