Laboratoire d’analyse et d’architecture des systèmes
A.SEURET, C.PRIEUR, S.TARBOURIECH, L.ZACCARIAN
Revue Scientifique : IEEE Transactions on Automatic Control, Vol.64, N°5, pp.2061-2068, Mai 2019 , N° 17179
We first propose a nonsmooth hybrid invariance principle with relaxed conditions stemming from the fact that flowing solutions evolve only in the tangent cone, and complete jumping solutions cannot jump ouside the jump and flow sets. We then show an application consisting in the design of event-triggered rules to stabilize a class of uncertain linear control systems. The event-triggering rule depends only on local information, that is it uses only the output signals available to the controller. The approach proposed combines a hybrid framework to describe the closed-loop system with looped functionals based techniques. The proposed design conditions are formulated in terms of linear matrix inequalities (LMIs) ensuring global robust asymptotic stability of the closed-loop system. A tunable parameter is also available to guarantee an adjustable dwell-time property of the solutions. The effectiveness of the approach is evaluated through an example borrowed from the literature.
C.GAZZINO, D.ARZELIER, L.CERRI, D.LOSA, C.LOUEMBET, C.PITTET
MAC, ROC, CNES, Thalès Alenia Space
Revue Scientifique : Acta Astronautica, Vol.158, pp.12-22, Mai 2019 , N° 18029
In this paper, a control scheme is elaborated in order to perform the station keeping of a geostationary satellite equipped with electric propulsion while minimizing the fuel consumption. The use of electric thrusters imposes to take into account some additional non linear and operational constraints that make the overall station keeping optimal control problem difficult to solve directly. That is why the station keeping problem is decomposed in three successive control problems. The first one consists in solving a classical optimal control problem with an indirect method initialized by a direct method without enforcing the thrusters operational constraints. Starting from this non feasible solution for the genuine problem, the thrusters operating constraints are incorporated in the second problem, whose solution produces a feasible but non optimal control profile via two different ways. Finally, the third optimizes the commutation times thanks to a method borrowed to the switched systems theory. Simulation results on a realistic example validate the benefit of this particular control scheme in the reduction of the fuel consumption for the geostationary station keeping problem.
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
A.SEURET, H.OZBAY, C.BONNET
MAC, Bilkent University, INRIA Paris
Ouvrage (éditeur) : Low-Complexity Controllers for Time-Delay Systems, N°ISBN 978-3-319-05575-6, Mars 2019 , N° 14820
This volume in the newly established series Advances in Delays and Dynamics (ADD@S) provides a collection of recent results on the design and analysis of Low Complexity Controllers for Time Delay Systems. A widely used indirect method to obtain low order controllers for time delay systems is to design a controller for the reduced order model of the plant. In the dual indirect approach, an infinite dimensional controller is designed first for the original plant model; then, the controller is approximated by keeping track of the degradation in performance and stability robustness measures. The present volume includes new techniques used at different stages of the indirect approach. It also includes new direct design methods for fixed structure and low order controllers. On the other hand, what is meant by low complexity controller is not necessarily low order controller. For example, Smith predictor or similar type of controllers include a copy of the plant internally in the controller, so they are technically infinite dimensional. However, they have very nice numerical properties from the point of reliable implementation. Therefore, such predictor-based controllers are considered as low complexity. This book includes new predictor-based design techniques, with several application examples.
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.
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.
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.
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.
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.