DISCO is a joint team with Laboratoire des Signaux et Systèmes (L2S) U.M.R. C.N.R.S. 8506, and Supélec, which has been created in January 2010.

The goal of the project is to better understand and well formalize the effects of complex environments on the dynamics of the interconnections, as well as to develop new methods and techniques for the analysis and control of such systems.

It is well-known that the interconnection of dynamic systems has for consequence an increased complexity of the behavior of the “total” system both in the presence and absence of feedback control loops.

In a simplified way, as the concept of dynamics is well-understood, the interconnections can be seen as associations (by connections of materials or information flows) of distinct systems to ensure a pooling of the resources with the aim of obtaining a better operation with the constraint of continuity of the service in the event of a fault. In this context, the environment can be seen as a collection of elements, structures or systems, natural or artificial constituting the neighborhood of a given system. The development of interactive games through communication networks, control from distance (e.g. remote surgical operations) or in hostile environment (e.g. robots, drones), as well as the current trend of large scale integration of distribution (and/or transport and/or decision) and open information systems with systems of production, lead to new modeling schemes in problems where the dynamics of the environment have to be taken into account.

In order to tackle the control problems arising in the above examples, the team investigates new theoretical methods, develop new algorithms and implementations dedicated to these techniques.

Silviu Iulian Niculescu obtained the Silver Medal from CNRS in December 2011.

José Luis Avila Alonso won the Best Poster Price at the 4th DIGITEO Annual Forum.

Benjamin Bradu won the Best PhD Price of the GDR MACS.

We want to model phenomena such as a temporary loss of connection (e.g. synchronisation of the movements through haptic interfaces), a nonhomogeneous environment (e.g. case of cryogenic systems) or the presence of the human factor in the control loop (e.g. grid systems) but also problems involved with technological constraints (e.g. range of the sensors). The mathematical models concerned include integro-differential, partial differential equations, algebraic inequalities with the presence of several time scales, whose variables and/or parameters must satisfy certain constraints (for instance, positivity).

Algebraic analysis of linear systems

Study of the structural properties of linear differential time-delay systems and linear infinite-dimensional systems (e.g. invariants, controllability, observability, flatness, reductions, decomposition, decoupling, equivalences) by means of constructive algebra, module theory, homological algebra, algebraic analysis and symbolic computation , , , , , .

Robust stability of linear systems

Within an interconnection context, lots of phenomena are modelled directly or after an approximation by delay systems. These systems might have fixed delays, time-varying delays, distributed delays...

For various infinite-dimensional systems, particularly delay and fractional systems, input-output and time-domain methods are jointly developed in the team to characterize stability.
This research is developed at four levels: analytic approaches (

Robustness/fragility of biological systems

Deterministic biological models describing, for instance, species interactions, are frequently composed of equations with important disturbances and poorly known parameters. To evaluate the impact of the uncertainties, we use the techniques of designing of global strict Lyapunov functions or functional developed in the team.

However, for other biological systems, the notion of robustness may be different and this question is still in its infancy (see, e.g. ). Unlike engineering problems where a major issue is to maintain stability in the presence of disturbances, a main issue here is to maintain the system response in the presence of disturbances. For instance, a biological network is required to keep its functioning in case of a failure of one of the nodes in the network. The team, which has a strong expertise in robustness for engineering problems, aims at contributing at the develpment of new robustness metrics in this biological context.

Linear systems: Analytic and algebraic approaches are considered for infinite-dimensional linear systems studied within the input-output framework.

In the recent years, the Youla-Ku

A central issue studied in the team is the computation of such factorizations for a given infinite-dimensional linear system as well as establishing the links between stabilizability of a system for a certain norm and the existence of coprime factorizations for this system. These questions are fundamental for robust stabilization problems , , , .

We also consider simultaneous stabilization since it plays an important role in the study of reliable stabilization, i.e. in the design of controllers which stabilize a finite family of plants describing a system during normal operating conditions and various failed modes (e.g. loss of sensors or actuators, changes in operating points) . Moreover, we investigate strongly stabilizable systems , namely systems which can be stabilized by stable controllers, since they have a good ability to track reference inputs and, in practice, engineers are reluctant to use unstable controllers especially when the system is stable.

Nonlinear systems

The project aims at developing robust stabilization theory and methods for important classes of nonlinear systems that ensure good controller performance under uncertainty and time delays. The main techniques include techniques called backstepping and forwarding, contructions of strict Lyapunov functions through so-called "strictification" approaches and construction of Lyapunov-Krasovskii functionals , , .

Predictive control

For highly complex systems described in the time-domain and which are submitted to constraints, predictive control seems to be well-adapted. This model based control method (MPC: Model Predictive Control) is founded on the determination of an optimal control sequence over a receding horizon. Due to its formulation in the time-domain, it is an effective tool for handling constraints and uncertainties which can be explicitly taken into account in the synthesis procedure . The team considers how mutiparametric optimization can help to reduce the computational load of this method, allowing its effective use on real world constrained problems.

The team also investigates stochastic optimization methods such as genetic algorithm, particle swarm optimization or ant colony as they can be used to optimize any criterion and constraint whatever their mathematical structure is. The developed methodologies can be used by non specialists.

PID controllers

Even though the synthesis of control laws of a given complexity is not a new problem, it is still open, even for finite-dimensional linear systems. Our purpose is to search for good families of “simple” (e.g. low order) controllers for infinite-dimensional dynamical systems. Within our approach, PID candidates are first considered in the team , .

Predictive control

The synthesis of predictive control laws is concerned with the solution of multiparametric optimization problems. Reduced order controller constraints can be viewed as non convex constraints in the synthesis procedure. Such constraints can be taken into account with stochastic algorithms.

Finally, the development of algorithms based on both symbolic computation and numerical methods, and their implementations in dedicated Scilab/Matlab/Maple toolboxes are important issues in the project.

In collaboration with the BANG project-team at INRIA Paris-Rocquencourt, the DRACULA team at INRIA Grenoble - Rhône-Alpes, the COMMANDS project team at INRIA Saclay-Île-de-France, INSERM, Cordeliers Research Center and St Antoine Hospital, Paris, we consider the modeling and control of Acute Myeloid Leukemia (AML).

The main goal of this project is the theoretical optimization of drug treatments used in AML, with experimental validation in cell cultures, aiming at proposing efficient therapeutic strategies in clinic.

We work on an discrete maturity-structured model of hematopoiesis introduced in . In this model, several generations of cells are considered and, for the first time, the cell cycle duration is assumed to be distributed. At each level, the population of immature cells are divided into two subpopulations: proliferating and non proliferating cells. Physiological phenomena of re-introduction from the non proliferative into the proliferative subpopulation is modeled in the team as a nonlinear dynamical interconnection between the two sub-populations, and input-output tools seem to be useful in this context .

We study problems of coexistence or regulation of species of micro-organisms in bio-reactors called chemostats.

In and , we applied the technique of backstepping and of construction of strict Lyapunov functions to solve a tracking probelm for the celebrated aircraft model PVTOL (Planar Vertical Takeoff and Landing). It is a benchmark dynamics for an aircraft moving in a vertical plane that contains the important features needed to design controllers for real aircraft. The controllers are the thrust out of the bottom and the rolling moment controller. The main challenges are that the thrust controller must remain nonnegative and that the system is underactuated. We overcame these challenges through a change of variables that transforms the PVTOL tracking dynamics into a chain of three subsystems and then applying asymptotic strict Lyapunov function methods and bounded backstepping. Relative to the PVTOL model literature, the significance of our PVTOL work was (a) the global boundedness of our controllers in the decoupled coordinates, (b) their applicability to cases where the velocity measurements are not available, by using an observer, (c) the positive lower bound on the thrust controller, (d) our allowing a very general class of reference trajectories, and (e) our use of ISS to certify good performance under actuator errors, which would not be possible using LaSalle invariance or nonstrict Lyapunov functions.

The YALTA package is dedicated to the study of classical and fractional systems with delay in the frequency-domain. Its objective is to provide basic but important information such as, for instance, the position of the neutral chains of poles and unstable poles, as well as the root locus with respect to the delay of the system. The corresponding algorithms are based on recent theoretical results (see, for instance, and ) and on classical continuation methods exploiting the particularities of the problem , . Some rafinments have been included this year in order to deal with systems with tricky numerical behaviour. The YALTA package will be available in the first semester of 2012.

The
OreModulespackage
, based on the commercial Maple package Ore

The
Staffordpackage of
OreModules
contains an implementation of two constructive versions of Stafford's
famous but difficult theorem
stating that every ideal over the Weyl algebra
*Monge problem*), differential flatness, the reduction and decomposition problems and Serre's reduction problem. To our knowledge, the
Staffordpackage is the only implementation of Stafford's theorems nowadays available. The binary of the package is freely available at
http://

The
Quillen-Suslinpackage
contains an implementation of the famous Quillen-Suslin theorem
,
. In particular, this implementation allows us to compute bases of
free modules over a commutative polynomial ring with coefficients in a field (mainly

The
OreMorphismspackage
of
OreModules
is dedicated to the implementation of homological algebraic tools such
as the computations of homomorphisms between two finitely presented modules over certain noncommutative polynomial algebras (Ore algebras), of kernel, coimage, image and cokernel of
homomorphisms, Galois transformations of linear multidimensional systems and idempotents of endomorphism rings. Using the packages
Staffordand
Quillen-Suslin, the factorization, reduction and decomposition problems can be constructively studied for different classes of linear multidimensional
systems. Many linear systems studied in engineering sciences, mathematical physics and control theory have been factorized, reduced and decomposed by means of the
OreMorphismspackage. The binary of the package is freely available at
http://

The
JanetMorphismspackage is dedicated to a new mathematic approach to quasilinear systems of partial differential equations (e.g., Burger's equation,
shalow water equations, Euler equations of a compressible fluid) based on algebraic analysis and differential algebra techniques
. See Section
. This package computes symmetries, first integrals of motion, conservation laws,
study Riemann invariants... The
JanetMorphismspackage is based on the
`Janet`package (
http://

The PurityFiltrationpackage, built upon the OreModulespackage, is an implementation of a new effective algorithm obtained in , , which computes the purity/grade filtration , of linear functional systems (e.g., partial differential systems, differential time-delay systems, difference systems) and equivalent block-triangular matrices. See Section . This package is used to compute closed form solutions of over/underdetermined linear partial differential systems which cannot be integrated by the standard computer algebra systems such as Maple and Mathematica. This package will soon be available.

The
AbelianSystemspackage is an implementation of an algorithm developed in
,
,
for the computation of the purity/grade filtration
,
in the powerful
`homalg`package of GAP 4 dedicated to constructive homological algebra methods, and developed by Barakat (University of Kaiserslautern) and his collaborators (
http://
`homalg`procedure which computes purity filtration by means of time-consuming spectral sequences. Using the
`homalg`package philosophy, the
AbelianSystemspackage can be used for the computation of the purity filtration of objects in different constructive abelian categories such as sheaves
over projective varieties as demonstrated in the
`homag`package called
`Sheaves`(see
http://

The
SystemTheorypackage is a
`homalg`based package dedicated to mathematical systems. This package, still in development, will include the algorithms developed in the
OreModulesand
OreMorphismspackages. It currently contains an implementation of the
OreMorphismsprocedures which handle the decomposition problem aiming at decomposing a module/system into direct sums of submodules/subsystems.

In
,
,
, it is shown that every linear functional system (e.g., PD systems,
differential time-delay systems, difference systems) is equivalent to a linear functional system defined by an upper block-triangular matrix of functional operators: each diagonal block is
respectively formed by a generating set of the elements of the system satisfying a purely
`homalg`package of GAP 4 (see Section
).

Given a linear multidimensional system (e.g., ordinary/partial differential systems, differential time-delay systems, difference systems), Serre's reduction aims at finding an equivalent linear multidimensional system which contains fewer equations and fewer unknowns. Finding Serre's reduction of a linear multidimensional system can generally simplify the study of structural properties and of different numerical analysis issues, and it can sometimes help solving the linear multidimensional system in closed form. In , Serre's reduction problem is studied for underdetermined linear systems of partial differential equations with either polynomial, formal power series or analytic coefficients and with holonomic adjoints in the sense of algebraic analysis , . These linear partial differential systems are proved to be equivalent to a linear partial differential equation. In particular, an analytic linear ordinary differential system with at least one input is equivalent to a single ordinary differential equation. In the case of polynomial coefficients, we give an algorithm which computes the corresponding linear partial differential equation.

In , we give a complete constructive form of the classical Fitting's lemma in module theory which studies the relation between equivalences of linear systems and isomorphisms of their associated finitely presented modules. The corresponding algorithms were implemented in the OreMorphismspackage (see Section ).

Many partial differential systems appearing in mathematical physics, engineering sciences and mathematical biology are nonlinear. Unfortunately, algebraic analysis and

In
,
,
, it was shown how the fractional representation approach to analysis
and synthesis problems developed by Vidyasagar, Desoer, Callier, Francis, Zames..., could be recast into a modern algebraic analysis approach based on module theory (e.g., fractional ideals,
algebraic lattices) and the theory of Banach algebras. This new approach successfully solved open questions in the literature. Basing ourselves on this new approach, we explain in
why the non-commutative geometry developed by Alain Connes is a
natural framework for the study of stabilizing problems of infinite-dimensional systems. Using the 1-dimensional quantized calculus developed in non-commutative geometry and results obtained in
,
,
, we show that every stabilizable system and their stabilizing
controllers naturally admit geometric structures such as connections, curvatures, Chern classes... These results are the first steps toward the use of the natural geometry of the
stabilizable systems and their stabilizing controllers in the study of the important

In , we present results on algorithmic methods for singular boundary problems for linear ordinary differential equations. Moreover, the implementation of integro-differential operators and the corresponding algorithms for boundary problems in the computer algebra system Maple is discussed. The operations implemented for regular boundary problems include computing Green's operators as well as composing and factoring boundary problems. For singular boundary problems, compatibility conditions and generalized Green's operators can be computed. In , we give a survey and new results on our algebraic and symbolic approach to boundary problem developed over the last years. The construction of integro-differential operators and polynomials over an integro-differential algebra is described in detail along with a generic implementation of the corresponding canonical forms and algorithms.

In a joint work, Stefan Müller and G. Regensburger propose a notion of generalized mass action systems that could serve as a more realistic model for reaction networks in intracellular environments; classical mass action systems capture chemical reaction networks in homogeneous and dilute solutions, see e.g. and . We show that several results of Chemical Reaction Network Theory carry over to the case of generalized mass action kinetics. Our main result essentially states that, if the sign vectors of the stoichiometric and the kinetic-order subspace coincide, there exists a unique positive complex balancing equilibrium in every stoichiometric compatibility class.

In a cooperation with Hansjörg Albrecher, Corina Constantinescu (both University of Lausanne), Zbigniew Palmowski (University of Wroclaw), and Markus Rosenkranz (University of Kent), we developed a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differential equations with variable coefficients and the corresponding Green's operators (integral operators), generalizing the approach from . We obtain also closed-form solutions for more specific functions in the compound Poisson risk model.

A. Quadrat and G. Regensburger (in the frame of his grant) are working on a new approach for studying algebraic and algorithmic properties of systems of linear ordinary integro-differential equations with boundary conditions. In a recent series of papers, in particular, , , V. V. Bavula obtained numerous algebraic results for modules over the ring of integro-differential operators with polynomial coefficients using generalized Weyl algebras. We are interested in how far some of his approach can be made algorithmic and generalized to boundary problems. First results in this direction were presented at the Journées Nationales de Calcul Formel (JNCF 2011).

In order to yield the set of all stabilizing controllers of a large class of MIMO fractional time-delay systems, we may look for coprime factorizations of the transfer function and their
corresponding Bézout factors. As primary results, in considering

The

The technique, based on the notion of interval observer, is a recent state estimation technique, which offers the advantage of providing information on the current state of a system at any instant of time. The firts interval observers where relying on the assumption that the system was cooperative or, roughly speaking, "almost" cooperative.

In and , for families of partial differential equations (PDEs) with particular stabilizing boundary conditions, we have constructed strict Lyapunov functions. The PDEs under consideration were parabolic and, in addition to the diffusion term, might contain a nonlinear source term plus a convection term. The boundary conditions were the classical Dirichlet conditions, or the Neumann boundary conditions or a periodic one. The constructions relied on the knowledge of weak Lyapunov functions for the nonlinear source term. The strict Lyapunov functions were used to prove asymptotic stability in the framework of an appropriate topology. Moreover, when an uncertainty is considered, our construction of a strict Lyapunov function made it possible to establish some robustness properties of Input-to-State Stability (ISS) type.

In the contributions and , we revisited the problem of constructing globally asymptotically stabilizing control laws for nonlinear systems in feedback form with a known pointwise delay in the input. The result we obtained covers a family of systems wider than those studied in the literature and endows with control laws with a single delay, in contrast to those given in previous works which include two distinct pointwise delays or distributed delays. The strategy of design is based on the construction of an appropriate Lyapunov-Krasovskii functional. An illustrative example ends the paper.

The usual adaptive control problem is to design a controller that forces all trajectories of the system to track a prescribed trajectory, while keeping the estimator of the unknown constant parameter vector bounded. We studied the important and more difficult adaptive tracking and estimation problem of simultaneously (1) forcing the trajectories of the system to track a given trajectory and (2) identifying the parameter vector. This problem was known to be solvable when the regressor satisfies a persistency of excitation condition, but the known results did not provide a strict Lyapunov function for the augmented error dynamics and so could not certify good performance such as ISS with respect to uncertainty added to the controller.

Our main result from covers adaptively controlled first-order nonlinear systems that satisfy the persistency of excitation condition and are affine in the unknown parameter vector. Our contribution consists in particular in constructing global strict Lyapunov functions for the augmented error dynamics In , we extended to adaptive tracking for nonlinear systems in feedback form with multiple inputs and unknown high-frequency gains multiplying the controllers. The control gains must be identified as part of the control objective. High-frequency gains are important for electric motors, flight dynamics, and robot manipulators. We used a persistency of excitation condition that again ensured tracking and parameter identification and led to the explicit construction of a global strict Lyapunov function for the closed loop augmented error dynamics. The strict Lyapunov function was key to proving integral ISS with respect to time varying uncertainties added to the unknown parameters.

Efficient dedicated methods have been developed for Hinfinity controller synthesis. However, such methods require translating the design objectives using weighting filters, whose tuning is not easy; in addition they lead to high order controllers which have to be reduced. A particle swarm optimization method is used to solve both problems successively: after having optimized the filters according to the design specifications using a full order controller but no reformulation of the constraints, a reduced-order one is computed using the obtained filters. Experimental tests for a pendulum in the cart exhibit much than satisfactory results , . In addition, the design of Hinfinity static output feedback has been done and tested using the Compleib librairy and exhibiting similar results to those obtained with the HIFOO solver .

The identification of systems is a key feature to get representative models and so to design efficient control laws. Numerous methods exist to identify the parameters of nonlinear systems when the global structure of the model is given. The problem appears to be much more difficult when this structure is unknown (symbolic regression). We introduces ant colony optimization (ACO) in solving the problem of non linear systems identification in the case of an unknown structure of the mode . Numerical results prove the viability of the approach.

Many studies have considered the solution of Unit Commitment problems for the management of energy networks. In this field, earlier work addressed the problem in determinist cases and in cases dealing with demand uncertainties. In this paper , the authors develop a method to deal with uncertainties related to the cost function. Indeed, such uncertainties often occur in energy networks (waste incinerator with a priori unknown waste amounts, cogeneration plant with uncertainty of the sold electricity price...). The corresponding optimization problems are large scale stochastic non-linear mixed integer problems. The developed solution method is a recourse based programming one. The main idea is to consider that amounts of energy to produce can be slightly adapted in real time, whereas the on/off statuses of units have to be decided very early in the management procedure. Results show that the proposed approach remains compatible with existing Unit Commitment programming methods and presents an obvious interest with reasonable computing loads.

In order to better take into account physiological phenomena as well as better understand the effect of the new anti-FLT3 therapy for AML, we have modified the model M. Adimy and F. Crauste in two ways :

- we have introduced a modeling of quick self-renewal of cells in each stage of maturation.

- we have modeled each phase of the proliferating compartment (that is

In parallel to this modeling task, Faten Merhi and Annabelle Ballesta have performed experiments in order to identify parameters of the model. These experiments (which will continue in 2012) tend to show that we will converge to a patient-dependant model.

The works , was inspired by the recent Deepwater Horizon oil spill disaster. The goal was to develop and implement robotic surveying methods to evaluate the immediate and longer term environmental impacts of the oil spills. It was joint with Michael Malisoff from the LSU and a Georgia Tech robotics team led by Fumin Zhang. Robotic surveying methods provide a low cost and convenient way to collect data in marsh areas that are difficult to access by human based methods. We designed strict Lyapunov functions that made it possible to use ISS to quantify the robustness of collision avoiding curve tracking controllers under controller uncertainty. The controllers are designed to keep the robot a fixed distance from, but moving parallel to, a two dimensional curve. Four challenges in applying ISS to curve tracking are (a) the need to restrict the magnitudes of the uncertainty to keep the state in the state space and build a strict Lyapunov function, (b) the likelihood of time delays in the controllers in real time applications, (c) possible parameter uncertainty such as unknown control gains, and (d) generalizations to three dimensional curve tracking. We overcame challenge (a) by finding maximum bounds on the perturbations that maintain forward invariance of a nested family of hexagons that fill the state space and transforming a nonstrict Lyapunov function into a strict Lyapunov function on the full state space. To address challenge (b), we used a Lyapunov-Krasovskii approach from to convert the strict Lyapunov function into a Lyapunov-Krasovskii functional. This led to an upper bound on the admissible controller delay that can be introduced into the controller while still maintaining ISS.

Alban Quadrat and Arnaud Quadrat (SAGEM Défense Sécurité, Etablissement de MASSY) have initiated discussions between SAGEM, the DISCO project and the L2S about a future collaboration in the direction of the analysis of the effect of the time-delay in inertially stabilized platforms for optical imaging systems. We hope that these discussions will conclude in a contract in 2012 on this subject.

DIGITEO Project (DIM LSC) ALMA

Project title: Mathematical Analysis of Acute Myeloid Leukemia

Decembrer 2010 - December 2013

Coordinator: Catherine Bonnet

Other partners: Inria Paris-Rocquencourt, France, L2S, France, INSERM, Cordeliers Research Center, France.

Abstract: this project studies a model of leukaemia based on previous works by M. Adimy and F. Crauste (Lyon), with theoretical model design adjustments and analysis in J. L. Avila Alonso's Ph D thesis and experimental parameter identification initiated by F. Merhi, postdoc of Bang (Dec. 2010-Nov. 2011), working at St. Antoine Hospital (Paris) on biological experiments on leukaemic cells.

DIGITEO Project (DIM Cancéropôle) ALMA2

Project title: Mathematical Analysis of Acute Myeloid Leukemia - 2

October 2011 - March 2013

Coordinator: Jean Clairambault (Inria Paris-Rocquencourt)

Other partners: Inria Saclay-Île-de-France, France, L2S, France, INSERM, Cordeliers Research Center, France.

Abstract: This project has taken over the experimental identification part in St. Antoine Hospital, together with further model design with the postdoc of A. Ballesta (BANG). With this postdoc project will also be developed the theoretical and experimental - in leukaemic cell cultures - study of combined therapies by classical cytotoxics (anthracyclins, aracytin) and recently available targeted therapies (anti-Flt-3).

DIGITEO Project (DIM LSC) MOISYR

Project title: Monotonie, observateurs par intervalles, et systèmes à retard

Decembre 2011 - Decembre 2014

Coordinator: Frédéric Mazenc

Other partners: organisme, labo (pays) L2S, France, Mines-ParisTech, France.

Abstract: MOISYR is concerned with the creation of the problem of extending the theory of monotone systems to the main families of continuous time systems with delay along with the application of this theory to the design of observers and interval observers. In particular, nonlinear systems with pointwise and distributed delays and stabilizable systems with delay in the input shall be considered. In a second setp, we shall extend our result to discrete time systems and to a specific class of continuous/discrete systems called Networked Control Systems.

A. Quadrat has a long term collaboration with T. Cluzeau and M. Barkatou (University of Limoges, XLIM).

A. Quadrat has developed a strong collaboration with the members of the Lehrstuhl B für Mathematik and particularly with Daniel Robertz and Mohamed Barakat. He is a member of a PHC Procope developed in collaboration with the University of Limoges (XLIM) and the Lehrstuhl B für Mathematik, RWTH Aachen University (2011-2012) which aims at developing computer algebra aspects to mathematical systems theory and control theory.

C. Bonnet has developed a long term collaboration with J.R. Partington, Department of Pure Mathematics of the University of Leeds on the robust control of distributed parameter systems.

C. Bonnet and S.I. Niculescu have started a collaboration with H. Özbay, Bilkent University some years ago on various subjects including stability analysis of linear and nonlinear delay systems.

- C. Bonnet has started a collaboration with Unicamp, Sao Paulo Brazil and a collaboration with University of Kyoto, Japan.

- F. Mazenc has a strong collaboration with M. Malisoff, Louisiana State University, USA.

Corina Constantinescu, University of Lausanne, Switzerland, 5–9 July 2011.

André Fioravanti, Unicamp, Sao Paulo, Brazil, 22 November - 5 December 2011.

Anja Korporal, Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, 28 March–9 April 2011 and 29 November–9 December 2011.

Hitay Özbay, Bilkent University, Turkey, 14-18 November 2011.

Stefan Müller, Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, 2–9 June 2011.

Daniel Robertz, RWTH Aachen University, 3–8 October, (PHC Procope).

- Le Ha Vy Nguyen, internship 3rd year ESISAR Valence and M2R Grenoble, February-June 2011.

- Alice Clément, Fénelon Sainte Marie High School , Paris, 20-24 june 2011.

C. Bonnet is a member of the IFAC Technical Comittee on Robust Control, of the Program Committee of the Septiéme Conférence Internationale Francophone d'Automatique,
CIFA 2012, Grenoble and of the CNU61 (National Council of Universities). She is also in the boards of the assciation
*Femmes et Mathématiques*and of the consortium Cap'Maths. She is co-organizer of the “Séminaire du Plateau de Saclay”.

Frédéric Mazenc was associate editor for the conferences : 2012 Chinese Control and Decison Conference, Taiyuan, China, 2012 American Control Conference, Montréal, Canada, Septième Conférence Internationale Francophone d'Automatique, CIFA 2012, Grenoble, 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA, He is co-organizer of the `Séminaire du Plateau de Saclay”.

A. Quadrat is an Associate Editor` of the international journal “Multidimensional Systems and Signal Processing” (Springer). With Thierry Coquand, he organized a
mini-workshop on constructive homological algebra, its applications and its implementations at the CIRM, Luminy, 24–28/01. He was a member of the Program Committee of the “7th International
Workshop on Multidimensional Systems” (nDS'11, Poitiers, 05–07/09). He was an invited speaker at the “2nd workshop on Differential Equations by Algebraic Methods” (DEAM2, Linz, 09–11/02), at
the conference “Functional Equations at Limoges” (FELIM, Limoges, 14–16/03), and at the conference “Modern Constructive Algebra

G. Regensburger coedited with Markus Rosenkranz and William Sit a double special issue on “Algebraic and Algorithmic Aspects of Differential and Integral Operators”
(AADIOS) in Mathematics in Computer Science, which was published in February 2011, see
and
http://

*Teaching*

Sorin Olaru and Guillaume Sandou are associate Professors at SUPELEC.

S.I. Niculescu: differential and integral calculus, 60h, L3, Mines Paris Tech, Paris, France; signals ans dystems, 16h, M2R, ESIEE, Marne-la-vallée, France; Stability and control of time-delay systems, 15h, KU Leuven, Belgium.

G. Sandou : identification for control , 21h, M2, ENSTA, Paris, France.; signal analysis, 15h, M1, Ecole Militaire, Paris, France; mu-analysis, nonlinear systems, 22h,
M2, Ecole des Mines de Nantes, France; Linear Quadratic and

*PhD & HdR*:

HdR : Sorin Olaru, La commande des systèmes dynamiques sous contrainte. Interaction optimisation-géométrie-commande, University of Paris-Sud, 24 may 2011.

PhD : André Fioravanti,

Fernando Francisco Mendez Barrios, Low-order controllers for time-delay systems. An analytical approach, University of Paris-Sud, July 2011. Supervisor : S.I. Niculescu.

Warody Lombardi, Constrained control for time-delay systems, September 2011. Supervisor : S. Olaru, Co-Supervisor : S.I. Niculescu.

PhD in progress :

José Luis Avila Alonso, Mathematical Analysis of Acute Myeloid Leukemia, December 31st 2011. Supervisors : C. Bonnet, J. Clairambault and S.I. Niculescu.

Mounir Bekaik, Observation and control of time-varying delay systems, octoble 2010,. Supervisors:Frédéric Mazenc, Silviu I. Niculescu.

Abdelkarim Chakhar, Algebraic Analysis Approach to Nonlinear PD systems, September 1st 2010. Supervisors : M. Barkatou, T. Cluzeau and A. Quadrat.

Ngoc Thach Dinh, Monotony, Internal Observers and Delay systemsMonotonie, décembre 2011. Supervisors: Frédéric Mazenc, Silvère Bonnabel, Silviu I. Niculescu.

Le Ha Vy Nguyen,

Nikola Stankovic, Fault tolerant control for delay-time systems, Supervisor: S. Olaru, Co-Supervisor: S.I. Niculescu.