17058

22/03/2017

A.SFERLAZZA, S.TARBOURIECH, L.ZACCARIAN

UNINA, MAC

Rapport LAAS N°17058, Mars 2017, 11p.

Lien : https://hal.archives-ouvertes.fr/hal-01488636

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In this paper a time-varying observer for a linear continuous-time plant with asynchronous sampled measurements is proposed. The observer is contextualized in the hybrid systems framework providing an elegant setting for the proposed solution. In particular some theoretical tools are provided, in terms of LMIs, certifying asymptotic stability of a certain compact set where the estimation error is zero. We consider sampled asynchronous measurements that occur at arbitrary times in a certain window with an upper and lower bound. The design procedure, that we propose for the selection of the time-varying gain, is based on a constructive algorithm that is guaranteed to find a solution to an infinite-dimensional LMI whenever a feasible solution exists. Finally a numerical example shows the effectiveness of the proposed approach.

17057

22/03/2017

M.M.JOLDES, J.M.MULLER, V.POPESCU

MAC, ENS Lyon

Rapport LAAS N°17057, Mars 2017, 9p.

Lien : https://hal.archives-ouvertes.fr/hal-01491255

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Semidefinite programming (SDP) is widely used in optimization problems with many applications, however , certain SDP instances are ill-posed and need more precision than the standard double-precision available. Moreover, these problems are large-scale and could benefit from parallelization on specialized architectures such as GPUs. In this article, we implement and evaluate the performance of a floating-point expansion-based arithmetic library (newFPLib) in the context of such numerically highly accurate SDP solvers. We plugged-in the newFPLib with the state-of-the-art SDPA solver for both CPU and GPU-tuned implementations. We compare and contrast both the numerical accuracy and performance of SDPA-GMP,-QD and-DD, which employ other multiple-precision arithmetic libraries against SDPA-newFPLib. We show that our newFPLib is a very good trade-off for accuracy and speed when solving ill-conditioned SDP problems.

17059

22/03/2017

V.MAGRON, P-L.GAROCHE, D.HENRION, X.THIRIOUX

VERIMAG, ONERA, MAC, IRIT-UPS

Rapport LAAS N°17059, Mars 2017, 24p.

Lien : https://hal.archives-ouvertes.fr/hal-01490897

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We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semi-algebraic set constraints. Assuming inclusion in a given simple set like a box or an ellipsoid, we provide a method to compute certified outer approximations of the reachable set. The proposed method consists of building a hierarchy of relaxations for an infinite-dimensional moment problem. Under certain assumptions, the optimal value of this problem is the volume of the reachable set and the optimum solution is the restriction of the Lebesgue measure on this set. Then, one can outer approximate the reachable set as closely as desired with a hierarchy of super level sets of increasing degree polynomials. For each fixed degree, finding the coefficients of the polynomial boils down to computing the optimal solution of a convex semidefinite program. When the degree of the polynomial approximation tends to infinity, we provide strong convergence guarantees of the super level sets to the reachable set. We also present some application examples together with numerical results.

17047

21/03/2017

M.BRENTARI, L.URBINA IGLESIAS, D.ARZELIER, C.LOUEMBET, L.ZACCARIAN

Trento, MAC, ROC

Rapport LAAS N°17047, Mars 2017, 13p.

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We focus on the problem of satellite rendezvous between two spacecraft in elliptic orbits. Using a linearized model of the relative dynamics, we first propose a periodic similarity transformation based on Floquet-Lyapunov theory, leading to a set of coordinates under which the free motion is linear time-invariant. Then we address the problem of impulsive control of satellite rendezvous as a hybrid dynamical system, and we show that the arising elegant representation enables designing impulsive control laws with different trade-offs between computational complexity and fuel consumption. The adopted hybrid formalism allows us to prove suitable stability properties induced by the proposed controllers. The results are comparatively illustrated on simulation examples.

17051

21/03/2017

J.B.LASSERRE

MAC

Rapport LAAS N°17051, Mars 2017, 5p.

Lien : https://hal.archives-ouvertes.fr/hal-01487006

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Given e ∈ (0, 1), a probability measure µ on Ω ⊂ Rp and a semi-algebraic set K ⊂ X × Ω, we consider the feasible set X(e) = {x ∈ X : Prob[(x, ω) ∈ K] ≥ 1 − e } associated with a chance-constraint. We provide a sequence outer approximations X_d(e) = {x ∈ X : h_d (x) ≥ 0}, d ∈ N, where h_d is a polynomial of degree d whose vector of coefficients is an optimal solution of a semidefinite program. The size of the latter increases with the degree d. We also obtain the strong and highly desirable asymptotic guarantee that λ(X_d(e) \X (e)) → 0 as d increases, where λ is the Lebesgue measure on X

17044

16/03/2017

Y.DE CASTRO, F.GAMBOA, D.HENRION, R.HESS, J.B.LASSERRE

LM, Orsay, IMT, Toulouse, MAC

Rapport LAAS N°17044, Mars 2017, 16p.

Lien : https://hal.laas.fr/hal-01483490

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We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically and approximately the optimal design problem. The geometry of the design is recovered with semidefinite programming duality theory and the Christoffel polynomial.

17029

07/03/2017

H.LEDUC, C.PITTET-MECHIN, D.PEAUCELLE

MAC, CNES

Rapport LAAS N°17029, Mars 2017, 9p.

Lien : https://hal.archives-ouvertes.fr/hal-01473674

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A robust direct adaptive attitude law is implemented in a attitude control system simulator. The meaning of robustness here is with respect to uncertainties in the inertia of the satellite. The controller has already been proved to be more robust than a corresponding robustly stabilizing static output feedback. The aim of the study is to show that in practice as well, only the adaptive controller can stabilize the satellite whatever the number of deployed/folded payload masts, namely whatever the value of its inertia.

17025

03/03/2017

C.ARTIGUES

ROC

Revue Scientifique : Operations Research Letters, Vol.45, N°2, pp.154-159, Mars 2017 , N° 17025

Lien : https://hal.archives-ouvertes.fr/hal-01461447

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For non-preemptive scheduling, time-indexed zero-one linear programming formulations have been deeply analyzed. This note clarifies the current knowledge about the strength of these formulations and shows that some formulations that have been proposed " new " in the literature are in fact weaker or equivalent to those already known. Much of the arguments used follow from a PhD thesis by Sousa, which has been largely overlooked in the literature.

17019

01/03/2017

A.BISOFFI, L.ZACCARIAN, M.DA LIO, D.CARNEVALE

Trento, MAC, Rome

Revue Scientifique : Automatica, Vol.77, pp.344-352, Mars 2017 , N° 17019

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In AC/DC converters, a peculiar periodic nonsmooth waveform arises, the so-called ripple. In this paper we propose a novel model that captures this nonsmoothness by means of a hybrid dynamical system performing state jumps at certain switching instants, and we illustrate its properties with reference to a three phase diode bridge rectifier. As the ripple corrupts an underlying desirable signal, we propound two observer schemes ensuring asymptotic estimation of the ripple, the first with and the second without knowledge of the switching instants. Our theoretical developments are well placed in the context of recent techniques for hybrid regulation and constitute a contribution especially for our second observer, where the switching instants are estimated. Once asymptotic estimation of the ripple is achieved, the ripple can be conveniently canceled from the desirable signal, and thanks to the inherent robustness properties of the proposed hybrid formulation, the two observer schemes require only that the desirable signal is slowly time varying compared to the ripple. Exploiting this fact, we illustrate the effectiveness of our second hybrid observation law on experimental data collected from the Joint European Torus tokamak.

16132

01/03/2017

O.LOPEZ SANTOS, L.MARTINEZ SALAMERO, G.GARCIA, H.VALDERRAMA-BLAVI, D.A.ZAMBRANO-PRADA

MAC, URV, Unibague

Revue Scientifique : IEEE Transactions on Power Electronics, Vol.32, N°3, pp.2253-2264, Mars 2017, DOI 10.1109/TPEL.2016.2557582 , N° 16132

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The conduction modes of the quadratic boost converter are explored in the context of high DC gain applications. A complete analytical description of the steady-state behavior of the converter operating in four possible inductor current discontinuous conduction modes is presented. Boundaries between modes are determined together with the corresponding transitions. The study covers the operation of the converter using a pulse width modulator (PWM) for constant switching frequency, and employing a hysteresis comparator for variable switching frequency. Both cases are analyzed for the same set of converter parameters and different constant resistive loads, while the converter is fed by a low DC voltage ranging from 20 to 30 VDC. Several simulations are used to verify the waveforms and average values predicted by the theoretical analysis. Experimental results in a 60 W prototype are in good agreement with the theoretical predictions, and efficiency measurements reveal that one of the discontinuous conduction modes can compete with the continuous conduction mode in high DC gain applications.

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