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

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 ( -stability, BIBO-stablity, robust stability, robustness metrics) , , , , symbolic computation approaches (SOS methods are used for determining easy-to-check conditions which guarantee that the poles of a given linear system are not in the closed right half-plane, certified CAD techniques), numerical approaches (root-loci, continuation methods) and by means of softwares developed in the team , .

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
era parametrization (which gives the set of all
stabilizing controllers of a system in terms of its
coprime factorizations) has been the cornerstone of the
success of the
-control since this parametrization allows one to
rewrite the problem of finding the optimal stabilizing
controllers for a certain norm such as
or
H_{2}as affine, and thus, convex problem.

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, INSERM, Cordeliers Research Center and St Antoine Hospital, Paris, we consider the modelling 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 modelled in the team as a nonlinear dynamical interconnection between the two sub-populations, and input-output tools allow a complete stability analysis of the model.

We study problems of coexistence or regulation of species in chemostats with one or several limiting substrate, which are important bioreactor models in bioengineering. We consider some distinct contexts (Monod or Haldane functions as growth functions, presence of pointwise delays, presence of two or an arbitrary number of species, dilution rate and/or input nutrient concentration as controls).

We are also working on the control of human heart rate during exercise, which is a problem that has implications for the development of protocols for athletics, assessing physical fitness, weight management, and the prevention of heart failure. We provide new stabilization techniques for a recently-proposed nonlinear model for human heart rate response that describes the central and peripheral local responses during and after treadmill exercise. We plan to consider more realistic systems incorporating delays in the model.

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 , . Although the YALTA package is still in development, it will be freely available in the first semester of 2011.

The
OreModulespackage
, based on the commercial Maple
package Ore
_{-}algebra
, is dedicated to the study of
linear multidimensional systems defined over certain Ore
algebras of functional operators (e.g., ordinary or partial
differential systems, time-delay systems, discrete systems)
and their applications in mathematical systems theory,
control theory and mathematical physics. The main novelty of
OreModulesis to
combine the recent developments of the Gröbner bases over
some noncommutative polynomial rings
,
with new algorithms of algebraic
analysis in order to effectively check classical properties
of module theory (e.g., existence of a non-trivial torsion
submodule, torsion-freeness, reflexiveness, projectiveness,
stably freeness, freeness), give their system-theoretical
interpretations (existence of autonomous elements or
successive parametrizations, existence of minimal/injective
parametrizations or Bézout equations)
,
,
and compute important tools of
homological algebra (e.g., (minimal) free resolutions, split
exact sequences, extension functors, projective or Krull
dimensions, Hilbert power series)
. The abstract language of
homological algebra used in the algebraic analysis approach
carries over to the implementations in
OreModules: up to
the choice of the domain of functional operators which occurs
in a given system, all algorithms are stated and implemented
in sufficient generality such that linear systems defined
over the Ore algebras developed in the Ore
_{-}algebra package are covered at the same time.
Applications of the
OreModulespackage
to mathematical systems theory, control theory and
mathematical physics are illustrated in a large library of
examples. The binary of the package is freely available at
http://

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
A_{n}(
k)(resp.,
B_{n}(
k)) of partial differential
operators with polynomial (resp., rational) coefficients over
a field
kof characteristic 0 (e.g.,
,
) can be generated by two generators. Based on this
implementation and algorithmic results developed in
by the authors of the package,
two algorithms have been implemented which compute bases of
free modules over the Weyl algebras
and
. The development of the
Staffordpackage
was motivated by the problem of computing injective
parametrizations of underdetermined linear systems of partial
differential equations with polynomial or rational
coefficients (the so-called
*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 rings with coefficients in a
field (mainly
) and in a principal ideal domain (mainly
). The development of the
Quillen-Suslinpackage was motivated by different
constructive applications of the Quillen-Suslin theorem in
multidimensional systems theory
(e.g., the Lin-Bose conjectures,
the computation of (weakly) left/right/doubly coprime
factorizations of rational transfer matrices, the computation
of injective parametrizations of flat linear multidimensional
systems with constant coefficients, the reduction and
decomposition problems, Serre's reduction problem). To our
knowledge, the
Quillen-Suslinpackage is the only implementation of
the Quillen-Suslin theorem nowadays available. For more
details, see
http://

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
PurityFiltrationpackage, built upon the
OreModulespackage,
is an implementation of a new effective algorithm obtained in
,
which computes the purity
filtration
,
of linear multidimensional
systems (e.g., partial differential systems, differential
time-delay systems, difference systems) and their equivalent
block-triangular matrices. This package is used to solve in
closed form solutions over/underdetermined linear partial
differential systems which cannot be directly integrated by
the standard computer algebra systems such as Maple and
Mathematica. The binary of the package is freely available at
http://

The
AbelianSystemspackage is an implementation of the
algorithm developed in
,
for the computation of the purity
filtration
,
in the powerful
`homalg`package of GAP4 dedicated to constructive
homological algebra methods, developed by Barakat (University
of Kaiserslautern) and his collaborators (
http://
`homalg`procedure which computes purity filtrations
based on the computation of spectral sequences and the
PurityFiltrationpackage which is based on the rather
slow Maple Gröbner basis computation (see Section
). Using the design of the
`homalg`package, where the different layers such as
the computational engine (which can the computer algebra
systems
`Singular`,
`Macaulay2`,
OreModules,
`MAGMA`,
`SAGE`), the module-theoretic results, and the
homological ones are separated, the
AbelianSystemspackage can be used for the computation
of purity filtration of different objects in abelian
categories (e.g., purity filtration of sheaf cohomology of
projective varieties). This package will be soon available on
the
`homalg`website and at
http://

Both in the time-domain and frequency-domain approaches to stability of delay systems, neutral type systems are the most difficult systems to analyze since they may have chains of poles asymptotic to the imaginary axis in the complex plane. In , we provide the location of all asymptotic poles for classical systems, and for the fractional case in . In both cases, necessary and sufficient conditions for -stability are derived. Preliminary results about the robustness relative to a change in the delay or in the parameters are given.

Many important properties of time-delay systems cannot be obtained in a pure algebraic form. In those cases, numerical methods have proved to be extremely efficient and precise. But most of the time, only classical retarded systems are considered. We studied how those algorithms can be adapted to the cases of neutral and fractional systems, and if not, how to obtain new algorithms for this class of systems , . Those results will be implemented in the YALTA toolbox described in Section .

Based on an extension of Stafford's classical theorem in noncommutative algebra developed in , we prove in that a controllable linear ordinary differential system with convergent power series coefficients (i.e., germs of real analytic functions) and at least two inputs is differentially flat . This result extends a result obtained in for linear ordinary differential systems with polynomial coefficients. The algorithm developed in for the computation of injective parametrizations and bases of free differential modules with polynomial coefficients can be used to compute injective parametrizations and flat outputs of these classes of differentially flat systems. This algorithm allows us to remove artificial singularities which naturally appear in the computation of injective parametrizations and flat outputs obtained by means of Jacobson normal form computations.

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 , , , a constructive approach to Serre's reduction is developed for determined and underdetermined linear systems. In particular, an algorithm is given for the class of controllable 2D systems, which is used to find explicit Serre's reduction of many classical control differential time-delay systems. Serre's reduction of these systems generally simplifies their analysis and their synthesis.

In and , 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.

The algorithms obtained in , , , and are implemented in the Serrepackage in development.

In
,
, it is shown that every linear
system of partial differential equations in
nindependent variables is equivalent to a linear
system of partial differential defined by an upper
block-triangular matrix of partial differential operators:
each diagonal block is respectively formed by the elements
of the system satisfying an
i-dimensional (resp.,
(
n+
i)-dimensional) dynamics if the
coefficients of the system are either constant or rational
functions (resp., the coefficients are either polynomial,
formal power series or convergent power series). Hence, the
system can be integrated in cascade by successively solving
(inhomogeneous) linear
j-dimensional systems of partial differential
equations to get a Monge parametrization of its solution
space
. The results are based on an
explicit construction of the purity filtration of the
differential module associated with the linear systems of
partial differential equations, which does not use spectral
sequences
,
. These results can be extended
to other classes of linear multidimensional systems such as
differential time-delay systems or difference systems.

Within the algebraic analysis approach to multidimensional linear systems defined by linear systems of partial differential equations with constant coefficients , , , we show in how to use different mathematical results developed in the literature of algebraic analysis , to obtain new characterizations of the concepts of controllability in the sense of Willems and Pillai-Shankar , observability, flatness and autonomous systems in terms of the possibility to extend (smooth or distribution) solutions of the multidimensional system and of its formal adjoint. Each characterization is equivalent to a module-theoretic property that can be constructively checked by means of the OreModulesand QuillenSuslinpackages.

Within the algebraic analysis approach to linear systems theory , , , shows how the behaviour homomorphisms (namely, transformations which send the solutions of a linear multidimensional system to the solutions of another linear system ) induce natural transformations on the autonomous elements of these systems (e.g., on the obstructions to controllability) and on the potentials (e.g., flat outputs) of their parametrizable parts (e.g., controllable parts). Extension of these results are then considered for linear systems inducing a chain of successive parametrizations (e.g., the divergence operator, the first group of Maxwell equations, the stress tensor in linear elasticity).

In , within the constructive algebraic analysis approach to linear systems , , , we study classical linear systems of partial differential equations in two independent variables with constant coefficients appearing in mathematical physics and engineering sciences such as the Stokes and Oseen equations studied in hydrodynamics and the Navier-Cauchy equations in linear elasticity. In particular, a precise description of the endomorphism ring of the differential module associated with the Stokes and Oseen, Navier-Cauchy equations is given. Using the fact that the endomorphism ring of the Stokes and Oseen equations in defines a cyclic differential module, we decide about the existence of factorizations of the matrices of differential operators defined by these systems and the decomposition of their solution spaces in direct sums.

Within the framework of the PEPS Maths-ST2I SADDLES
(Symbolic Algebra, Domain Decomposition, Linear Equations
and Systems), the purpose of this work is to use algebraic
and symbolic computation techniques such as Smith normal
forms and Gröbner basis techniques to develop new Schwarz
algorithms for domain decompositions and for
preconditionners of linear systems of partial differential
equations, especially for the Stokes and Oseen equations
studied in hydrodynamics and the Navier-Cauchy equations in
linear elasticity. New algorithms are developed to reduce
the interface conditions and to solve the completion
problem built on physical Smith variables. They are
implemented in the
Schwarzpackage
(to appear) built upon the
OreModulespackage. For more details, see
http://

The
*interval observer*method is a recent state estimation
technique. It is used in particular in biological contexts,
where taking into account the presence of uncertainties is
essential. We have completed the theory of the linear
interval observers in several works.

2. The work (see also ) presents a solution to the problem of constructing exponentially stable interval observers for any time-invariant exponentially stable system. This result, which is constructible, relies on two crucial steps. The first step consists in transforming, through a time-invariant change of coordinates, the system under consideration into a system of the Jordan form. The second consists in determining a time-varying change of coordinates which transforms the system in Jordan form into a cooperative time-invariant system (recall that a linear system is cooperative if it is associated to a matrix whose off-diagonal entries are nonnegative).

In (see also ), a new technique of design of feedbacks for systems with pointwise delays is developed. It relies on the introduction of an operator which has remote connections with the ones used in reduction model approaches. Using this operator, one succeeds, in many cases, to rewrite the closed-loop system we consider into the interconnection of an ordinary differential equation with an integral equation. An important advantage of this representation, is that it allows to derive simple conditions, in terms of initial conditions, ensuring that the resulting solutions of the closed-loop systems are positive. It is worth mentioning that our wish to determine positive solutions for systems with delay had several strong motivations: when this objective is reached, one can easily solve more general problems: in particular, we have shown that our new result can be used to generate solutions which respect to more general constraints than the constraint of sign and solutions which can be compared between each other, which is useful when is only available an approximate knowledge of the initial condition and an estimation of the state variables at each instant is desirable.

We did some works in which strict Lyapunov functions play a central role.

1.
*Systems with quantized feedback.*

Quantized control systems are systems in which the control law is a piece-wise constant function of time taking values in a finite set. The design of quantized control systems is based on a partition of the state space. The aim of was to design control laws for general families of quantized time-delay control systems. Our approach relies on the construction of Lyapunov-Krasowskii functionals and provided with quantized feedbacks which are parametrized with respect to the quantization density. Our approach leads to a set of conditions to design quantized control systems which are robust with respect to delays.

2.
*Strict Lyapunov functions under LaSalle
conditions*.

3.
*Adaptive control*.

In and , we studied adaptive tracking problems for nonlinear systems with unknown control gains. We constructed controllers that yield uniform global asymptotic stability for the error dynamics, hence tracking and parameter estimation for the original systems. Our result is based on a new explicit, global, strict Lyapunov function construction. We illustrated our work using a brushless DC motor turning a mechanical load. We quantified the effects of time-varying uncertainties on the motor electric parameters.

1. In , new results have been obtained toward predictive control design for nonlinear systems upon optimization-in-the-loop techniques for an air ventilation problem. From a methodological point of view, the use of local embeddings of the nonlinearity led to polytopic differential inclusions . This were further used for the nonlinear predictive control synthesis. A generic procedure which deals with the state-space partitioning for a multi-model description and subsequently obtain the control law by means of LMIs have been presented in . An interesting aspect of this result is the explicit formulation of the control law in terms of patchy feedback gains.

2. On NCS related topics, several results can be mentioned with respect to the construction of polytopic embeddings for linear systems affected by variable time delays. In , the Cayley-Hamilton approach was investigated while in a comparison is made with respect to the alternative methods (Taylor series approximations, truncations, Jordan normal forms). For the same class of systems, several results have been reported for the adaptation of predictive control techniques for their constraints handling mechanisms (see and ). For the stability point of view, an interesting aspect is the characterization of terminal invariant sets , a research subject which receives currently a renewed attention.

3. The fragility of proportional-derivative controllers has been studied in relation with robotics/tele-operation application in the two recent publications , .

A new idea to the study of -stability and filter and control designs can be obtained from the Rekasius transformation of the delay term in frequential term. After the relations of stability and norms between the comparison and real systems are obtained, classical techniques involving Riccati equation from the theory of LTI systems are used to derive infinite-dimensional filters and controllers for time-delay systems. All implementation issues are discussed in order to provide a new and easy to implement technique.

In the last years, the interest on networked control has
enormously increased. Actually, communication networks
inherently introduce packet dropouts, quantisation errors,
time-delays and limited bandwidths. Up to now, the most
successful way to model packet dropouts are stochastic
markovian systems, since they are the basic mathematical
tool for the models of many different networks. In
and
, the
H_{2}and
-filtering, and in
, the state feedback design
problems of those systems are addressed.

Continuing the collaboration with the Energy Department of Supélec, the use of robust optimization methods has allowed the computation of energy production control laws taking into account various uncertainties on the plant. Main uncertainties, which have been taken into account, are the consumer load prediction, the maximum unit production level and the production costs. Results exhibit a more robust technical behavior together with a decrease of global operation costs , , .

The development of generic methodologies for automatic control based on metaheuristic methods has led to several promising results. Among them are the automatic computation of weigthing filters and the design of static output feedbacks using Particle Swarm Optimization, and the use of ant colony optimization for the identification of nonlinear systems. Some promising results have also been obtained using multiobjective Particle Swarm Optimization ,

We solved several problems of control and stability analysis for different types of biological models.

The paper extends the results of and by designing a dilution rate and input substrate feedback controllers when only the substrate concentration is measured. More precisely, we achieved the coexistence by designing a novel output-feedback controller that globally asymptotically stabilizes a periodic reference state trajectory of the system. It is worth mentioning that, in practice, measuring the values of the concentration of each species is not feasible but measuring the substrate concentration is. Therefore, considering the substrate concentration as the output is a reasonable choice which is frequently made in the literature. The dynamic output feedback we proposed relies on an observer.

The stabilization of equilibria in chemostats with measurement delays is a complex and challenging problem, and is of significant ongoing interest in bioengineering and population dynamics. In (see also ), we solved an output feedback stabilization problem for chemostat models having two species, one limiting substrate, and either Haldane or Monod growth functions. Our feedback stabilizers depend on a given linear combination of the species concentrations, which are both measured with a constant time delay. Our work is based on a Lyapunov-Krasovskii argument.

In (see also ), we studied feedback stabilization problems for chemostats with two species and one limiting substrate, which play an important role in systems biology and population dynamics. We constructed new dilution rate output feedbacks that stabilize a componentwise positive equilibrium, and only depend on the sum of the species levels. We proved that the feedbacks are robust to model uncertainty. The novelty and importance of our new contribution is in our dropping the usual assumption on the relative sizes of the growth yield constants, and our allowing uncertain uptake functions that are not necessarily concave. The proofs are based on classical results of ordinary differential equations (as for instance the Poincaré-Bendixson theorem and Dulac' criterion).

The control of human heart rate during exercise is an important problem that has implications for the development of protocols for athletics, assessing physical fitness, weight management, and the prevention of heart failure. In , we provided a new stabilization technique for a recently-proposed nonlinear model for human heart rate response that describes the central and peripheral local responses during and after treadmill exercise. The control input is the treadmill speed, and the control objective is to make the heart rate track a prescribed reference trajectory. We used a strict Lyapunov function analysis to design new state and output feedback tracking controllers that render the error dynamics globally exponentially stable. This allowed us to prove robustness stability properties for our feedback stabilized systems relative to actuator errors.

We have worked on a nonlinear PDE model of hematopoeisis designed by Adimy and Crauste , more precisely on its approximation by a nonlinear system with multiple distributed delays.

A complete stability analysis with therapeutic implications has been performed in , and . Moreover, a simulation program of this model is already available.

Through the DIGITEO project ALMA, parameters of this model will be identified through experiments and the model will be changed in order to take more precisely into account some biological phenomena in hematopoiesis.

C. Bonnet is the coordinator of the DIGITEO project ALMA (December 2010 - December 2013), which involves the BANG project team at INRIA Paris-Rocquencourt, L2S, INSERM Paris (team 18 of UMR 872), Cordeliers research center and the COMMANDS team at INRIA Saclay-Île-de-France.

C. Bonnet is a member of the ANR
Program
*Bimod*(December 2010 - December 2014) coordinated
by V. Volpert and involving 3 partners: CNRS
(Institut Camille Jordan), University of Bordeaux II and
INRIA (Paris-Rocquencourt and Saclay-Île-de-France).

F. Mazenc is a member of the ARC Vitelbio (January 2009 - January 2011). Participants: EPI MERE (Montpellier), EPI IPSO (Rennes), Society ITK (Montpellier), UMR Geosciences (Rennes), INRA UREP (Clermont-Ferrand) UMR Eco et Sols (Montpellier).

S.-I. Niculescu is a member of a PEPS INST2I with the Centre d'Enseignement et de Recherche sur l'Environnement et la Société (CERES).

A. Quadrat is a member of the PEPS Maths-ST2I: SADDLES (Symbolic Algebra, Decomposition Domains, Linear Equations and Systems) in collaboration with V. Dolean (University of Nice), F. Nataf (CNRS, Paris 6) and T. Cluzeau (University of Limoges). A. Quadrat has a long term collaboration with T. Cluzeau, M. Barkatou and J.-A. Weil (University of Limoges, XLIM).

C. Bonnet has a long term collaboration with J. R. Partington, School of mathematics, Leeds, United Kingdom.

S. Olaru is the project manager for the bi-lateral PHC projects Brâncusi with the University of Craiova, Romania, and van Gogh with the University of Eindhoven, The Netherlands.

S.-I. Niculescu is a member of the MAE with the Institute of Physics, Belgrade, Serbia, a member of the MAE with the University of Bilkent, Ankara, a member of a PHC Brâncusi with the University of Craiova, Romania, and a member of a PHC van Gogh with the University of Eindhoven, The Netherlands.

A. Quadrat has developed a strong collaboration with the Lehrstuhl B für Mathematik of Wilhelm Plesken, RWTH Aachen University, and particularly with Daniel Robertz and Mohamed Barakat. He is a member of an accepted PHC Procope developed in collaboration with the University of Limoges (XLIM) and the Lehrstuhl B für Mathematik, RWTH Aachen University (2011-2012).

F. Mazenc has a strong collaboration with Michael Malisoff and Marcio De Queiroz of, respectively the Department of Mathematics and the Department of Mechanical Engineering of the Louisiana State University.

S.-I. Niculescu is the head of a CNRS exchange convention with the Laboratory for Advanced Robotics at the Korea University of Seoul, South Korea.

C. Bonnet is a member of the
IFAC Robust Control Technical Committee, of the CNU 61
(National Council of Universities), of the scientific
council of Île-de-France region (CCRRESTI) until April
2010, in charge with B. Eurin of the working group
on Student Life. She is also in the board of the
association
*Femmes et Mathématiques*and a member of the
National INRIA working group on Scientific
Mediation.

F. Mazenc is member of the COST (Scientific and technological Orientation Council) in the team GTAI (Groupe de travail Actions Incitatives). The main mission of the GTAI: organization, selection and supervision of INRIA's incentive initiatives, such as the Cooperative research Initiatives (ARC) of the Scientific Management and the Software Development Operations (ODL) and Standardization operations of the Department of Development and Industrial Relations.

S.-I. Niculescu is the head of the Laboratory of Signals and Systems (L2S), UMR 8506. Moreover, he is a member of the “commission de spécialistes” CCSU 60-61-62 of the University of Paris-Sud, a member of the scientific and administrative board of the Romanian National University Research Council, a member of the Programme Committee of DIGITEO, Saclay, Île-de-France, and a member of council Ecole Doctorale STITS of the University Paris-Sud.

S. Olaru is the co-organizer of the meetings of the French Research Group on Nonlinear Predictive Control within GDR MACS.

A. Quadrat was a member of a Selection Committee for an assistant professorship position at the University Limoges (sections 25-26) and at the University Toulouse III (section 61).

C. Bonnet was a member of the scientific committe of the 10th forum des Jeunes Mathématiciennes, CIRM, Marseille, France.

F. Mazenc was an Associate Editor, Conference Editorial Board, for the American Control Conference (ACC) 2010.

S.-I. Niculescu is an Associate Editor of Journal of Control Science and Engineering. Moreover, he was International Program Committee (IPC) of the Conférence Internationale Francophone d'Automatique (CIFA) 2010, Nancy, France, of the 18th Mediterranean Conference on Control and Automation, Marrakech, Morocco, of the 2nd IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys'10), Annency, France, of the 14th International Conference on Systems Theory and Control, Sinaia, Romania, of the IFAC World Congress, Milano, Italy, of the 9th IFAC Workshop on Time-Delay Systems, Prague, Czech Republic, of the International Conference on Control, Automation and Systems (ICCAS), Gyeonggi-do, South Korea, of the IFAC Symposium on System Structure and Control (SSSC'10), Ancona, Italy, and of the 2011 IEEE International Conference on Communications, Computing and Control Applications (CCCA'11), Hammamet,Tunisia. He was also an associated editor of the special issue “Time-delay systems” of IMA Journal on Mathematical Control and Information (2011). Finally, he is member of IFAC Technical Committee on Linear Systems (since 2002) and is the responsible of the IFAC Research Group on "Time-delay systems" since its creation in October 2007.

S. Olaru was member of the program committee of the 14th International Conference on System Theory and Control (SINTES 2010), Sinaia, Romania, and has been appointed in the program committee for 2011 JD MACS, Marseille, France.

A. Quadrat is an Associate Editor of the international journal Multidimensional Systems and Signal Processing (Springer).

F. Mazenc co-organized with
M. Malisoff and H. Ito the invited session
*New directions in stability and stabilization*at
the American Control Conference, Baltimore, USA.

S. Olaru organized the invited
session
*Predictive control*at CIFA 2010 (with A. Chemori,
LIRMM as chairman), Nancy, France.

A. Quadrat organized 3 invited
sessions
*New mathematical methods in multidimensional systems
theory*at the 19th International symposium on
Mathematical Theory of Networks and Systems (MTNS2010),
Budapest, Hungary.

F. Mazenc was a referee of
Ixbalank Torres' Ph.D. thesis,
*Simulation and control of denitrification biofilters
described by PDEs*, University of Toulouse III
- Paul Sabatier (May 2010). Moreover, he was a referee
of Pierre Masci's Ph.D. defense committee,
*Control and optimization of ecosystems in
bioreactors for bioenergy production*, University of
Nice Sophia-Antipolis (November 2010).

S. Olaru was appointed member of the Ph.D. defense committee of Khaoula Nagoudi-Layerle, University of Rouen.

C. Bonnet was an invited speaker at the Conference MACS4 (Modélisation, Analyse et Contrôle des Systèmes), Meknès, Marocco. She also participated at the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010), Budapest, Hungary.

André Fioravanti won the Fall 2010 Matlab Programming Contest.

F. Mazenc participated at the American Control Conference, Baltimore. He also participated at the IFAC Symposium on Nonlinear Control Systems (NOLCOS 2010) and at the IEEE Conference on Decision and Control, Atlanta, USA.

S.-I. Niculescu was invited speaker at the IFAC Symposium on System, Structure and Control (SSSC'10), Ancona, Italy. He was also invited at the Ecole Polytechnique and Concordia University of Montreal, Canada.

A. Quadrat was invited speaker at the French National Days on Symbolic Computation (JNCF 2010), CIRM, France. He was an invited speaker at the Sage Days 24, RISC, Austria. He also participated at the the 19th International symposium on Mathematical Theory of Networks and Systems (MTNS 2010), Budapest, Hungary.

S. Olaru is an associate professor in Supélec.

G. Sandou is an associate professor in Supélec (250 hours).

S.-I. Niculescu taught a course on Robust Control at ESIEE (8 hours) and tutorials in Mathematics at Ecole Nationale Supérieure des Mines de Paris (30 hours).

A. Quadrat gave a lecture at the French National Days on Symbolic Computation (JNCF), CIRM, Luminy, France (3 hours).

G. Sandou is a free lance teacher at the University of Evry-Val d'Essonne (7 hours), at the Ecole Centrale Paris (20 hours), at the Ecole des Mines de Nantes (22 hours), at the Ecole Nationale Supérieure de Techniques Avancées (ENSTA) (21 hours) and at the Ecole Militaire (15 hours).

Mounir Bekaik,
*Commande et observation de systèmes variant dans le
temps à retard*.

Abdelkarim Chakhar,
*Etude des systèmes différentiels quasi-linéaires par
l'analyse algébrique et l'algèbre
différentielle*.

André Fioravanti,
*-analysis and control of some classes of
(possibly fractional) time-delay systems by frequential
methods*.

Warody Lombardi,
*Synthèse des lois de commande basées sur prédiction
pour des systèmes à retard*.

Bogdan Liacu,
*Commande prédictive MPC pour la
télé-opération*.

Benjamin Bradu,
*Modélisation, simulation et contrôle des
installations cryogéniques du CERN*, L2S, CERN,
Geneva, Switzerland, March 2010.

Houda Benjelloun,
*Mathematical analysis of acute myeloid leukemia*,
final project, INSA Rouen (6 months). She was also an
engineer in the team for three months.

Saïd Ighobriouen,
*Use of metaheuristic optimization methods for the
design of controllers*, final project, master RVSI
(University of Evry - Val d'Essonne) (5 months).

Bianca Minodora Heiman,
*Ant colony optimization for the identification of
non linear systems*, final project (University of
Bucarest) (4 months).

Catalin Raduinea,
*Predictive control for a NCS for a positioning
benchmark*, final project (University of Bucarest)
(4 months).

Gabriela Raduinea,
*Particle Swarm Optimization for the design of LPV
controllers*, final project, master ATSI (Supélec,
University Paris XI) (5 months).

Jorge Luis Reyespesantez,
*Robust optimization for energy management*, final
project, master ATSI (Supélec, University Paris XI), (5
months).

Andrei Spanu,
*Fault detection and isolation for a wind
turbine*, final project, master ATSI (Supélec,
University Paris XI), (5 months).