Semidefinite approximations of the polynomial abscissa
| Autor: | Tien-Son Pham, Roxana Heß, Jean B. Lasserre, Didier Henrion |
|---|---|
| Přispěvatelé: | Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Czech Technical University in Prague (CTU), Department of Mathematics (DEPARTMENT OF MATHEMATICS), Dalat University [Vietnam] (DLU)-University of British Columbia (UBC), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées |
| Rok vydání: | 2015 |
| Předmět: |
0209 industrial biotechnology
Polynomial Control and Optimization Linear systems control MathematicsofComputing_NUMERICALANALYSIS Hölder condition 02 engineering and technology symbols.namesake non-convex non-smooth optimization 020901 industrial engineering & automation Linear differential equation ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION FOS: Mathematics Applied mathematics polynomial approximations Mathematics - Optimization and Control semialgebraic optimization Mathematics Semidefinite programming Applied Mathematics Mathematical analysis Regular polygon Abscissa semidefinite programming Lipschitz continuity Optimization and Control (math.OC) Norm (mathematics) symbols [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] |
| Zdroj: | SIAM Journal on Control and Optimization SIAM Journal on Control and Optimization, 2016, 54 (3), pp. 1633-1656 SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2016, 54 (3), pp. 1633-1656 |
| ISSN: | 0363-0129 1095-7138 |
| DOI: | 10.48550/arxiv.1507.08463 |
| Popis: | International audience; Given a univariate polynomial, its abscissa is the maximum real part of its roots. The abscissa arises naturally when controlling linear differential equations. As a function of the polynomial coefficients, the abscissa is Hölder continuous, and not locally Lipschitz in general, which is a source of numerical difficulties for designing and optimizing control laws. In this paper we propose simple approximations of the abscissa given by polynomials of fixed degree, and hence controlled complexity. Our approximations are computed by a hierarchy of finite-dimensional convex semidefinite programming problems. When their degree tends to infinity, the polynomial approximations converge in norm to the abcissa, either from above or from below. |
| Databáze: | OpenAIRE |
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