The present project is an evolution from the initial INRIA Futursaction (ALIEN, February 2004) regrouping the following five researchers: Michel FLIESS, Polytechnique; Cédric JOIN, Nancy; Mamadou MBOUP, Paris V; François OLLIVIER, Polytechnique; Alexandre SEDOGLAVIC, Lille. The five following colleagues joined ALIEN in 2006: JeanPierre BARBOT, CergyPontoise; Lotfi BELKOURA, Lille; Thierry FLOQUET, Lille; Wilfrid PERRUQUETTI, Lille; JeanPierre RICHARD, Lille.
As before the members of the new ALIEN are distributed between 3 locations: Paris, Lille and Nancy. In the new team there is a perfect balance between members working in the Paris and Lille areas, whereas in the old one Paris had a clear majority.
Besides the notable reenforcement of the ALIEN's research potential from 5 to 10 permanent researchers, this reasoned evolution both corresponds to:
An upholding of the initial scientific objectives: The project still aims at developing upstream researches in fast identification and estimation, as well as concrete applications to signal (including image, video and fault detection) and control (including realtime control and diagnosis).
A broadening of the potential applications: Whereas the objectives remain unchanged, the class of workable models is enlarged, in particular, to timedelay systems and variable structure ones. Let us first recall some of the signaloriented applications already present in the original project: Denoising, demodulation, compression of mono or multidimensional signals, break detection... Roughly speaking, the recently opened applications are a bit more ``controloriented'': Highspeed or highprecision mechanical devices ( viaactive magnet bearings or friction compensation); Embedded systems (networked control, cooperative robotics); Aeronautics (flight model identification)...
All the ALIEN participants are invested in both theoretical advances and applicationoriented ones. All of them share the algebraic tool and the nonasymptotic estimation aim, which constitutes the natural kernel of the project and was already grounding ALIEN 1. However, ALIEN 2 will take advantage of the various participants backgrounds and favourite domains, the complementarity of which is going to be depicted in the following subsection.
So, each of the ALIEN members contributes to both theoretical and applied sides of the global project. Even if it is not possible to clearly distinguish between the future contributions of each one, it is possible to draw up a scheme of some of the specialities. Of course, algebraic tools, identification and estimationare not recalled here since everybody in ALIEN is concerned with.
Upstream Researches  Application Fields  
Saclay LIX  Computer algebra  Nonstandard analysis  Signal Linear & nonlinear control  Delays  
Paris 5  Signal processing  Numerical analysis  Digital communications, Signal denoising, Industrial processes 
Cergy ECS  Nonlinear observers  Hybrid systems  Cryptography  Multicell chopper/converter 
Lille LIFL  Computer algebra  Biology  Dedicated software 
Lille LAGIS  Delay systems  Nonlinear control  Observers(finitetime/unknown input)  Magnet bearing  Frictions  Robotics  Aeronautics 
Nancy CRAN  Diagnosis  Control  Signal  Industrial processes  Signal & image processing 
Parametric estimation may often be formalized as follows:
y=
F(
x,
) +
n,
where:
the observed signal
yis a functional
Fof the ``true'' signal
x, which depends on a set
of parameters,
nis a noise corrupting the observation.
Finding a ``good'' approximation of the components of
has been the subject of a huge literature in various fields of applied mathematics. Most of those researches have been done in a probabilistic setting, which necessitates a good
knowledge of the statistical properties of
n. Our project
differential algebra
module theory, i.e., linear algebra over rings which are not necessarily commutative;
operational calculus which was the most classical tool among control and mechanical engineers
Ris not.
Let us briefly mention some topics which will be studied in this project. In automatic control we will be dealing with:
identifiability and identification of uncertain parameters in the system equations, including delays;
estimation of state variables, which are not measured;
fault diagnosis and isolation;
observerbased chaotic synchronization.
A major part of signal and image processing is concerned with noise removal, i.e. estimation. Its role in fundamental questions like signal modelling, detection, demodulation, restoration, (blind) equalisation, etc, cannot be overestimated. Data compression, which is another key chapter of communication theory, may be understood as an approximation theory where well chosen characteristics have to be estimated. Decoding for error correcting codes may certainly also be considered as another part of estimation. We know moreover that any progress in estimation might lead to a better understanding in other fields like mathematical finance or biology.
People involved in this project are working either in:
control or signal,
(applied) algebra.
This unusual mixture is easily explained as follows:
Most methods which are utilised are of algebraic flavour.
Recent techniques – introduced and developed in particular by some members of this project for solving systems of polynomial equations (see publications of the group TERA
These algorithms have to be implemented in a computer algebra system, to take advantage of their algebraic nature, and run as preprocessing before a final numerical treatment.
Studies related in one way or the other to identification and estimation are of course well represented at INRIA. An exceptional cooperation is already existing between some of us and the SOSSO project on questions pertaining to mathematical modelling in biology. The rich intellectual atmosphere of INRIA will most certainly facilitate cross fertilisation with other groups. The strong ties of INRIA with the industrial world will moreover yield an easier access to applications.
Let us illustrate on a very basic exmple, the grounding ideas of the ALIEN approach, based on algebra. For this, consider the first order, linear system:
where
ais an unknown parameter to be identified and
_{0}is an unknown, constant perturbation. With the notations of operational calculus and
y_{0}=
y(0), equation (
) reads:
In order to eliminate the term
_{0}, multiply first the two handsides of this equation by
sand, then, take their derivatives with respect to
s:
Recall that
corresponds to

t
y(
t). Assume
y_{0}= 0for simplicity's sake
y_{0}0one has to take above derivatives of order 2 with respect to
s, in order to eliminate the initial condition.
For
= 3, we obtained the estimated value
a:
Since
T>0can be very small, estimation
via(
) is very fast.
Note that equation (
) represents an online algorithm that only involves two
kinds of operations on
uand
y:(1) multiplications by
t, and (2) integrations over a preselected time interval.
If we now consider an additional noise, of zero mean, in ( ), say:
it will be considered as fast fluctuating signal. The order in ( ) determines the order of iterations in the integrals (3 integrals in ( )). Those iterated integrals are lowpass filters which are attenuating the fluctuations.
This example, even simple, clearly demonstrates how ALIEN's techniques proceed:
they are algebraic: operations on
sfunctions;
they are nonasymptotic: parameter
ais obtained from (
) in finite time;
they are deterministic: no knowledge of the statistical properties of the noise
nis required.
Now, let us consider the first order, linear system with constant input delay
Here we use a distributionallike notation where
denotes the Dirac impulse and
His its integral, i.e., the Heaviside function (unit step)
Hand the integration operator. To be rigorous, the iterated integration (
ktimes) corresponds, in the operational domain, to a division by
s^{k}, whereas the convolution with
H(
ktimes) corresponds to a division by
s^{k}/(
k1)!. For
k= 0, there is no difference and
H*
yrealizes the integration of
y. More generally, since we will always apply these operations to complete equations (left and righthand sides), the factor
(
k1)!makes no difference.ais known. The parameter to be identified is now the delay
. As previously,
_{0}is a constant perturbation,
a,
b, and
are constant parameters. Consider also a step input
u=
u_{0}H. A first order derivation yields:
where
denotes the delayed Dirac impulse and
, of order 1 and support
{0}, contains the contributions of the initial conditions. According to Schwartz theorem, multiplication by a function
such that
,
(
) = 0yields interesting simplifications. For instance, choosing
(
t) =
t^{3}
t^{2}leads to the following equalities (to be understood in the distributional framework):
The delay
becomes available from
k1successive integrations (represented by the operator
H), as follows:
where the
w_{i}are defined, using the notation
z_{i}=
t^{i}y, by:
These coefficients show that
k2integrations are avoiding any derivation in the delay identification.
Figure
gives a numerical simulation with
k= 2integrations and
a= 2,
b= 1,
= 0.6,
y(0) = 0.3,
_{0}= 2,
u_{0}= 1. Due to the non identifiability over
(0,
), the delay
is set to zero until the numerator or denominator in the right hand side of (
) reaches a significant nonzero value.
Again, note the realization algorithm (
) involves two kinds of operators: (1) integrations and
(2) multiplications by
t.
It relies on the measurement of
yand on the knowledge of
a. If
ais also unknown, the same approach can be utilized for a simultaneous identification of
aand
. The following relation is derived from (
):
H^{k}w_{1}) +
a(
H^{k}w_{2})
a(
H^{k}w_{3}) =
H^{k}w_{0},
and a linear system with unknown parameters
(
,
a
,
a)is obtained by using different integration orders:
The resulting numerical simulations are shown in Figure
. For identifiability reasons, the obtained linear system
may be not consistent for
t<
.
Parameter identification is a key step in modelling. When trying to describe a process by differential equations, the validation of a model implies to be able to compute a set of parameters allowing to product a theoretical behaviour corresponding to experimental data. A preliminary issue is to study identifiabilitywhich means that there is a unique set of parameters corresponding to a given behaviour of the system.
For algebraic differential systems, identifiability may be tested in various ways, especially those stemming from differential algebra. In many cases, one can replace the inputoutput behaviour of the system by some polynomial or rational mapping. Testing identifiability reduces then to test the injectivity of that mapping. One can also reduce the problem to that of testing algebraic dependence of the parameters on the differential field generated by the inputs and outputs. This may be done by characteristic set computations.
Although those algebraic tools have made great progress during the last decade, the intrinsic complexity of those elimination tools is exponential in the generic case, for one has to express the relations of algebraic dependence, whose size is exponential.
One could expect to escape from this trouble by choosing to represent polynomials not as a sum of monomials but as a program computing them. It has been a fruitful approach for solving algebraic systems.
Another solution is to restrict oneself to
localidentifiability, requiring the set of parameters to be unique not on the whole space but only on some open neighbourhood. This allows to test identifiability in polynomial time,
for one only has to compute the rank of Jacobian matrices. The Maple package of A. Sedoglavic
This approach has already been of great help in biology. A. Sedoglavic was able to show that some model describing the action of an antibiotic was not identifiable. The computation of a one parameter group of symmetry has shown that the blood volume could not be computed. This suggested a new identifiable model by taking the blood volume as a unit, the exact knowledge of this volume being unimportant for studying the efficiency of the antibiotherapy.
In most problems appearing in linear control as well as in signal processing, the unknown parameters are linearly identifiable: standard elimination procedures are yielding the following matrix equation
where:
Pis a
r×
rsquare matrix and
Qis a
r×1column matrix,
the entries of
Pand
Qare finite linear combinations of terms of the form
,
,
0, where
is an input or output signal,
the matrix
Pis
genericallyinvertible, i.e.,
det(
P)
0.
With noisy measurements equation ( ) becomes:
where
Ris a
r×1column matrix, whose entries are finite linear combination of terms of the form
,
,
0, where
is a perturbation or a noise.
A perturbation
is said to be
structuredif, and only if, it is annihilated by a linear differential operator of the form
, where
a_{k}(
t)is a rational function of
t, i.e.,
. Note that many classical perturbations like a constant bias are annihilated by such an operator. An
unstructurednoise cannot be annihilated by a nonzero differential operator.
By well known properties of the noncommutative ring of differential operators, we may multiply both sides of equation ( ) by a suitable differential operator such that equation ( ) becomes:
where the entries of the
r×1column matrix are unstructured noises.
Unstructured noises are usually dealt with stochastic processes like white Gaussian noises. They are considered here as highly fluctuating phenomena, which may therefore be attenuated vialow pass filters. Note that no precise knowledge of the statistical properties of the noises is required.
Although the previous noise attenuation
The time derivatives of the input and output signals appearing in equations ( ), ( ), ( ) may be suppressed in the two following ways which might be combined:
integrate both sides a sufficient number of times,
take the convolution product of both sides by a suitable low pass filter.
Obtaining the numerical values of the unknown parameters may be achieved by integrating both sides of the modified equation ( ) during a very short time interval.
Determining derivatives of various orders of a noisy time signal is a fundamental issue, which has been often tackled in signal processing as well as in automatic control. We have recently proposed a quite efficient solution which may be explained as follows:
The coefficients of a polynomial time function are linearly identifiable. Their estimation can therefore be achieved as above.
For an arbitrary analytic time function, apply the preceding calculations to a suitable truncated Taylor expansion.
As we have seen in the introductive example of subsection
, the framework of convolution equations can be used for
fast identification issues and leads to computations analogous to the algebraic framework (multiplications by
tand integrations). This link was pointed out for the first time in our communication: ``Online identification of systems with delayed inputs" (Belkoura, Richard &
Fliess 2006)
. Further works will extend this first result
within both the algebraic and distributional formalisms.
In the case of systems with one delay, we achieved the identification of both unknown parameters and delay by using, as a starting point, an eigenvalue problem of the form:
P
_{1}+
P
_{2})
= 0,
where the unknown delay
and parameters
= (
_{1}, ...,
_{r}, 1)
^{T}are identified as the constant pair eigenvalue/eigenvector. In case of delayed and piecewise constant inputs, matrices
P_{1}and
P_{2}share the same structure as the above linear problem, while for general input and/or state delay, convolution products are required. Numerical simulations as well as experimental
results have shown the feasibility of the proposed technique.
In many practical situations, parameter identification has to be achieved in real time, i.e., in closed loop while the plant is working. This most important problem remains largely open,
even for simple and elementary linear systems. Our method allows to achieve closed loop identification even for nonlinear systems
The values of system variables, state variables especially, which cannot be directly measured have nevertheless to be determined. Classical means for doing this are for linear systems:
asymptotic observers,
Kalman filters,
which have enjoyed an immense popularity. Note however that:
asymptotic observers are quite sensitive to mismatches and perturbations,
Kalman filters are necessitating the solution of a Riccati equation, where the precise statistics of the noise has to be quite accurately known. It is moreover well known that the extended Kalman filtersfor nonlinear systems has never received a fully satisfactory justification.
For nonlinear systems the question has remained largely open in spite of a huge literature.
When those quantities are considered as unknown parameters, our previous techniques are applicable. We obtain state reconstructorswhich yield excellent estimates even with nonclassic stochastic noises, with poorly known statistics.
Note that, in the case of a finitetime reconstructor, the separation principle holds for a large class of nonlinear systems, i.e.control and reconstruction can be achieved separately. This reduces the complexity at the global design level.
Another field of interest in the framework of state reconstruction is the design of socalled ``unknown input observers''. The objective is to recover the value of the state in spite of the presence of unknown inputs. Some members of the project recently derived an observation algorithm that allows for the relaxation of some structural conditions usually assumed in most of the works related to unknown input observers , . Actually, it appears that such a method can be performed for a class of left invertible linear systems under the possibility to design finite time observers (or fast estimators). This method is being extended for a special class of nonlinear systems using differential geometric concepts. It is believed that algebraic methods can be a powerful tool in this area: to derive structural conditions whether the aforementioned algorithm might work or not both for linear and nonlinear systems, to numerically test these conditions and to quickly compute the required variables.
For a better understanding of complex industrial processes, fault diagnosis has recently become an important issue, which has been studied under various guises (See, e.g., M. Blanke, M. Kinnaert, J. Lunze, M. Staroswiecki, Diagnosis and FaultTolerant Control, Springer, 2003). In spite of this, the crucial problem of detecting and isolating a fault in closed loop for a possibly uncertain system remains largely open. Our estimation techniques enabled us to give a clearcut answer, which is easily implementable.
A fault occurrence can lead to a reduction in performance or loss of important function in the plant. The quite particular problem to consider is the design of a faulttolerant controller. Indeed, the number of possible faults, drastic change in system behaviour and time of fault occurrence play a crucial role. However, ensuring that the performances of the system remain close to the nominal desired performance after a fault occurrence, represents a challenge, which we are now solving: for instance, we presented an invited paper for the Festsschriftof Prof. Dr.Ing. M. Zeitz which took place in September 2005.
Three patents are already pending in those topics:
compression of audio signals,
demodulation and its theoretical background
compression, edge and motion detection of image and video signals
It is therefore difficult in this report to give too much details. We will limit ourselves to:
an academic example which indicates that our approach is indeed powerful enough for detecting abrupt changes in real time.
This last example as well as the two examples of the note have been borrowed from the famous book by Prof. S. Mallat ( A Wavelet Tour of Signal Processing, 2 ^{nd}ed., Academic Press, 1999), where he writes that no convincing treatment has yet been obtained viaexisting theories.
Abrupt changes in a signal generally represent important informationbearing parameters. The presence of such transient phenomena in the electroencephalogram (EEG) records may reveal pathology in the brain activity. In such an instance, the detection and location of the change points may be critical for a correct diagnostic. As a first step towards a more general study of gap detection, we have considered a nonstationary piecewise polynomial signal. With our method, it is possible
to calculate the coefficients of the various polynomials in the presence of noises which might be nonGaussian,
to determine quite precisely the locations of the change points.
As an example, consider the estimation of the sequence
of unknown time polynomial signals measured by
y_{i}(
t) =
p_{i}(
t) +
(
t)where
(
t)is a zero mean value stochastic process constituted, at each time
t, by a rectangularly distributed computergenerated random variable. Figure 3 shows the sequence of polynomials estimates, which are seen to converge quite fast to the
ideal signal and the results of the constant parameter identification in the noisy environment. It should be pointed out that in the previous simulations, the instants
t_{i}, at which the polynomial signal
p_{i}(
t)changed into a new one
p_{i+ 1}(
t), were known beforehand. It is not difficult to see that the proposed identification algorithm is also capable of depicting the instant at which the new polynomial
signal arrives, when such discontinuity instants are randomly selected. Being unaware of the signal change, results in a noticeable drifting of the constant values of the parameters being
currently identified. This allows for a simple and timely reinitialization of the estimation algorithm. Figure 4 depicts an example of the estimated parameters drift that occurs when a
second order polynomial signal is suddenly changed to a different one.
ALIEN aims at developing algorithms, but not commercial softwares. However, we intend to make available part of the programs used in our researchs and publications in order to make easier the diffusion of our ideas.
The Maple package developped by Alexandre Sedoglavic to test observability is available at url: http://www2.lifl.fr/ sedoglav/Software/ObservabilityTest/
The manifold success of our viewpoint in various branches of mathematical engineering is indicating directions for researches in a near future.
Our calculations are resting on the two following aspects:
Algebraic elimination of some system variables. Here again the use of non classical data structures forms a keystone for accelarating algebraic computations and eventually producing naturally efficient numerical programs.
Manipulation of matrices, which are illconditioned since the integration time is very short.
Improving our results will therefore necessitate a combination of algorithms stemming from computer algebra and numerical analysis which needs to be better understood.
New concrete examples from various technological fields will be investigated. It is worth noticing that several experimental benchmarks are already available at LAGIS laboratory (mobile robots, stepper motor, cartpendulum) as well as at ECS laboratory (benchmark on multicell chopper).
The cooperation between several agents is a challenging trend from both economical and scientific points of view. A large number of applicative fields can be cited: Transportation (unit of mobile robots), Health (remotelyoperated surgery robots), Environment or Defence (fleet of drones or UAV), Space (constellation of satellites), Machining (overactuated systems)... The cooperating devices have to fulfill a common objective, subject to environment perturbations and using a limited number of sensors. Then, it makes sense to use fast reconstruction of state variables as well as of exogenous parameters (force feedback, obstacle positions...). It is aimed at designing computationally efficient algorithms, based on algebraic estimation techniques, and working out the required information on the basis of the available sensors and communication links.
Magnetic levitation systems have received much attention as a way of eliminating Coulomb friction due to mechanical contact. Levitation bearing has been used from the beginning in rotating machinery to support rotors without friction providing low energy consumption, high rotational speed, with no lubrication and greater reliability. It also allows a simpler and safer mechanical design as in the case of pumps used in nuclear installations where fluid leakage avoidance is of primary importance. Magnetic bearings are also becoming increasingly popular in the precision industry, with significant demands on accurate positioning. One can quote nanometric servoposition actuator in microlithography industry as well as vibration isolation in precision scientific instruments. Highspeed ground transportation systems constitute another application, probably the most famous: Japanese ``Maglev'' and German ``Transrapid'' are very fast trains using the principle of a linear motor hanged up over a magnetic rail.
Magnetic levitation systems highlight phenomena like strong nonlinearities, fast dynamics, actuator saturations and uncertain parameters. Many control techniques have been quite successfully implemented on levitation systems. Within the control methodologies, one can cite, for instance, feedback linearization control, flatness based control, passivity based control, or backstepping design approach. However the performances are limited by the model relevance as well as its parameters accuracy. Estimation of these parameters is a motivating problem and it is aimed at developing and testing control laws based on closedloop identification methods. In the next few months, a magnetic shaft benchmark will be developed in Lille in collaboration with Dr. Joachim Rudolph from the University of Dresden.
Modelling or estimating
onlinethe viscous or dry friction in mechanical systems is a challenging problem with an industrial impact. To mention only the regional framework of ``Region Nord  Pas de Calais'',
several programs are concerned with brake systems management (ST2 pole
By using the fast estimation capabilities, we hope to drastically simplify some difficult modelling problems arising while studying friction. Two benchmarks at LAGIS can be used to illustrate the efficacy of the algebraic methods for the control of electromechanical systems with friction: A linear drive actuating a cartpendulum, and a stepper motor. Note that the latter is a flat system and so, a linearizing control law based on the fast and robust estimation of the time derivatives of the sensor signals can be considered.
Multicell choppers and converters are more and more popular in power electronic, due to three main reasons: (1) The possibility with the same switching component of covering a wide voltage scale. (2) The modularity and flexibility introduced in the design of such choppers or converters. (3) The drastic decreasing of the dv over dt phenomenon.
Unfortunately, due to the complexity of the control (i.e. hybrid system, non universal input...), many of the industrial applications are considered in the vicinity of a given, staticrequested behavior. The algebraic techniques could be considered so to design an observerbased control algorithm valid for more general dynamicbehaviors. Application domains of such a breakthrough are for instance: Railway traction, Active filter for networks.....
Delay estimation may also be a crucial question in concrete situations, since most of the efficient control techniques need the delay as a parameter. Real time identification of delay was considered as an open problem. Scarce results , manage an asymptotic identification, the convergence time of which does not guaranty an efficient combination with control or fault diagnosis techniques. The approach introduced in opens a promising track to fast estimation of delays, including the case of variable ones. Several fields of application are concerned.
A wide class of plants (chemical engineering, food industry...) can be approached efficiently by a simple linear model with input delay. If it turns out to be possible, the development of a software that provides both the model and the associate controller from industrial data mining (thus, offline data) is very relevant to industrial concerns.
Among the various approaches that model the longitudinal flight of an aircraft through a vertical gust, a delaybased description was introduced so to represent the effects of the penetration of the aircraft through the gust. Combining this description with a fast identification algorithm constitutes a track for the aerodynamic coefficients identification. Tests will be carried out at the Flight Analysis laboratory of the DCSD of ONERA in Lille. During those experiments, a model of civil aircraft equipped with an embedded instrumentation will be catapulted and will cross, during a free flight, a turbulence generated by a vertical blower.
Communication networks (ethernet, wifi, internet, CAN... ) have a huge impact on the flexibility and integration of control systems (remote control, wireless sensors, collaborative systems, embedded systems...). However, a network unavoidably introduces time delays in the control loops, which may put the stability and safety performances at risk. Such delays are varying (jitter) and efficient control techniques (predictorbased) take advantage of their knowledge. Two approaches have to be combined: (1) use delay identification algorithms and improve the control; (2) design control/estimation algorithms that can stand variations of the delay.
In the directsequence codedivision multiple access(DSCDMA) system, several users share a common propagation channel, by use of spread spectrum signalling. Each user is assigned a unique code sequence corresponding to its signature. This signature sequence allows the user to modulate and spread the informationbearing signal across the available frequency band. It is also on the basis of this signature that the receiver distinguishes and separates the corresponding user among the others.
As the different users access the channel asynchronously, the optimum maximum likelihood receiver, which is based on a bench of correlators, has a computational complexity which grows exponentially with the number of users. It seems that our method should lead to a more efficient detection with a reasonable level of complexity.
The problem of estimating the directionofarrival of multiple sources incident on a uniform array has received much attention in recent years, especially for wide band sources for which
the existing solutions are rather computationally demanding. If
s_{k}(
t),
, denotes the
k^{th}source signal, the signal
y_{i}(
t)received then by the
i^{th}sensor,
is of the form:
where:
n_{i}(
t)is an additive noise,
_{i}( _{k})is the (relative) delay of a signal from direction _{k}.
The problem of estimating the directionofarrival is equivalent to the estimation of those delays. When a model for the source signal is known
The famous discovery of turbocodesby Prof. C. Berrou and the late Prof. A. Glavieux has certainly been the main achievement in the 90s of the theory of error control codes. Besides completely changing not only the theory but also the practical implications of this field, it has given birth to various extensions in signal processing such as turboequalisation. It seems that turbodecoding might benefit from our new understanding of estimation.
Watermarking, which is becoming a hot topic, may be viewed as a type of cryptography where a hidden message has to be inserted in an image or a video. Our approach to image and video
processing, which unfortunately could not be reviewed in this report for legal reasons
After Pecora and Carroll (1991) successfully synchronized two identical chaotic systems with different initial conditions, chaos synchronization has been intensively studied in various fields and in particular in secure communications (because chaotic systems are extremely sensitive to their initial conditions and parameters). The idea is to use the output a particular dynamical (chaotic) system to drive the response of an identical system so that they oscillate in a synchronized manner. An interesting application in secure communication uses such a chaotic master dynamics to mask a message and a synchronized slave system to recover the message.
Since the work of Nijmeijer and Mareels (1997), the chaotic system synchronization problem has been intimately related to the design of a nonlinear state observer for the chaotic encoding system. Many techniques issued from observation theory have been applied to the problem of synchronization, where the receiving system asymptotically tracks the states of the transmitting system: observers with linearizable dynamics, adaptive or sliding mode observers, generalized hamiltonian form based observers, etc.
The key issue here is to take an algebraic viewpoint for the state estimation problem associated with the chaotic encryptiondecoding problem and to emphasize its use for the efficient and fast computation of accurate approximations to the successive time derivatives of the transmitted observable output signal received at the decoding end. Those methods should also be useful in new encryption algorithms that require fast estimation of the state variables and the masked message.
Remark 1Note that the technological aspects of this new kind of cryptography has nothing to do with numbertheoretic cryptography which has become very popular in computer sciences.
People of the project who belong to LAGIS, as well as JeanPierre Barbot, have been working for many years on other methods for fast estimation (of state variables or unknown parameters). Those techniques, that have been widely developed during the last decade in the literature, are often referred as ``finite time'' observers or estimators: The knowledge of the variables or the parameters is theoretically recovered after a finite time and not asymptotically (as it is usually the case). This approach involves notions such as homogeneous functions or discontinuous functions (one can refer to higher order sliding mode theory or the larger area of variable structure systems). Thus, for several fields of applications, the members of the project have the required background to perform comparisons of variable structure techniques and algebraic methods in the framework of fast estimation and identification.
Michel Fliess has obtained a DGA contract of 25 Keur on signal processing.
Thematic research on Automatic control and Man  Machine systems with Application to Transport. Grant in the framework of the program ``TAT Technologies Avancées pour les Transports'' (Advanced Technologies for Transport) Regional Council of Nord Pas de Calais, French Ministery of Research, European Community (FEDER)
J.P. RICHARD (manager)
This program joints a fundamental research with applications to transport systems. This includes works devoted to observation of nonlinear systems and delay systems, as well as their application to vehicle control. The global allocated ceiling is 1894 kEuros (including a 1497 kEuros subvention from Region+FEDER) for the GRAISyHM teams (GRAISyHM is a Federation of Automatic control labs in North France). Within this global ceiling, 46.4 kEuros (36.9 kEuros subvention) are concerning J.P. Richard's team.
``Robocoop : cooperative strategies within teleoperated formations''.
This Arcir ("Actions de recherches concertées d'initiative régionale") has a global funding of 142 200 Eurs (the region Nord PasdeCalais is supporting 71 100 Eurs, the remaining being suported by the feder).
This project aims at developing technics belonging to the research field of automatic control that should take into account cooperation and delays due to communications between the robots. The obtained results will be demonstrated on two test benches: one composed of mobile robots and the other one of two manipulators.
``Action Spécifique TRACTECO : Méthodes de commande, d'observation et d'identification de systèmes non linéaires avec application aux paliers magnétiques'' Applied research on Control, observation and identification of nonlineaur systems with application to magnetic bearings.
Grant of 45 Keuros in the framework of the program ``TAT Technologies Avancées pour les Transports'' (Advanced Technologies for Transport) Regional Council of Nord Pas de Calais, French Ministery of Research, European Community (FEDER)
T. FLOQUET (manager)
The main objective of this program is the design of fast estimation algebraic methods for the control of magnetic bearings. The resulting control laws will be experimentally tested on a benchmark developed in collaboration with J. Rudolph from the University of Dresden, Germany.
 The case of adherence coefficients for tyre efforts
Grant supported by GdR CNRS 717 MACS ``Modélisation, Analyse et Commande des Systèmes dynamiques'' (Modelling, Analysis and Control of dynamic Systems). Category ``Exploratory research on interdisciplinary joint research''.
H. MOUNIER (manager), Institut d'Electronique Fondamentale, CNRS and University of Paris 11, 8 kEuros
DSPComCollaboration with the Laboratory of signal processing for communication (DSPCom) of the Faculty of Electrical Engineering and Computer Science (FEEC) of UNICAMP (University of Campinas  Brasil). This collaboration includes Prof. Joao Marcos Romano (head of the laboratory) and Aline Neves who defended her PhD in 2005 with M. Mboup (see ).
UPMThere is another collaboration with the team of research in numerical communication of Universidade Presbiteriana Mackenzie (UPM), Brasil, involving Maria Miranda who came for two weeks in 2006.
Mamadou Mboup has been invited for two weeks at Unicamp in april 2006.
In september 2005, we made a proposal for a STICINRIA project with Tunisia (Modeling and system identification). This project has been renewed in 2006.
This summer school was devoted to the new fast methods developped by Alien.
Scientific coordinator : Michel Fliess, Main speakers : Michel Fliess; Cédric Join; John masse, Société APPEDGE; Mamadou Mboup; Johann Reger, University of the Army, Munich; Joachim Rudolph, Technical University, Dresde; Kurt Schlacher, Johannes Kepler University, Linz; Hebertt SiraRamirez, CINVESTAVIPN, Mexico City; Alina VODA, Université Joseph Fourier, Grenoble.
During 2006 IEEE International Conference on Accoustics, Speech and Signal Processing, may 14–19 2006, Toulouse, France, the tutorial lecture: ``Towards new estimation techniques: Reconciling signal processing and control'' was presented by Michel Fliess and Mamadou Mboup.
During the school ``Digital control of industrial processes'', Douz, Tunisia, 5–8 November 2006, lectures were given by Alien members:
``Une introduction aux particularités et généralités des systèmes à retards'', J.P. RICHARD;
``Systèmes à retards : Identifiabilité et Identification'', L. BELKOURA;
During the Seminar of the ``Identification'' workshop of CNRS GDR MACS, ENSAM Paris, 17 November 2005, the following lectures were given:
``Identification des paramètres et retards des systèmes linéaires'', L. BELKOURA and J.P. RICHARD;
``Identification de systèmes à entrées retardées'', L. BELKOURA, J.P. RICHARD;
During the seminar of the NECS project ``Networked Controlled Systems'', LAG, Grenoble, 27 September 2005 (NECS is now an INRIA project), the following lecture was given:
``Rudiments on Delay Systems and their relation with networked control'', J.P. RICHARD.
Seminar ``Networked Control Systems'' of the CNRS Research Group GdR ARP, theme RealTime Systems  QoS, Paris, 17 June 2005, the following lecture was given:
``Systèmes à retards : une introduction à l'usage des nonautomaticiens'', J.P. RICHARD.
The Multipartner Marie Curie Training Site, entitled Control Training Site is funded by the European Commission with a global support over four years (Starting January, 2002) of 960 fellowmonths. The lead organization is the CNRS at GifsurYvette, France.
This site organizes international doctoral studies in the scientific area of control theory, optimization and applications. The CTS is addressed to any European student starting the doctoral studies or pursuing doctoral studies in the large domain of Control and Optimization, including various domains of control theory, optimization and control engineering.
Michel Fliess has given 12 hours lectures on Alien's estimation methods.
Michel fliess has given 25 hours lectures at École polytechnique of Tunis in 2006.
François Ollivier has given level 2 lectures in the course ``Algorithms in Computer Algebra and Control'' of the Parisian Master of Research in Computer Science (MPRI).