Laboratoire d’analyse et d’architecture des systèmes
M.ZHANG, Z.LI, M.CABASSUD, B.DAHHOU
GUIZHOU, LGC, DISCO
Manifestation avec acte : Chinese Control Conference ( CCC ) 2017 du 26 juillet au 28 juillet 2017, Dalian (Chine), Juillet 2017, 7p. , N° 17141
M.SAFI, L.BAUDOUIN, A.SEURET
Manifestation avec acte : IFAC World Congress 2017 du 09 juillet au 14 juillet 2017, Toulouse (France), Juillet 2017, 6p. , N° 17073
The objective of this contribution is to improve recent stability results for a system coupling ordinary differential equations to a vectorial transport partial differential equation by proposing a new structure of Lyapunov functional. Following the same process of most of the investigations in literature, that are based on an a priori selection of Lyapunov functionals and use the usual integral inequalities (Jensen, Wirtinger, Bessel...), we will present an efficient method to estimate the exponential decay rate of this coupled system leading to a tractable test expressed in terms of linear matrix inequalities. These LMI conditions stem from the new design of a candidate Lyapunov functional, but also the inherent properties of the Legendre polynomials, that are used to build a projection of the infinite dimensional part of the state of the system. Based on these polynomials and using the appropriate Bessel-Legendre inequality, we will prove an exponential stability result and in the end, we will show the efficiency of our approach on academic example.
L.BAUDOUIN, A.SEURET, F.GOUAISBAUT, M.DATTAS
Manifestation avec acte : IFAC World Congress 2017 du 09 juillet au 14 juillet 2017, Toulouse (France), Juillet 2017, 6p. , N° 17102
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.
Ouvrage (contribution) : Advances and Trends in Optimization with Engineering Applications, N°ISBN 978-1-61197-467-6, Juin 2017, Chapter 10, pp.121-133 , N° 14357
Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual linear problem consists of finding the largest lower bound on the value function of the optimal control problem. Various approximation results relating the original optimal control problem and its linear conic formulations are developed. As illustrated by a couple of simple examples, these results are relevant in the context of finite-dimensional semidefinite programming relaxations used to approximate numerically the solutions of the infinite-dimensional linear conic problems.
T.GUEROUT, P.LOPEZ, T.MONTEIL, C.ARTIGUES, Y.GAOUA, G.DA COSTA
SARA, ROC, IRIT-UPS
Revue Scientifique : Future Generation Computer Systems, Vol.71, pp.1-17, Juin 2017 , N° 17006
The analysis of the Quality of Service (QoS) level in a Cloud Computing environment becomes an attractive research domain as the utilization rate is daily higher and higher. Its management has a huge impact on the performance of both services and global Cloud infrastructures. Thus, in order to nd a good trade-off, a Cloud provider has to take into account many QoS objectives, and also the manner to optimize them during the virtual machines allocation process. To tackle this complex challenge, this article proposed a multiobjective optimization of four relevant Cloud QoS objectives, using two different optimization methods: a Genetic Algorithm (GA) and a Mixed Integer Linear Programming (MILP) approach. The complexity of the virtual machine allocation problem is increased by the modeling of Dynamic Voltage and Frequency Scaling (DVFS) for energy saving on hosts. A global mixed-integer non linear programming formulation is presented and a MILP formulation is derived by linearization. A heuristic decomposition method, which uses the MILP to optimize intermediate objectives, is proposed. Numerous experimental results show the complementarity of the two heuristics to obtain various trade-offs between the different QoS objectives.
Manifestation avec acte : Chinese Control and Decision Conference ( CCDC ) 2017 du 28 mai au 30 mai 2017, Chongqing (Chine), Mai 2017, 6p. , N° 17142
A.CHEREF, A.AGNETIS, C.ARTIGUES, J.C.BILLAUT
ROC, UNISI, LI
Rapport LAAS N°17126, Mai 2017
In this paper, we consider an integrated production and outbound delivery scheduling problem. In particular, we address the situation in which the scheduling sequence and the delivery sequence are the same and predefined. A set of jobs are processed on a single machine and finished jobs are delivered to the customers by a single capacitated vehicle. Each job has a processing time and transportation times between customers are taken into account. Since the sequence is given, the problem consists to form batches of jobs and our objective is to minimize the sum of the delivery times or general functions of the delivery times. The NP-hardness of the general problem is established and a pseudopolynomial time dynamic programming algorithm is given. Some particular cases are treated, for which NP-hardness proofs and polynomial time algorithms are given. Finally, a fixed-parameter tractability result is given.
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
In many resource allocation problems, optimal allocation strategies must be determined when only a quantized version of the relevant parameters are available, for instance, power allocation in wireless communications. The contribution of this work is threefold. First, the quantization problem is revisited and a framework which encompasses the classical problem of quantization is proposed. Instead of minimizing the distortion, the goal is to minimize the gap between the maximum of a general payoff function (which would be reached by knowing all parameters of the function) and what is effectively reached when only the quantized version of the parameters is available. Then, to determine such a quantizer, the well-known Lloyd-Max algorithm is generalized. At last, we show how this framework can be applied to the problem of power control in wireless communications; the obtained numerical results clearly show the potential of such a framework.
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.