Laboratoire d’analyse et d’architecture des systèmes
D.HENRION, M.KRUZIK, T.WEISSER
MAC, CzechTech. Univ.
Revue Scientifique : Automatica, Vol.103, pp.159-165, Mai 2019 , N° 18218
Optimal control problems with oscillations (chattering controls) and concentrations (impulsive controls) can have integral performance criteria such that concentration of the control signal occurs at a discontinuity of the state signal. Techniques from functional analysis (anisotropic parametrized measures) are applied to give a precise meaning of the integral cost and to allow for the sound application of numerical methods. We show how this can be combined with the Lasserre hierarchy of semidefinite programming relaxations
C.GAZZINO, D.ARZELIER, C.LOUEMBET
Revue Scientifique : Journal of Guidance, Control, and Dynamics, Février 2019, doi10.2514/1.G003644 , N° 18024
The problem of the computation of correction maneuvers for the fuel-optimal long-term station-keeping within a predefined longitude and latitude window of a geostationary satellite equipped with electric propulsion is investigated. The use of electric thrusters imposes some additional operational constraints on actuation that can be reformulated as logical constraints on the control function. The resulting fuel-optimal station-keeping problem is therefore transformed into a mixed linear integer programming problem. The long-term horizon of station-keeping is divided in shorter control cycles synchronized with the cycles of orbit determination, and the long-term station-keeping problem amounts to solve a sequence of similar mixed linear integer programming problems with different initial conditions. Two different terminal constraints on geographical positions and/or linear velocities are added to the formulation of the mixed linear integer programming problems to ease the feasibility of the whole sequence of successive resolutions. Nonlinear perturbed simulations of the computed control strategies show their efficiency on a long-term station-keeping problem lasting one year.
P.FRASCA, S.TARBOURIECH, L.ZACCARIAN
Revue Scientifique : Automatica, Vol.100, pp.153-161, Février 2019 , N° 18402
This paper is a first attempt at using tools from the theory of hybrid systems to study opinion dynamics on networks with opinion-dependent connectivity. According to the hybrid framework, our dynamics are represented by the combination of continuous flow dynamics and discrete jump dynamics. The flow embodies the attractive forces between the agents and is defined by an ordinary differential equation whose right-hand side is a Laplacian, whereas the jumps describe the activation or deactivation of the pairwise interactions between agents. We first reformulate the classical Hegselmann–Krause model in this framework and then define a novel interaction model, which has the property of being scale-invariant. We study the stability and convergence properties of both models by a Lyapunov analysis, showing convergence and clusterization of opinions.
MAC, University of Groningen
Revue Scientifique : Automatica, Vol.99, pp.289-300, Janvier 2019 , N° 18387
This paper studies detectability for switched linear differential–algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor at the end of that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component of the system is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption.
L.BAUDOUIN, A.SEURET, F.GOUAISBAUT
Revue Scientifique : Automatica, Vol.99, pp.195-202, Janvier 2019 , N° 17247
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov functional technique. Inspired from recent developments in the area of time delay systems, a new methodology to study the stability of such a class of distributed parameter systems is presented here. The idea is to use a polynomial approximation of the infinite dimensional state of the heat equation in order to build an enriched energy functional. A well known efficient integral inequality (Bessel inequality) will allow to obtain stability conditions expressed in terms of linear matrix inequalities. We will eventually test our approach on academic examples in order to illustrate the efficiency of our theoretical results.
D.HENRION, S.NALDI, M.SAFEY EL DIN
MAC, LIP6-CNRS, TU Dortmund
Revue Scientifique : Optimization Methods and Software, Vol.34, N°1, Janvier 2019 , N° 16375
This document briefly describes our freely distributed Maple library spectra, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities in exact arithmetic and it is targeted to small-size, possibly degenerate problems for which symbolic infeasibility or feasibility certificates are required.
Y.DE CASTRO, F.GAMBOA, D.HENRION, R.HESS, J.B.LASSERRE
LM, Orsay, IMT, Toulouse, MAC
Revue Scientifique : Annals of Statistics, Vol.47, N°1, pp.127-155, Janvier 2019 , N° 17044
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.
A.RODRIGUES DEL NOZAL, P.MILLAN GATA, L.ORIHUELA, A.SEURET, L.ZACCARIAN
Loyola Andalucía, MAC
Revue Scientifique : Automatica, Vol.99, pp.213-220, Janvier 2019 , N° 18383
This paper deals with the problem of distributedly estimating the state of an LTI plant through an interconnected network of agents. The proposed approach results in an observer structure that incorporates consensus among the agents and that can be distributedly designed, achieving a robust solution with a good estimation performance. The developed solution is based on an iterative decomposition of the plant in the local observable staircase forms. The proposed observer has several positive features compared to recent results in the literature, which include milder assumptions on the network connectivity and the ability to set the convergence rate.
Q.L.HAN, X.M.ZHANG, A.SEURET, F.GOUAISBAUT, Y.HE
Revue Scientifique : IET Control Theory & Applications, Vol.13, N°1, 15p., Janvier 2019, doi 10.1049/iet-cta.2018.5188 , N° 18362
This paper provides an overview and in-depth analysis of rec ent advances in stability of linear systems with time-varyi ng delays. First, recent developments of a delay convex analys is approach, a reciprocally convex approach and the constru ction of Lyapunov-Krasovskii functionals are reviewed insightful ly. Second, in-depth analysis of the Bessel-Legendre inequ ality and some affine integral inequalities is made, and recent stability r esults are also summarized, including stability criteria f or three cases of a time-varying delay, where information on the bounds of the t ime-varying delay and its derivative is totally known, part ly known and completely unknown, respectively. Third, a number of stabi lity criteria are developed for the above three cases of the t ime-varying delay by employing canonical Bessel-Legendre inequalitie s, together with augmented Lyapunov-Krasovskii functiona ls. It is shown through numerical examples that these stability criteria o utperform some existing results. Finally, several challen ging issues are pointed out to direct the near future research.
N.BRISEBARRE, M.M.JOLDES, J.M.MULLER, A.M.NANES, J.PICOT
LIP, Lyon, MAC, ENS Lyon, UTCLUJ
Rapport LAAS N°18428, Décembre 2018, 32p.
We are interested in obtaining error bounds for the classical FFT algorithm in floating-point arithmetic, for the 2-norm as well as for the infinity norm. For that purpose we also give some results on the relative error of the complex multiplication by a root of unity, and on the largest value that can take the real or imaginary part of one term of the FFT of a vector x, assuming that all terms of x have real and imaginary parts less than some value b.