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

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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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION

Additional Classification:
  J. Computer Applications
  J.6 COMPUTER-AIDED ENGINEERING
      Subjects: Computer-aided design (CAD)

General Terms:
Algorithms, Experimentation

Keywords:
Gröbner basis, parametric optimization, polynomial spectral factorization, quantifier elimination, H₂ control, sum of roots