A symbolic-numeric method for the parametric ...
Type de document :
Communication dans un congrès avec actes
Titre :
A symbolic-numeric method for the parametric H$\infty$ loop-shaping design problem
Auteur(s) :
Rance, Guillaume [Auteur]
SAFRAN Electronics & Defense
Bouzidi, Yacine [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Quadrat, Alban [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Quadrat, Arnaud [Auteur]
SAFRAN Electronics & Defense
SAFRAN Electronics & Defense
Bouzidi, Yacine [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Quadrat, Alban [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Quadrat, Arnaud [Auteur]
SAFRAN Electronics & Defense
Titre de la manifestation scientifique :
22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS)
Ville :
Minneapolis
Pays :
Etats-Unis d'Amérique
Date de début de la manifestation scientifique :
2016-07-12
Titre de l’ouvrage :
22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS)
Date de publication :
2016-07
Mot(s)-clé(s) en anglais :
Robust control and H-infinity control
Algebraic Riccati equations
Parametric control theory
Polynomial systems
Algebraic Riccati equations
Parametric control theory
Polynomial systems
Discipline(s) HAL :
Mathématiques [math]/Optimisation et contrôle [math.OC]
Mathématiques [math]/Systèmes dynamiques [math.DS]
Informatique [cs]/Calcul formel [cs.SC]
Mathématiques [math]/Géométrie algébrique [math.AG]
Mathématiques [math]/Systèmes dynamiques [math.DS]
Informatique [cs]/Calcul formel [cs.SC]
Mathématiques [math]/Géométrie algébrique [math.AG]
Résumé en anglais : [en]
In this paper, we present a symbolic-numeric method for solving the H_infinity loop-shaping design problem for low order single-input single-output systems with parameters. Due to the system parameters, no purely numerical ...
Lire la suite >In this paper, we present a symbolic-numeric method for solving the H_infinity loop-shaping design problem for low order single-input single-output systems with parameters. Due to the system parameters, no purely numerical algorithm can indeed solve the problem. Using Gröbner basis techniques and the Rational Univariate Representation of zero-dimensional algebraic varieties, we first give a parametrization of all the solutions of the two Algebraic Riccati Equations associated with the H_infinity-control problem. Then, following the works H. Anai, S. Hara, M. Kanno, K. Yokoyama, Parametric polynomial factorization using the sum of roots and its application to a control design problem, J. Symb. Comp., 44 (2009), 703-725, and M. Kanno, S. Hara, Symbolic-numeric hybrid optimization for plant/controller integrated design in H_infinity loop-shaping design, Journal of Math-for-Industry, 4 (2012), 135-140, on the spectral factorization problem, a certified symbolic-numeric algorithm is obtained for the computation of the positive definite solutions of these two Algebraic Riccati Equations. Finally, we present a certified symbolic-numeric algorithm which solves the H_infinity loop-shaping design problem for the above class of systems. This algorithm is illustrated with a standard example.Lire moins >
Lire la suite >In this paper, we present a symbolic-numeric method for solving the H_infinity loop-shaping design problem for low order single-input single-output systems with parameters. Due to the system parameters, no purely numerical algorithm can indeed solve the problem. Using Gröbner basis techniques and the Rational Univariate Representation of zero-dimensional algebraic varieties, we first give a parametrization of all the solutions of the two Algebraic Riccati Equations associated with the H_infinity-control problem. Then, following the works H. Anai, S. Hara, M. Kanno, K. Yokoyama, Parametric polynomial factorization using the sum of roots and its application to a control design problem, J. Symb. Comp., 44 (2009), 703-725, and M. Kanno, S. Hara, Symbolic-numeric hybrid optimization for plant/controller integrated design in H_infinity loop-shaping design, Journal of Math-for-Industry, 4 (2012), 135-140, on the spectral factorization problem, a certified symbolic-numeric algorithm is obtained for the computation of the positive definite solutions of these two Algebraic Riccati Equations. Finally, we present a certified symbolic-numeric algorithm which solves the H_infinity loop-shaping design problem for the above class of systems. This algorithm is illustrated with a standard example.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Collections :
Source :
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