Past events 2009

PhD - Visitors - Conferences - Missions - Seminars organised by the group - Other

  • PhD
    06 November : PhD defence of Tais Calliero Tognetti from Brasil, 11h30 visio-conférence, salle de Direction
    Titre :  Commande de systèmes dynamiques : stabilité absolue, saturation et bilinéarité
    Jury :   J. Daafouz (CRAN, Nancy, France)
                J.M. Gomes da Silva Jr (UFRGS, Porto Alegre, Brasil)

        V.F. Montagner (UFSM, Santa Maria, Brasil)

        I. Queinnec (LAAS-CNRS, Toulouse, France)

        PhD Directors

        S. Tarbouriech (LAAS-CNRS) 

        P.L.D. Peres (UNICAMP, Brasil) 

    Abstract : This thesis presents contributions to the solution of the problems of stability analysis and synthesis of state feedback controllers for dynamic systems with non-linear elements, by means of conditions based on linear matrix inequalities and Lyapunov functions. For switched systems subject to saturation in the actuators, convex conditions to design switched and robust controllers are presented. The saturation is modeled as a sector non-linearity and an estimate of the domain of stability is determined.

    For linear systems with polytopic uncertainties and sector non-linearities, convex conditions of finite dimension to build Lur’e functions with homogeneous polynomially parameter dependence are provided. If satisfied, the conditions guarantee the stability of the entire domain of uncertainty for all sector non-linearities, allowing the design of linear and non-linear robust state feedback stabilizing controllers.

    For continuous and discrete-time unstable bilinear systems, a procedure to design a state feedback stabilizing control gain is proposed. The method is based on the alternate solution of two convex optimization problems described by linear matrix inequalities, providing an estimate of the domain of stability. Extensions to handle robust and linear parameter varying controllers are also presented.

    Key-words: Bilinear systems. Switching systems. Saturation of actuators. Lyapunov functions. Linear matrix inequalities. Sector non-linearities. Stability domain.

  •  09 November:  C. Prieur will defend his habilitation thesis. More information
  • 23 Novembre : PhD Defence of Yassine Ariba, from 14:30 in the Conference Room.
    Title :  On the stability of time-varying delay systems: theory and application to congestion control of a router
    Jury :   Olivier Sename, professeur à l'INP de Grenoble, laboratoire gipsa-lab

        Hugues Mounier, maitre de conf à l'université de Paris sud 11

        Jean-pierre Richard, professeur à l'Ecole Centrale de Lille

        Chaouki T. Abdallah, professeur à l'université de New Mexico, USA

        Jean-Louis Calvet, professeur à l'université Paul Sabatier de Toulouse 

    Abstract:

    This thesis investigates the existing links between the control theory and the communication networks supporting the well-known communication protocol TCP (Transmission Control Protocol). The key idea consists in using the tools from control theory for the network traffic stabilization. Hence, this manuscript has naturally been turned towards two research lines: the design of stability and stabilization conditions for delay systems and the congestion control issue in IP network (Internet Protocol).

    First, we have addressed the stability analysis of time-varying delay systems via two temporal approaches.  On one hand, we consider the well-known Lyapunov-Krasovskii method in which new functionals are built according to original modelings of the system. To this end, we proceed to a model augmentation through delay fractionning or with the use of the system derivative. On the other hand, the stability is also assessed with an input-output approach, borrowing then tools from the robust control framework. More precisely, the time delay system is rewritten as the interconnection of a linear application with a uncertain matrix consisting in a set of operators that defines the former system. Thus, having revisited the quadratic separation principle, additional auxiliary operators are proposed in order to provide an enhanced modeling of the delayed dynamic of the system. In both cases, we aim at taking into account relevant informations on the system to reduce the conservatism of the stability analysis. All the stability criteria are expressed as linear matrix inequality conditions.

    In a second part, the developed methodology is used to cope with the congestion phenomenon in a router supporting TCP communications. This end-to-end protocol is sensitive to packet losses and adjusts thereof its sending rate with respect to the AIMD (Additive-Increase Multiplicative-Decrease) algorithm. Based on the Active Queue Management (AQM)   principle, we design a controller embedded into the router that monitors the packet losses. A such mechanism allows to stabilize the network traffic and to control the congestion phenomenon in spite of the delays induced by the network. All theoretical results are tested through nonlinear simulations in Matlab as well as some experiments under the network simulator NS-2.

    • Visitors
    • 27-29 October: A. Karimi from EPFL, Lausanne, Switzerland, visits the group MAC. 
    • 16 November 2009 - 13 January 2010 : L. Rodrigues,  Associate Professor Department of Mechanical and Industrial Engineering,  Concordia University, visits the Group MAC.
    •  22-24 November : C. Abdallah, University of New Mexico (Albuquerque, USA), visits the Group MAC.
    • 06-16 December : J. F. Camino, Professor at the Universidade Estadual de Campinas, visits the Group MAC. 
        • Conferences
        • 13-19 December: V. Andrieu, D. Peaucelle, G. Garcia and P. Pakshin are at the48th CDC Conference in Shangaï, China.  
        • 15-22 December : G. Garcia is at a PhD students meeting in Tunis and at the STA'09 Conference in Monastir, Tunisia.
        • Missions
          • 17-22 November : S. Tarbouriech is at the LAGEP, Lyon, France. 
          • 20-21 Novembre : D. Bily, M. Kara-Zaitri, B. Robu and V. Mahout will be presenting the "Helicopter" demo and accompanying visitors around the laboratory during the "Fête de la Science".
          • 24-26 November : D. Henrion is at Birmingham for the Royal Project Society UK.
          • 26 November : S. Tarbouriech is at the JESA Editing Comity meeting in Paris, France.
          • 29-30 November : L. Baudouin is at the Frick Laboratory, Dept. of Chemistry, Princeton University for a PICS meeting 'Manipulation and identification of quantum phenomena: numerical and theoretical approaches', New York, United States.
          • 03-04 December : L. Douat is at LIRMM for the PAR2 Robo project, France.

          • Seminars and Conferences organised by the group
            • 28 October: Alireza Karimi from EPFL, Lausanne, Switzerland, gives a talk, salle du Conseil at 14h00.
              Title: Robust controller designfor nonparametric models by convex optimization.
              Abstract: A new approach for robust fixed-order H-infinity controller design by convex optimization is proposed. Linear time-invariant single-input single-output systems represented by nonparametric models in the frequency domain are considered. It is shown that the H-infinity robust performance condition can be represented by a set of linearor convex constraints with respect to the parameters of a linearly parameterized controller in the Nyquist diagram. Multimodel and frequency-domain uncertainty can be considered straightforwardly in the proposed approach. The extension to multivariable systems and gain-scheduled controller design are also discussed. The effectiveness of the approach is illustrated via the solution to an international benchmark problem.
            • 19 November: Vadim Utkin, from the Ohio State University, United States, gives a talk on 'Salle du Conseil' from 15:00.
              Title: SLIDING MODE CONTROL: MATHEMATICAL TOOLS, DESIGN AND APPLICATIONS.
              AbstractControl actions of the systems under study are assumed to be discontinuous function of the system state. For the principle operation mode the state trajectories are in the vicinity of discontinuity points. This motion is referred to as sliding mode.

              The scope of sliding mode control studies embraces 

              -mathematical methods of  discontinuous differential equations, 

              -design of manifolds in the state space  and discontinuous control functions  enforcing motions along the manifolds, 

              -implementation of sliding mode controllers and their applications to control of dynamic plants.

               The first problem concerns development of the tools to derive the equations governing sliding modes and the conditions for this motion to exist. Formally motion equations of SMC do not satisfy the conventional uniqueness-existence theorems of the ordinary differential equations theory. The reasons of ambiguity are discussed. The regularization approach to derive sliding motion equations is demonstrated. The sliding mode existence problem is studied in terms of the stability theory.

                Enforcing sliding modes enables decoupling of the design procedure, since the motion preceding sliding mode and motion in sliding mode are of lower dimensions and may be designed independently. On the other hand, under so-called matching conditions the sliding mode equations depend neither plant parameter variations nor external disturbances. Therefore sliding mode control algorithms are efficient when controlling nonlinear dynamic plants of high dimension operating under uncertainty conditions. The design methods are demonstrated mainly for systems in the regular form. The design methodology is illustrated for sliding mode control in linear systems.

                The sliding mode control methodology is generalized for discrete-time systems to make feasible its implementation for the systems with digital controllers. The concept ?sliding mode? is introduced for arbitrary dynamic systems.

                New mathematical and design methods are needed for sliding mode control in infinite-dimensional systems including systems governed by PDE. The recent results in this area are briefly surveyed. The control design is illustrated for the flexible shaft and plate.

                The problem of chattering caused by unmodeled dynamics is discussed in the context of applications.  The systems with asymptotic observers are shown to be free of chattering. Sliding mode control of electric drives, mobile robots, in automotive applications is demonstated.

            • 19-20 November: Seminar on geometry and algebra of linear matrix inequalities organized at LAAS-CNRS, Toulouse, France.
            • 09 December : Martin Mevissen, Phd Candidate at Tokyo Institue of Technology, gives a talk at 14h00, salle Europe
              Title :   Sparse SDP relaxation techniques for solving differential equations
              Abstract : To solve a system of differential equations numerically, we formulate it as a polynomial optimization problem (POP) by discretizing it via a finite difference approximation. The resulting POP satisfies a structured sparsity, which we can exploit to apply the sparse SDP relaxation of Waki, Kim, Kojima and Muramatsu to the POP to obtain a roughly approximate solution of the differential equation. More accurate solutions are derived by additionally applying local convergent optimization methods as sequential quadratic programming. The main features  of this approach are: (a) we can choose an appropriate objective function, and (b) we can add inequality constraints on the unknown variables and their derivatives, in order to compute specific solutions of the system of differential equations. Fine grid discretizations of differential equations result in high dimensional POPs and large-scale SDP relaxations. We discuss a technique to reduce the size of sparse SDP relaxation by tran!  sforming general POPs into quadratic optimization problems. Finally, we will demonstrate this approach on examples arising in different fields such as, reaction-diffusion equations, fluid dynamics and optimal control.
          Last update 05/01/2010