Laboratoire d’analyse et d’architecture des systèmes
D.SIMON, A.SEURET, O.SENAME
LIRMM, MAC, GIPSA-Lab
Rapport LAAS N°17125, DOI 10.1080/00207721.2017.1316879, Mai 2017, 11p.
The efficient control of real-time distributed systems, where continuous components are governed through digital devices and communication networks, needs a careful examination of the constraints arising from the different involved domains inside co-design approaches. Thanks to the robustness of feedback control, both new control methodologies and slackened real-time scheduling schemes are proposed beyond the frontiers between these traditionally separated fields. A methodology to design robust aperiodic controllers is provided, where the sampling interval is considered as a control variable of the system. Promising experimental results are provided to show the feasibility and robustness of the approach.
C.ZHANG, N.KHALFET, S.LASAULCE, V.VARMA, S.TARBOURIECH
L2S, CRAN, Vandoeuvre, MAC
Manifestation avec acte : International Workshop on Resource Allocation, Cooperation and Competition in Wireless Networks ( RAWNET ) 2017 du 15 mai au 15 mai 2017, Paris (France), Mai 2017, 6p. , N° 17114
E.PAUWELS, D.HENRION, J.B.LASSERRE
Ouvrage (contribution) : Geometric and Numerical Foundations of Movements, Springer, N°ISBN 978-3-319-51546-5, Mai 2017 , N° 16159
We propose a tutorial on relaxations and weak formulations of optimal control with their semidefinite approximations. We present this approach solely through the prism of positivity certificates which we consider to be the most accessible for a broad audience, in particular in the engineering and robotics communities. This simple concept allows to express very concisely powerful approximation certificates in control. The relevance of this technique is illustrated on three applications: region of attraction approximation, direct optimal control and inverse optimal control, for which it constitutes a common denominator. In a first step, we highlight the core mechanisms underpinning the application of positivity in control and how they appear in the different control applications. This relies on simple mathematical concepts and gives a unified treatment of the applications considered. This presentation is based on the combination and simplification of published materials. In a second step, we describe briefly relations with broader literature, in particular, occupation measures and Hamilton-Jacobi-Bellman equation which are important elements of the global picture. We describe the Sum-Of-Squares (SOS) semidefinite hierarchy in the semialgebraic case and briefly mention its convergence properties. Numerical experiments on a classical example in robotics, namely the nonholonomic vehicle, illustrate the concepts presented in the text for the three applications considered.
A.BENOIT, M.M.JOLDES, M.MEZZAROBBA
EXT, MAC, LIP6-CNRS
Revue Scientifique : Mathematics of Computation , Vol.86, N°305, pp.1303-1341, Mai 2017 , N° 14329
A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of such methods in the context of rigorous computing (where we need guarantees on the accuracy of the result), and from the complexity point of view. It is well-known that the order-n truncation of the Chebyshev expansion of a function over a given interval is a near-best uniform polynomial approximation of the function on that interval. In the case of solutions of linear differential equations with polynomial coefficients, the coefficients of the expansions obey linear recurrence relations with polynomial coefficients. Unfortunately, these recurrences do not lend themselves to a direct recursive computation of the coefficients, owing among other things to a lack of initial conditions. We show how they can nevertheless be used, as part of a validated process, to compute good uniform approximations of D-finite functions together with rigorous error bounds, and we study the complexity of the resulting algorithms. Our approach is based on a new view of a classical numerical method going back to Clenshaw, combined with a functional enclosure method.
G.MICHIELETTO, A.CENEDESE, L.ZACCARIAN, A.FRANCHI
RIS, University of Padova, MAC
Rapport LAAS N°17111, Avril 2017, 6p.
A quaternion-based nonlinear control strategy is here presented to steer and keep a generic multi-rotor platform in a given reference position. Exploiting a state feedback structure, the proposed solution ensures the stabilization of the aerial vehicle so that its linear and angular velocity are zero and its attitude is constant. The main feature of the designed controller is the identification of a zero-moment direction in the feasible force space, i.e., a direction along which the control force intensity can be assigned independently of the control moment. The asymptotic convergence of the error dynamics is confirmed by simulation results on a hexarotor with tilted propellers.
C.GAZZINO, D.ARZELIER, L.CERRI, D.LOSA, C.LOUEMBET, C.PITTET-MECHIN
MAC, ROC, CNES, Thalès Alenia Space
Rapport LAAS N°17110, Avril 2017, 6p.
In this paper, a fuel optimal rendezvous problem is tackled in the Hill-Clohessy-Wiltshire framework with several operational constraints as bounds on the thrust, non linear non convex and disjunctive operational constraints (on-off profile of the thrusters, minimum elapsed time between two consecutive firings...). An indirect method and a decomposition technique have already been combined in order to solve this kind of optimal control problem with such constraints. Due to a great number of parameters to tune, satisfactory results are hard to obtain and are sensitive to the initial condition. Assuming that no singular arc exists, it can be shown that the optimal control exhibits a bang-bang structure whose optimal switching times are to be found. Noticing that a system with a bang-bang control profile can be considered as two subsystems switching from one with control on to with control off, and vice-versa, a technique coming from the switching systems theory is used in order to optimise the switching times.
S.TARBOURIECH, A.SEURET, L.MOREIRA, J.M.GOMES DA SILVA Jr
Rapport LAAS N°17103, Avril 2017, 6p.
The paper presents an observer-based event-triggered control strategy for linear systems subject to input cone-bounded nonlinearities by using only available measurable variables. Sufficient conditions based on linear matrix inequalities are proposed to ensure the asymptotic stability of the closed loop and the avoidance of Zeno behavior in an emulation context. Based on these conditions, a convex optimization problem to compute the parameters of the event-trigger rule aiming at reducing the number of control updates is proposed. The approach is illustrated on a numerical example that considers the control of a linear system with a logarithmic input quantization constraint.
L.BAUDOUIN, A.SEURET, F.GOUAISBAUT, M.DATTAS
Rapport LAAS N°17102, Avril 2017, 6p.
This paper addresses the stability analysis of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov approach. Relying on recent developments in the area of time-delay systems, a new method to study the stability of such a class of coupled finite/infinite dimensional systems is presented here. It consists in a Lyapunov analysis of the infinite dimensional state of the system using an energy functional enriched by the mean value of the heat variable. The main technical step relies on the use an efficient Bessel-like integral inequality on Hilbert space leading to tractable conditions expressed in terms of linear matrix inequalities. The results are then illustrated on academic examples and demonstrate the potential of this new approach.
L.DAL COL, S.TARBOURIECH, L.ZACCARIAN, M.KIEFFER
Rapport LAAS N°17081, DOI: 10.1002/rnc.3739, Avril 2017, 19p.
In this paper, we provide necessary and sufficient conditifor the quality-fair delivery of multimedia contents to mobile users. We control the encoding rates and the transmission rates of the video streams, delivered through a limited capacity channel. This problem is cast into a problem of consensus among identical discrete-time linear systems, connected through a network with fixed and fully connected topology. The information exchanged over the communication network is the measure of the quality of the encoded videos. Based on a consensus result for identical linear systems, we reduce the problem of designing the proportional and integral gains of the encoding rate and transmission rate controllers to a linear static output feedback. We propose an iterative design technique based on linear matrix inequalities to solve the corresponding nonconvex problem, thereby providing a constructive optimality-based approach to the proportional and integral gains tuning problem. We demonstrate the effectiveness of our method in simulations, where we compare it with pre-existing approaches
Y.ARIBA, D.ARZELIER, L.URBINA IGLESIAS
Rapport LAAS N°17095, Avril 2017, 6p.