Article

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

Authors:

Kazuhiro Yokoyama,

Shinji HaraAuthors Info & Claims

ISSAC '07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation

Pages 211 - 218

https://doi.org/10.1145/1277548.1277578

Published: 29 July 2007 Publication History

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.

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Cited By

Iwane HKira AAnai H(2011)Construction of explicit optimal value functions by a symbolic-numeric cylindrical algebraic decompositionProceedings of the 13th international conference on Computer algebra in scientific computing10.5555/2040148.2040167(239-250)Online publication date: 5-Sep-2011
https://dl.acm.org/doi/10.5555/2040148.2040167
Iwane HKira AAnai H(2011)Construction of Explicit Optimal Value Functions by a Symbolic-Numeric Cylindrical Algebraic DecompositionComputer Algebra in Scientific Computing10.1007/978-3-642-23568-9_19(239-250)Online publication date: 2011
https://doi.org/10.1007/978-3-642-23568-9_19
Anai HHara SKanno MYokoyama K(2009)Parametric polynomial spectral factorization using the sum of roots and its application to a control design problemJournal of Symbolic Computation10.1016/j.jsc.2008.04.01544:7(703-725)Online publication date: 1-Jul-2009
https://dl.acm.org/doi/10.1016/j.jsc.2008.04.015
Show More Cited By

Index Terms

Parametric optimization in control using the sum of roots for parametric polynomial spectral factorization
1. Applied computing
  1. Arts and humanities
    1. Architecture (buildings)
      1. Computer-aided design
  2. Physical sciences and engineering
    1. Engineering
      1. Computer-aided design
2. Computing methodologies
  1. Symbolic and algebraic manipulation

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Published In

cover image ACM Conferences

ISSAC '07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation

July 2007

406 pages

ISBN:9781595937438

DOI:10.1145/1277548

General Chair:
Dongming Wang
Beihang University and UPMC-CNRS (China/France)

Copyright © 2007 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 29 July 2007

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ISSAC07: International Symposium on Symbolic and Algebraic Computation

July 29 - August 1, 2007

Ontario, Waterloo, Canada

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Citations

Cited By

Iwane HKira AAnai H(2011)Construction of explicit optimal value functions by a symbolic-numeric cylindrical algebraic decompositionProceedings of the 13th international conference on Computer algebra in scientific computing10.5555/2040148.2040167(239-250)Online publication date: 5-Sep-2011
https://dl.acm.org/doi/10.5555/2040148.2040167
Iwane HKira AAnai H(2011)Construction of Explicit Optimal Value Functions by a Symbolic-Numeric Cylindrical Algebraic DecompositionComputer Algebra in Scientific Computing10.1007/978-3-642-23568-9_19(239-250)Online publication date: 2011
https://doi.org/10.1007/978-3-642-23568-9_19
Anai HHara SKanno MYokoyama K(2009)Parametric polynomial spectral factorization using the sum of roots and its application to a control design problemJournal of Symbolic Computation10.1016/j.jsc.2008.04.01544:7(703-725)Online publication date: 1-Jul-2009
https://dl.acm.org/doi/10.1016/j.jsc.2008.04.015
HARA SKANNO M(2008)Sum of Roots Characterization for H2 Control Performance LimitationsSICE Journal of Control, Measurement, and System Integration10.9746/jcmsi.1.581:1(58-65)Online publication date: 2008
https://doi.org/10.9746/jcmsi.1.58
Kanno MHara S(2008)Sum of Roots Characterization for Parametric State Feedback H∞ ControlIFAC Proceedings Volumes10.3182/20080706-5-KR-1001.0023041:2(1342-1347)Online publication date: 2008
https://doi.org/10.3182/20080706-5-KR-1001.00230
Kanno MYokoyama KAnai HHara SSendra JGonzalez-Vega L(2008)Symbolic optimization of algebraic functionsProceedings of the twenty-first international symposium on Symbolic and algebraic computation10.1145/1390768.1390791(147-154)Online publication date: 20-Jul-2008
https://dl.acm.org/doi/10.1145/1390768.1390791
Hara SKanno M(2008)When Is a Linear Continuous-time System Easy or Hard to Control in Practice?Recent Advances in Learning and Control10.1007/978-1-84800-155-8_8(111-124)Online publication date: 2008
https://doi.org/10.1007/978-1-84800-155-8_8
Kanno MHara SHirokazu Anai Kazuhiro Yokoyama (2007)Sum of roots, polynomial spectral factorization, and control performance limitations2007 46th IEEE Conference on Decision and Control10.1109/CDC.2007.4434562(2968-2973)Online publication date: Dec-2007
https://doi.org/10.1109/CDC.2007.4434562

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