222documents trouvés
A hierarchy of LMI inner approximations of the set of stable polynomials}
M.AIT RAMI, D.HENRION
Valladolid, MAC
Revue Scientifique : Automatica, Vol.47, N°7, pp.1455-1460, Juillet 2011 , N° 10934
Lien : http://hal.archives-ouvertes.fr/hal-00496527/fr/
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Abstract
Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMI) in the coefficients. As an application of these results, we derive a hierarchy of convex LMI inner approximations (affine sections of the cone of positive definite matrices of size $m$) of the nonconvex set of Schur stable polynomials of given degree $n < m$. It is shown that when $m$ tends to infinity the hierarchy converges to a lifted LMI approximation (projection of an LMI set defined in a lifted space of dimension quadratic in $n$) already studied in the technical literature.
Minimizing the sum of many rational functions
F.BUGARIN, D.HENRION, J.B.LASSERRE
CROMeP , MAC
Rapport LAAS N°11100, Mars 2011, 16p.
Lien : http://hal.archives-ouvertes.fr/hal-00569067/fr/
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We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of variables can be large (10 to 100) provided some kind of sparsity is present. We describe a formulation of the rational optimization problem as a generalized moment problem and its hierarchy of convex semidefinite relaxations. Under some conditions we prove that the sequence of optimal values converges to the globally optimal value. We show how public-domain software can be used to model and solve such problems.
Les ovales des spectraèdres
D.HENRION
MAC
Revues de Vulgarisation : Images des Mathématiques, 15p., Février 2011 , N° 11078
Lien : http://images.math.cnrs.fr/
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124021Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities
A.DELIBASI, D.HENRION
MAC
Revue Scientifique : International Journal of Control, Vol.83, N°12, pp.2494-2505, Décembre 2010 , N° 10030
Lien : http://hal.archives-ouvertes.fr/hal-00448915/fr/
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Abstract
Using Hermite's formulation of polynomial stability conditions, static output feedback (SOF) controller design can be formulated as a polynomial matrix inequality (PMI), a (generally nonconvex) nonlinear semidefinite programming problem that can be solved (locally) with PENNON, an implementation of a penalty method. Typically, Hermite SOF PMI problems are badly scaled and experiments reveal that this has a negative impact on the overall performance of the solver. In this note we recall the algebraic interpretation of Hermite's quadratic form as a particular Bezoutian and we use results on polynomial interpolation to express the Hermite PMI in a Lagrange polynomial basis, as an alternative to the conventional power basis. Numerical experiments on benchmark problem instances show the substantial improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behavior of PENNON.
Les coupes des spectraèdres
D.HENRION
MAC
Revues de Vulgarisation : Images des Mathématiques, 14p., Décembre 2010 , N° 10810
Lien : http://images.math.cnrs.fr/
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123577Polinomial optimization and dynamical systems
D.HENRION
MAC
Conférence invitée : International Conference on Advances in Optimization and Related Topics (ADORT 2010), Barcelone (Espagne), 29 Novembre - 3 Décembre 2010 , N° 10909
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124314Semidefinite programming for optimizing convex bodies under width constraints
D.HENRION
MAC
Conférence invitée : Modern Trends in Optimization and Its Application Workshop I: Convex Optimization and Algebraic Geometry, Los Angeles (USA), 28 Septembre - 1er Octobre 2010, 35p. , N° 10910
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124312Polynomial LPV synthesis applied to turbofan engines
W.GILBERT, D.HENRION, J.BERNUSSOU, D.BOYER
MAC, FEL-CVUT
Revue Scientifique : IFAC Control Engineering Practice, Vol.18, N°9, pp.1077-1083, Août 2010 , N° 06691
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Results on polynomial fixed order controller design are extended to SISO gain-scheduling with guaranteed stability and H1 performance over the whole scheduling parameter range. Salient features of the approach are (a) the use of polynomials as modeling objects; (b) the use of flexible LMI conditions allowing polynomial dependence of the open-loop system and controller transfer functions in the scheduling parameters; and (c) the decoupling in the LMI conditions between the Lyapunov variables and the controller variables, allowing both parameterdependent Lyapunov functions and fixed-order controller design. The synthesis procedure is integrated into the ATOL framework developed by the manufacturer of aircraft and space engines Snecma to systematically design reduced complexity gain-scheduled control laws for aircraft turbofan engines.
LMI based design for the Acrobot walking
M. ANDERLE, D.HENRION, JZIKMUND, S.CELIKOVSKY
CzechTech. Univ., MAC, Czech Academy
Revue Scientifique : International Journal of Control, Vol.83, N°8, pp.1641-1652, Août 2010 , N° 09579
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122115Recovering semialgebraic shapes from their moments with semidefinite programming
D.HENRION
MAC
Conférence invitée : Joint French-Czech Workshop on Krylov Methods for Inverse Problems, Prague (République Tchèque), 19-20 Juillet 2010, 1p. (Résumé) , N° 10908
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