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 as consequence an increased complexity of the behavior of the total system.

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, develops new algorithms and implementations dedicated to these techniques.

Frédéric Mazenc in June 2013 for his presentation of the paper *IEEE Control Systems Society* the *Best Presentation of Session Presenter*.

Sorin Olaru got the Best paper award at the 17th International Conference on System Theory, Control and Computing

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.

The team considers control problems in the aeronautic area and studies delay effects in automatic visual tracking on mobile carriers in collaboration with SAGEM.

The team is also involved in life sciences applications. The two main lines are the analysis of bioreactors models and the modeling of cell dynamics in Acute Myeloblastic Leukemias (AML) in collaboration with St Antoine Hospital in Paris.

The team is interested in Energy management and considers optimization and control problems in energy networks.

The OreModules package , based on the commercial Maple package Ore

A Mathematica version of the OreModules package is in development. It is being developed by Maris Tõnso (Institute of Cybernetics, University of Tallinn), Thomas Cluzeau (ENSIL, University of Limoges) and A. Quadrat within the PHC Parrot project CASCAC. The Mathematica version of the OreModules package is based on the implementation of Gröbner bases over Ore algebras available in the Mathematica HolonomicFunctions package developed by Christoph Koutschan.

The Stafford package of OreModules contains an implementation of two constructive versions of Stafford's famous but difficult theorem stating that every ideal over the Weyl algebra

The Quillen-Suslin package 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 OreMorphisms package 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 Stafford and 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 OreMorphisms package. The binary of the package is freely available at http://

A Mathematica version of the OreMorphims package is in development. It is being developed by Maris Tõnso (Institute of Cybernetics, University of Tallinn), Thomas Cluzeau (ENSIL, University of Limoges) and Alban Quadrat within the PHC Parrot project CASCAC. The Mathematica version of the OreMorphims package is based on the implementation of Gröbner bases over Ore algebras available in the Mathematica HolonomicFunctions package developed by Christoph Koutschan.

The JanetMorphisms package 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 .
This package computes symmetries, first integrals of motion, conservation laws, study Riemann invariants...
The JanetMorphisms package is based on the `Janet` package (http://

The PurityFiltration package, built upon the OreModules package, 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 AbelianSystems package 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 AbelianSystems package can be used for the computation of the purity filtration of objects in different constructive abelian categories such as coherent sheaves over projective schemes as demonstrated in the `homag` package called `Sheaves` (see http://

The SystemTheory package is a `homalg` based package dedicated to mathematical systems. This package, still in development, will include the algorithms developed in the OreModules and OreMorphisms packages. It currently contains an implementation of the OreMorphisms procedures which handle the decomposition problem aiming at decomposing a module/system into direct sums of submodules/subsystems, and Serre's reduction problem aiming at finding an equivalent system defined by fewer unknowns and fewer equations.

The YALTA toolbox 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 , . For classical delay systems, a Pade2 approximation scheme is available as well as a finite-dimensional approximation of the system.

Binaries are freely available at http://

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 ). Classes of
overdetermined/underdetermined linear systems of partial differential
equations which cannot be directly integrated by Maple can be solved
using the PurityFiltration package.

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. The connection between Serre's reduction and the decomposition problem , which aims at finding an equivalent linear functional system which is defined by a block diagonal matrix of functional operators, is algorithmically studied in , . Moreover, a characterization of isomorphic finitely presented modules in terms of certain inflations of their presentation matrices is obtained in . This result yields a connection between a certain matrix completion problem and Serre's reduction .

In ,, algorithmic versions of Stafford's results (e.g., computation of unimodular elements, decomposition of modules, Serre's splitting-off theorem, Stafford's reduction, Bass' cancellation theorem, minimal number of generators) were obtained and implemented in the Stafford package . In particular, we show how a determined/overdetermined linear system of partial differential equations with either polynomial, rational, formal power series or locally convergent power series coefficients is equivalent to a linear system of partial differential equations with at most two unknowns. This result is a large generalization of the cyclic vector theorem which plays an important role in the theory of linear ordinary differential equations.

Within the algebraic analysis approach to behaviours
, , in , we propose to
consider a system not only as a behaviour

In , we study the construction of a double complex
leading to a Grothendieck spectral sequence converging to the
obstructions

Within the algebraic analysis approach to behaviours
, , in , we explain how the concept
of inverse image of a finitely presented left

In , we study algorithmic aspects of linear ordinary
integro-differential operators with polynomial coefficients. Even
though this algebra is not noetherian and has zero divisors, Bavula
recently proved in that it is coherent, which
allows one to develop an algebraic systems theory. For an algorithmic
approach to linear systems theory of integro-differential equations
with boundary conditions, computing the kernel of matrices is a
fundamental task. As a first step, we have to find annihilators, which
is, in turn, related to polynomial solutions. We present an
algorithmic approach for computing polynomial solutions and the index
for a class of linear operators including integro-differential
operators. A generating set for right annihilators can be constructed
in terms of such polynomial solutions. For initial value problems, an
involution of the algebra of integro-differential operators also
allows us to compute left annihilators, which can be interpreted as
compatibility conditions of integro-differential equations with
boundary conditions. These results are implemented in Maple
based on the `IntDiffOp` and `IntDiffOperations`
packages.

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 developed in
, 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

Fractional neutral systems with commensurate delays have chains of poles aymptotic to vertical lines. The case where the imaginary axis is an asymptotic one is interesting. Indeed, if the system has some chains of poles asymptotic to the imaginary axis, then the fact that all poles lie in the open left half-plane does not guarantee the

This kind of systems was studied in , . In , systems with single
chains of poles asymptotic to the imaginary axis was considered and
necessary and sufficient conditions for

We consider fractional neutral systems with commensurate delays which
may have chains of poles asymptotic to vertical lines lying in the
open left half-plane and have chains clustering the imaginary
axis. Due to the latter, the system may possess infinitely many poles
in the right half-plane. We prove that a class of rational fractional
controllers cannot stabilize this kind of systems in the sense of

In order to yield the set of all the stabilizing controllers of a class of MISO fractional systems with delays by mean of Youla-Kucera parametrization regarding

We made several progresses in the domain of the construction of state estimators called interval observers.

2) The contributions and present a new major result for the design of interval observers for discete-time systems with input and output: it is explained how two classical Luenberger obsevers can be used, even in the absence of the positivity property as interval observer, provided two appropriate output, which compose the lower and the upper bound of the interval observer, are selected. In , coordinate transformations which change an arbitrary linear discrete-time system into a positive one and general nonlinear design of interval observers for nonlinear systems (satisfying a restricitive stability assumption) are proposed.

We solved several distinct problems entailing to the celebrated reduction model approach. Let us recall that this technique makes it possible to stabilize systems with arbitrarily large pointwise or distributed delay in the input.

1) For nonlinear systems with delay of neutral type, we developped a new technique of stability and robustness analysis. It relies on the construction of functionals which make it possible to establish estimates of the solutions different from, but very similar to, estimates of ISS or iISS type. These functionals are themselves different from, but very similar to, ISS or iISS Lyapunov-Krasovskii functionals. The approach applies to systems which do not have a globally Lipschitz vector field and are not necessarily locally exponentially stable. We apply this technique to carry out a backstepping design of stabilizing control laws for a family of neutral nonlinear systems .

We obtained new results on the robustness analysis of nonlinear systems belonging to a general family when they are globally stabilized by a state feedback corrupted by the presence of a delay and sampling , . The result is based on the construction of a non-quadratic Lyapunov-Krasovskii functional.

Fault-tolerant control theory is a well-studied topic but the use of the sets in detection, isolation and/or reconfiguration is rather tangential. Sorin Olaru together with his collaborators (and principally with F. Stoican) conducted a systematic analysis of the set-theoretic elements and devise approaches which exploit advanced elements within the field. The main idea is to translate fault detection and isolation conditions into those conditions involving sets. Furthermore, these are to be computed efficiently using positive invariance and reachability notions. Constraints imposed by exact fault control are used to define feasible references (which impose persistent excitation and, thus, non-convex feasible sets). Particular attention is given to the reciprocal influences between fault detection and isolation on the one hand, and control reconfiguration on the other. The recent results on this topic are gathered in the recent book .

A new result has been obtained by the use of controlled invariance for the separation of faulty/healthy invariant sets in the detection and isolation based on the necessary and sufficent conditions of George Bitsoris.

In a series of recent papers , , , , the link between the interval observers and the invariant sets have been investigated by establishing a series of formal results on the limit behaviour with potential applications in the detection and isolation of actuators faults

In , the mixt integer techniques have been analysed in the distributed model predictive control context, underlining the dependence of collision avoidance mechanism on the obstacle modeling and susequently on their treatement inside optimization-based control techniques as MPC (model predictive control). On the same topic of adversary consraints, a geometrical conditions has been establised in for the local stabilization of a linear dynamics on a boundary of a forbidden region in the state space.

The theoretical developments from the last two years on the MPC design for multi-agent control problem led to the succesful application of receding horizon flight control for trajectory tracking of autonomous aerial vehicles . In the same line or research, the predictive control for trajectory tracking and decentralized navigation of multi-agent formations has been presented in .

A predictive control-based algorithm for path following of autonomous aerial vehicles has been proposed in to improve the previous trajectory tracking mechanism. The ultimate goal oof both schemes is to avoid the real-time infeasibility problems in MPC.

The distributed predictive control mechanisms have been used for the control of a four interconnected tanks benchmark , proving the versatility of a nonlinear Distributed MPC technique previously proposed by A. Grancharova.

The longstanding research interest on the positive invaraince of a set with respect to the trajectories of the dynamical systems allowed recently the statement of explicit invariant approximation of the maximal robust positive invariant ser for LTI dynamics with zonotopic disturbances .

In the class of hybrid dynamical systems, explicit robustness and fragility margins for discrete-time linear systems with PWA control has been established in by means of positive invariance arguments.

The robustness against parametric uncertainties can be studied using the structured singular value mu. In that case, a normalization of the uncertain parameters is performed, and the mu analysis provides the larger parallelepiped centered in the nominal and included in the stability domain. However, results depend on the initial normalization. In this study, the normalization is optimized so as to get the largest guaranteed stability domain. The corresponding problem being highly nonlinear, a metaheuristic method, Particle Swarm Optimization, is used for that purpose. An academic and a real life example, namely the pendulum in the cart problem, have been used to prove the viability of the approach.

Hinfinity loop-shaping controllers have proven their efficiency to solve problems based on complex industrial specifications. However, the tuning of the weighting filters is a time consuming task. This work deals with the use of metaheuristics optimization for this weighting filter tuning. Whereas this topic has already been investigated in lot of works, all of them assume a particular pole/zero/damping/pulse expression for the searched transfer function. But choosing the best weight structure is not trivial and may lead to suboptimal solutions for the design process. That is why, we propose to enhance the weight selection problem by relaxing the structure constraints of transfer functions. The developed methodology is tested, using a real industrial example and leads to satisfactory results.

This study proposes to revisit the mu-synthesis problem with a recent and efficient meta-heuristic called Quantum Particle Swarm Optimization (QPSO). This algorithm allows us to optimizing dynamics (or static) D-scalings without fitting them which leads to robust performance controllers. This method has been applied to an industrial problem and has been proven to be better than the classical D-K iteration method.

In , , we study the stabilization
problem of a linear system formed by a simple integrator and a
time-delay system. We show that the stabilizing controllers of such a
system can be rewritten as the closed-loop system defined by the
stabilizing controllers of the simple integrator and a distributed
delay system. This result is used to study tracking problems appearing
in the study of inertially stabilized platforms for optical imaging
systems. Moreover, an elementary proof for the parametrization
of all stabilizing controllers of a stabilizable plant

We have considered the classical model of the chemostat (which is a bio-reactor) with one substrate, one species and a Haldane type growth rate function is considered. The input substrate concentration is supposed to be constant and the dilution rate is considered as the control. The problem of globally asymptotically stabilizing a positive equilibrium point of this system in the case where the measured concentrations are delayed and piecewise constant with a piecewise constant control is addressed. The result relies on the introduction of a dynamic extension of a new type. .

We have also studied a coupled model for healthy and cancer cell dynamics in Acute Myeloid Leukemia consisting of two stages of maturation for cancer cells and three stages of maturation for healthy cells. The cell dynamics are modelled by nonlinear partial differential equations. The interconnection phenomenon between the healthy and cancer cells takes place on the re-introduction functions leaving the resting compartments to the proliferating compartments of both populations of cells at the first stage. For a particular healthy equilibrium point, locally stability conditions involving the parameters of the mathematical model are obtained , .

A collaboration with SAGEM Défense Sécurité, Etablissement de Massy, has been developed on the effect of time-delay in inertially stabilized platforms for optical imaging systems. This collaboration led to research contract made by Alban Quadrat, Silviu Iulian Niculescu and Hugues Mounier (L2S, University Paris Sud).

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 have also been 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, observaterus par intervalles et systèmes à retard.

Dedember 2011- December 2014

Coordinator: Frédéric Mazenc

Other partners: L2S, France, Mines-ParisTech, France

Abstract: MOISYR is concerned with 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 step, we extend our result to discrete time systems and to a specific class of continuous/discrete systems calles Networked Control Systems.

An ANR Blanc SIMI 3 “Multidimensional Systems: Digression On Stabilities” (MSDOS) was submitted in 2013 and accepted. It will start in 2014 for a period of 4 years. Alban Quadrat is the local leader for Inria Saclay.
For more details, see http://

**Program: GDRI (European research network founded by CNRS)**

Project acronym: DelSys

Project title: Delay Systems

Duration: 2011-2015

Coordinator: Silviu Iulian Niculescu

Other partners: GIPSA-Lab and LAAS France, Ancona University Italy, Czech Technical University in Prague Czech Republic, Kent University Great-Britain, KTH Stockholm Sweden and KU Leuven Belgium.

Abstract: the aim of this GDRI is to bring together the main European teams which work in the fiels of Delay systems. This network meets once a year.

**Program: PHC Aurora (Norway)**

Project acronym: 28920SB

Project title: Connections between constrained control law synthesis and theory of positive dynamical systems

Duration: 2013

Coordinator: Sorin Olaru (French leader), Morten Hovd (Norwegian leader)

Other partners: NTNU Trondheim

Abstract: The project is constructed with two main scientific objectives: a) The (controlled) invariant set computation and their use in the stability analysis The main objective is the construction of invariant sets of reduced complexity in terms of generators (for example vertices in polyhedral/zonotopic sets). Such invariant sets are related to the positivity by the invariance of the positive orthant of a dual (comparison) state space. The existence of invariant sets will be subsequently linked through this comparison systems with the stability analysis of complex (large scale, interconnected, hybrid, delay-affected or nonlinear) dynamics. The results will be compared with the state of the art methods as for example those related to the feasible set description in Model Predictive Control related problems. b) Control design for constrained dynamical systems Once the invariance tools with manageable complexity are available, the respective set will be employed in the synthesis procedure as Lyapunov level sets. Practically this will lead to polyhedral Lyapunov functions type of constructions for which interpolation based techniques have recently been shown to be effective. Further, the robustness and the performance of the resulting closed-loop dynamics need to be adjusted in accordance with the choice of the interpolation factor. These control design degrees of freedom need to be adjusted with respect to positiveness or monotonicity requirements.

**Program: PHC Pessoa (Portugal)**

Project acronym: 28750QA

Project title: Robust Distributed Model Predictive Control of Medium- and Large- Scale Systems

Duration: 2013-2014

Coordinator: Cristina Stoica (French leader), Fernando Lobo Perreira (Portuguese leader)

Other partners: Sorin Olaru

**Program: PHC Brancusi (Romania)**

Project acronym: 28705PF

Project title: Adaptive and predictive control of bioprocesses (modelling, identification and control of interconnected bioprocesses)

Duration: 2013-2014

Coordinator: Sihem Tebbani (French leader), Dan Selisteanu (Romanain leader)

Other partners: Sorin Olaru

**Program: PHC Parrot**

Project acronym: CASCAC

Project title: Computer Algebra, Symbolic Computation, and Automatic Control

Duration: 2013 - 2014

Coordinator: Alban Quadrat (French leader), Maris Tõnso (Estonian leader)

Other partners: Institute of Cybernetics, University of Tallinn

Abstract: The CASCAC project is at the interfaces of control theory, computer algebra and software engineering. The goals of the project are: 1. Develop new theoretical results on nonlinear control systems defined by functional equations (e.g., ordinary differential equations, partial differential equations, differential time-delay equations, partial difference equations). 2. Implement them on dedicated softwares developed in the computer algebra system Mathematica. In particular, Mathematica versions of the OreModules
and OreMorphisms packages will be developed. 3. Develop an interface between the C library BLAD (http://

**Program: PHC Rila (Bulgaria)**

Project acronym: 29401YJ

Project title: Robust Distributed Model Predictive Control of Medium- and Large- Scale Systems

Duration: 2013-2014

Coordinator: Sorin Olaru (French leader), Alexandra Grancharova (Bulgarian leader)

Other partners: Bulgarian Academy of Science

Abstract: The project intends to address the control design of large scale dynamical systems with an emphasis on distributed predictive control strategies. There are two points of view with respect to the control synthesis in this framework: a. avoid the use of a global prediction model in the receding horizon optimal control of the subsystems and privilege the use of a coordination level in the decision process; b. consider the distributed synthesis for a network of discrete-time constrained linear systems without central coordinator. In the present project we intend to contribute to both of these directions by: a. Prediction of the interactions in between subsystems in a decomposition-coordination scheme. This can be done by imposing a reduced set of constraints for the MPC problems at the lower levels. b. With respect to the MPC design in the absence of coordination one of the issues will be the definition of appropriate terminal sets, ensuring invariance properties or at least recursive feasibility for the global functioning. We will investigate the construction of terminal set for a stabilizing centralized MPC decomposable in the form of a cross product of sets in each subsystem state space. An interesting idea on this direction was presented recently by the participants in this project.

**Partner 1:University of l'Aquila, Italy**

Nonlinear delay systems interconnected with a differential-difference equation.

**Partner 2: RWTH Aachen University, Germany**

Mathematical systems theory, control theory, symbolic computation

**Partner 3: Bilkent University, Turkey**

Control of linear and nonlinear systems with delays, medical applications

**Partner 4: Tel Aviv University, Israel**

Stability analysis of nonlinear Partial Differential Equations

- UNICAMP, Sao Paulo, Brazil

- Kyushu Institute of Technology, Iizuka, Fukuoka, Japan

- Louisiana State University, Baton Rouge, USA

- University of California, San Diego, CA, USA

Within the PHC Parrot (Inria Saclay - Institute of Cybernetics, University of Tallinn), Ülle Kotta, Maris Tõnso and Juri Belikov visited the DISCO project (twice for a week).

Within the invited Professor Program of DIGITEO, Prof. Georges BiTSORIS visited the DISCO project and Supélec from January-July 2013 and Emilia Fridman visited the DISCO project in September 2013.

Alban Quadrat was invited by the Mathematics department of the Universidad Nacional de Colombia Bogotá (Colombia) for two weeks, and at the Tempere University of Technology (Finland).

Catherine Bonnet is a member of the IFAC Technical Committee 2.5 on Robust
Control and of the IFAC Technical Committee 2.6 on Distributed Parameter Systems. She is also in the boards of the association *Femmes et Mathématiques* and of the consortium Cap'Maths.
She has been the co-chair of the NOC and a member of IPC of the first IFAC Workshop on Control of Systems Modeled by Partial Differential Equations, Paris September 2013 and has co-organized the workshop Modeling and Analysis of Cancer Cells Dynamics, Paris June 2013 (ISSSMA 2013). She is a member of the organizing committee of the *Colloque en l'honneur d'Abdelhad El Jai* to be held 29-30 May 2014 in Ifrane, Marocco.
She is a co-Editor of the book “Low Complexity Controllers for Time-Delay Systems” of the Springer Series *Advances in Dynamics and Delays*. She is co-organizer of the “Séminaire du Plateau de Saclay”. She has co-organized with K. Morris (Univ of Waterloo) the session *Analysis and Control of Infinite-Dimensional Systems* at the SIAM CT13 Conference.

Frédéric Mazenc was Associate Editor for the conferences 2014 American Control Conference, Portland, USA. and 52th IEEE Conference on Decision and Control, Florence, Italy, (2013). He is member of the Mathematical Control and Related Fields editorial board, member of the European Journal of Control editorial board and Associate Editor for the Asian Journal of control. He was member of the national organizing committee of 1st IFAC Worshop on Control of Systems Modeled by Partial Differential Equation, Paris 2013. He was member of the international program committee of the 2014 European Control Conference, Strasbourg, France, the 2013 IFAC Nolcos, Toulouse, France and the 5th IFAC International Workshop on Periodic Control Systems, Caen, France, 2013. He is evaluator for the National Agency for the Italian Evaluation of Universities and Research Institutes (ANVUR). He is evaluator for Partnershio Programme - Joint Applied Research Projects - PCCA of the Roumanian National Council for Development and Innovation. He was invited to the seminar of the Laboratoire d'Automatique, Ecole polytechnique Fédérale de Lausanne, Lausanne, Switzerland (13/03/2013 - 21/03/2013). He was invited to the seminar of the LAGEP, Université Claude Bernard, Lyon 1 in December 2013 (17/12/2013 - 20/12/2013).

Alban Quadrat is an Associate Editor of the journal “Multidimensional Systems and Signal Processing”, Springer. With Eva Zerz, he organized a special issue “Symbolic Methods in Multidimensional Systems Theory” for this journal (to appear in 2014). With Georg Regensburger, he organized an invited session “Algebraic and symbolic methods in mathematical systems theory” at the 5th Symposium on System Structure and Control (Grenoble, 4-6/02/2013).
With Eva Zerz, he organized an invited session “Algebraic and behavioural approaches to multidimensional system theory” at the 8th International Workshop on Multidimensional Systems (nDS13), Erlangen, Germany (9-11/09/13). Moreover, they have also proposed two invited sessions “Algebraic methods and symbolic-numeric computation in systems theory” at the forthcoming 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS), Groningen, the Netherlands (7-11/07/14). With Mohamed Barakat and Thierry Coquand, he organized a mini-workshop “Constructive homological algebra with applications to coherent sheaves and control theory” at Oberwolfach (12-18/5/2013). He was an International Programm Commitee member of the 8th International Workshop on Multidimensional (nD) Systems (

Alban Quadrat was a plenary speaker at the 5th International Workshop on Differential Algebra and Related Topics (DART V), Lille, France (24-26/06/13) and a semi-plenary speaker at the Colombian Congress of Mathematics, Barranquilla, Colombia (15-19/07/13). He was invited to give a talk at the University of Versailles (23/04/13), at the Centre Automatique et Systèmes (CAS), Mines ParisTech (20/06/13), at the Institute of Cybernetics of the University of Tallinn, Estonia (01/10/13), and at the Tampere University of Technology, Finland (24/10/13). Finally, he participated to the workshop Geometry and algebra of linear matrix inequalities, CIRM, Luminy (12-16/11/13).

Licence : Le Ha Vy Nguyen, Applied Informatics in Physics, 16h, L2, Paris-Sud University

Licence : Le Ha Vy Nguyen, Signals and Systems, 28h, L3, Paris-Sud University

Licence : Sorin Olaru, Numerical Methods and Optimization, 24h, L2, SUPELEC, France

Licence : Sorin Olaru, Hybrid Dynamical Systems, 18h, L3, SUPELEC, France

Licence : Guillaume Sandou, Signals and Systems, 87h, L3, Supélec

Licence : Guillaume Sandou, Mathematics and programming, 18h, L3, Supélec

Master : Le Ha Vy Nguyen, Information Processing and Source Coding, 12h, M1, Paris-Sud University

Master : Guillaume Sandou, Automatic Control, 8h, M1, Supélec

Master : Guillaume Sandou, Numerical methods and optimization, 28h, M1 and M2, Supélec

Master : Guillaume Sandou, Modelling and system stability analysis, 21h, M2, Suplec

Master : Guillaume Sandou, Control of energy systems, 22h, M2, Suplec

Master : Guillaume Sandou, Robust control and mu-analysis, 9h, M2, Suplec

Master : Guillaume Sandou, Systems identification, 32h, M2, ENSTA

Master : Guillaume Sandou, Embedded Systems, 18h, M2, Ecole Centrale Paris

Master : Guillaume Sandou, Automatic control, 23h, M2, Ecole Centrale Paris

Master : Guillaume Sandou, System Analysis, 22h, M2, Ecole des Mines de Nantes

Master : Guillaume Sandou, Multivariable control, 12h, M2, Evry University

PhD in progress José Luis Avila Alonso, Mathematical Analysis of Acute Myeloid Leukemia, December 31st 2011. University Paris-Sud, STITS. Supervisor : Catherine Bonnet. Co-supervisors : Jean Clairambault and Silviu Iulian Niculescu.

PhD in progress: Thach Ngoc Dinh, Interval Observers and Delay Systems, December 2011. University Paris-Sud STITS. Supervisor: Frédéric Mazenc. Co-Supervisor: Silviu Iulian Niculescu, Silvère Bonnabel.

PhD in progress Le Ha Vy Nguyen,

PhD in progress Nikola Stankovic, Set-based control methods for systems affected by time-varying delay, September 30th 2010, University Paris-Sud, STITS. Defense: 20 November 2013. Supervisor: Sorin Olaru Co-Supervisor: Silviu Iulian Niculescu

Catherine Bonnet was an examiner member and President of the jury of the PhD Thesis of Hao Lu entitled ”Approximation and Applications of Distributed Delays”, INSA Lyon, 1st October 2013; and an examiner member of the jury of the PhD Thesis of Julien Chaudenson entitled ”Analyse de robustesse par contraintes intégrales quadratiques, application aux lanceurs spatiaux”, Supélec, 4 December 2013.

She was a member of the Recruiting Committee of the *Chargé de Recherche de 2ème classe* competition of Inria Saclay-Ile-de-France and in the Recruiting Committee of the *Maître de Conférences* competition at University Paris-Sud.

Alban Quadrat was the opponent of the PhD thesis “Robust Regulation for Infinite-Dimensional Systems and Signals in Frequency Domain” by Petteri Laakkonen, Tampere University of Technology, Finland (25/11/13), and the reviewer of the PhD thesis “Ring and Module Theoretic Properties of

Catherine Bonnet spoke at the ”Cérémonie de remise des prix des Olympiades de Mathématiques, Ministère de l'éducation nationale, juin 2013. She gave a talk and met high school students groups at the event ”Sciences au Carrée” in the context of Fête de la Sciences, CNES, October 2013.

Alban Quadrat was invited to give a popularization talk on the development of ideas in mathematics and physics at the conference “Lieux de passage en Science-Fiction”, University of La Rochelle (France), Lettres, Langues, Arts et Sciences Humaines (FLASH), 11-13/04/13.