After being initiated as a team in 2004, the projectteam ALIEN was created in 2007, July 1st(see the 2006 activity report for the evolution from the initial group to the present one). Its evaluation was held in March 2009 in the framework of Theme 3 of INRIA (Modeling, Optimization and Control of Dynamic Systems). The Evaluation Committee decided (October 17, 2009) to support ALIEN for the next 4 years. Note that ALIEN was also evaluated in the framework of AERES in Lille, AERES in Saclay, and AERES in LilleLAGIS CNRS FRE 3303.
The ALIEN project aims at designing new realtime
estimation algorithms. Within the huge domain of estimation,
ALIEN addresses the following, particular trends:
softwarebased reconstruction of unmeasured variables (also
called "observation"), filtering of noisy variables,
estimation of the
nth order time derivatives of a signal, parametric
estimation of a linear/nonlinear model (including delay and
hybrid systems).
The novelty lies in the fact that ALIEN proposes algebrabased methods, leading to algorithms that are fast (realtime is one of our goals), deterministic (noise is considered as a fast fluctuation), and nonasymptotic (finitetime convergence). This is why we think that ALIEN's studies are shedding a new light on the theoretical investigations around estimation and identification. As it was told, estimation is a huge area. This explains the variety of possible application fields, which both concern signal processing and realtime control. Several cooperations have already been launched on various concrete industrial problems with promising results.
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, with applications in cryptography and secure systems.
A major part of signal and image processing is concerned with noise removal, i.e., estimation. Its role in fundamental questions like signal modeling, detection, demodulation, restoration, (blind) equalization, etc, cannot be overestimated. Data compression, which is another key chapter of communication theory, may be understood as an approximation theory where wellchosen 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.
The members of the ALIEN project work in different places: Paris, Lille, Reims and Nancy; they share the algebraic tool and the nonasymptotic estimation goal, which constitute the natural kernel of the project. Each of them contributes to both theoretical and applied sides of the global project. The following table draws up a scheme of some of their specialities. Of course, algebraic tools, identification and estimationare not recalled here since any member of ALIEN is concerned with.
Upstream Researches  Application Fields  
Computer algebra   
Saclay  Nonstandard analysis  Signal   
LIX  Linear & nonlinear control  Delays  
Reims  Signal  Numerical analysis  Denoising  Demodulation  
CReSTIC  Biomedical signal processing  
Cergy  Nonlinear observers   Cryptography  
ECS  Hybrid systems  Multicell chopper/converter 
Lille  Applied mathematics  High performance machining  
ENSAM  Precision sensors,
AFM


Lille  Delay systems   Aeronautics  
LAGIS  Nonlinear control  Observers  Magnetic bearings  Friction estimation  
(finitetime/unknown input)  Networked control  Robotics  
Nancy  Diagnosis  Control  Signal  Industrial processes  
CRAN  Signal & image processing 
Patent pending (FR0858532) with EDF on the control of hydroelectric dams.
Innovation Award 2010 of École Polytechnique for the patent with EDF on the control of hydroelectrical dams.
Confirmation of the importance of "modelfree control" from various concrete examples , , and .
JeanPierre Barbot, with colleagues,
creates a working group jointly with MACS (CNRS GDR 717)
and DYCOEC (CNRS GDR 2984) on control science and physics
(
http://
JeanPierre Barbot has been nominated for a new term as Invited Professor at Northumbria University, UnitedKingdom.
Mamadou Mboup is nominated as Guest
Professor of InnoLecture program at Saarland University,
Germany (
http://
PEPS/CNRS project: Cédric Join (UHP Nancy ALIEN), Mamadou Mboup (URCA  ALIEN) and Joachim Rudolph (LSR, Saarland University, Germany).
Plenary lecture by Lotfi Belkoura at IFAC TDS10 .
SemiPlenary lecture by JeanPierre Barbot at IEEE VSS10 .
SemiPlenary lecture by Wilfrid Perruqutti at IEEE VSS10 .
Parametric estimation may often be formalized as follows:
y=
F(
x,
) +
n,
where:
the measured 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 is devoted to a new standpoint which
does not require this knowledge and which is based on the
following tools, which are of algebraic flavor:
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
In most problems appearing in linear control as well as in signal processing, the unknown parameters are linearly identifiable: standard elimination procedures yield the following matrix equation
where:
_{i},
1
i
r, represents an unknown
parameter,
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, the equation ( ) becomes:
where
Ris a
r×1column matrix, whose entries
are finite linear combination of terms of the form
, 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 wellknown properties of the noncommutative ring of differential operators, we can multiply both sides of equation ( ) by a suitable differential operator such that equation ( ) becomes:
where the entries of the
r×1column matrix
R^{'}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 ( ), ( ), ( ) can be suppressed in the two following ways which might be combined:
integrate both sides of the equation a sufficient number of times,
take the convolution product of both sides by a suitable low pass filter.
The numerical values of the unknown parameters can be obtained by integrating both sides of the modified equation ( ) during a very short time interval.
Let us illustrate on a very basic example, 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:
where represents Laplace transform.
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.
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
(0) =
^{'}(0) = 0,
(
) =
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 the
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<
.
Numerical differentiation, i.e., determining the time derivatives of various orders of a noisy time signal, is an important but difficult illposed theoretical problem. This fundamental issue has attracted a lot of attention in many fields of engineering and applied mathematics (see, e.g. in the recent control literature , , , , , , and the references therein). A common way of estimating the derivatives of a signal is to resort to a least squares fitting and then take the derivatives of the resulting function. In , , this problem was revised through our algebraic approach. The approach can be briefly explained as follows:
The coefficients of a polynomial time
function are linearly identifiable. Their estimation can
therefore be achieved as above. Indeed, consider the
realvalued polynomial function
,
t0, of degree
N. Rewrite it in the well known notations of
operational calculus:
Here, we use
, which corresponds in the time domain to the
multiplication by

t. Multiply both sides by
,
. The quantities
,
are given by the triangular system of linear
equations:
The time derivatives, i.e.,
,
,
0
N, are removed by multiplying
both sides of Equation (
) by
,
.
For an arbitrary analytic time
function, apply the preceding calculations to a suitable
truncated Taylor expansion. Consider a realvalued
analytic time function defined by the convergent power
series
, where
0
t<
.
Approximate
x(
t)in the interval
(0,
),
0<
,
by its truncated Taylor expansion
of order
N. Introduce the operational analogue of
x(
t), i.e.,
. Denote by
,
0
N, the numerical estimate of
, which is obtained by replacing
X_{N}(
s)by
X(
s)in Eq. (
). It can be shown
that a good estimate is
obtained in this way.
Thus, using elementary differential algebraic operations,
we derive explicit formulae yielding pointwise derivative
estimation for each given order. Interesting enough, it turns
out that the Jacobi orthogonal polynomials
are inherently connected with the
developed algebraic numerical differentiators. A
leastsquares interpretation then naturally follows
,
and this leads to a key result:
the algebraic numerical differentiation is as efficient as an
appropriately chosen time delay. Though, such a delay may not
be tolerable in some realtime applications. Moreover,
instability generally occurs when introducing delayed signals
in a control loop. Note however that since the delay is known
a priori, it is always possible to derive a control
law which compensates for its effects (see
). A second key feature of the
algebraic numerical differentiators is its very low
complexity which allows for a realtime implementation.
Indeed, the
n^{th}order derivative estimate (that can be directly
managed for
n2,
without using
ncascaded estimators) is expressed as the output of the
linear timeinvariant filter, with finite support impulse
response
. Implementing such a stable and causal filter is easy
and simple. This is achieved either in continuoustime or in
discretetime when only discretetime samples of the
observation are available. In the latter case, we obtain a
tapped delay line digital filter by considering any numerical
integration method with equallyspaced abscissas.
Rather than being a project linked to a specific domain of application, we can say that ALIEN is a methoddriven project. However, one must not forget that applicability remains a guideline in all our research. Estimation is known to be a huge area, which explains the variety of possible application fields our new methods address. During these first few years, ALIEN's techniques have already generated 3 patents , , and the one pending with EDFCIH (FR0858532). It shows their efficiency in various industrial domains, including (see the previous reports):
Vehicle control (engine throttle , lateral and longitudinal velocities , stopandgo , tire/road contact condition ) with PSA, APEDGE, MinesParisTech, INRIA IMARA, Universidad Carlos III (Madrid, Spain), Université Paris Sud;
Hydroelectric power plants , with EDFCIH (patent pending FR0858532);
Shape memory actuators with Université de Bretagne Occidentale and ANR MAFESMA;
Magnetic actuators with Saarland University (Germany);
Power Electronics with Université du Québec (TroisRivières, Canada);
Aircraft identification with ONERA DCSD;
Secured communications (chaosbased cryptography , , , CPM demodulation ) with CINVESTAV (Mexico), Math. Dept. Tlemcen University (Algeria) and PRISME ENSIBourges.
Image and video processing (denoising , edge detection ) with INRIA QGAR, compression , compressive sensing , with CINVESTAV (Mexico) and Whuan University (China).
More recently, financial engineering with MEREOR Investment Management and Advisory SAS.
After the successful implementation of modelfree control , for several concrete situations in 2009:
Throttle control for IC engines (with APPEDGE and PSA) ;
Stopandgo automotive control strategy (in collaboration with the École des Mines de Paris and PSA) , , ;
Hydroelectrical dams modeling and control (in collaboration with EDF) , ;
Shape memory actuators (collaboration with the team directed by Prof. E. Delaleau at the École Nationale des Ingénieurs de Brest , );
this method makes more exciting achievements in 2010, listed as follows:
Modelfree control involves the design of the socalled "intelligent" PID controllers , , and a mathematical explanation via "intelligent" PID controllers of the strange ubiquity of PIDs has been developed in , and the simulations confirm the superiority of the new intelligent feedback design;
Delta hedging, which plays a crucial role in modern financial engineering, is a tracking control design for a "riskfree" management. The application of modelfree control method to set Delta hedging is reported in , which avoids most of the shortcomings encountered with the now classic BlackScholesMerton framework;
"Planar Vertical TakeOff and Landing" (PVTOL) aircraft has been largely studied in the academic literature via various advanced nonlinear control techniques. In , the modelfree control method was successfully used to easily yield the control strategy for PVTOL;
The modelfree control methodology is applied for the first time to power converters, and in particular to a buck converter, and to a Cuk converter in . We evaluate its performances regarding load and supply variations. Our approach, which utilizes "intelligent" PI controllers, does not require any converter identification while ensuring the stability and the robustness of the control synthesis;
The longitudinal control of the electrical vehicle is challenging, since the chassis and the engine dynamical equations exhibit complex unknown parameters and/or neglected terms. However, using modelfree control approach can bypass those parameter and model uncertainties, without the necessity of identifying them, and it is illustrated by convincing experimental results in ;
Automatic water level control for open channels have difficulties to keep good performances for a large range of flow and significant unknown disturbances. and used the modelfree control technique for controlling water level of hydroelectric runofthe river power plants with severe constraints and operating conditions. Numerous dynamic simulations show that with a simple and robust control algorithm, the setpoint is followed even in severe operating conditions.
Elementary techniques from operational calculus, differential algebra, and noncommutative algebra lead to a new algebraic approach for estimation and detection. It is investigated in various areas of applied sciences and engineering. The following lists only some applications:
To detect the changepoint of discontinuous signal is challenging, especially for applications requiring online detection. The difficulties are stemming from corrupting noises which are blurring the discontinuities, and the combined need of fast calculations for realtime implementation and of reliable detection. presented a new algebraic approach for changepoint detection, where numerical experiments illustrated the efficiency of the proposed method;
Single channel EEG systems are very useful in EEG based applications where real time processing, low computational complexity and low cumbersomeness are critical constrains. These include braincomputer interface and biofeedback devices and also some clinical applications such as EEG recording on babies or Alzheimer's disease recognition. proposed to use the algebraic approach to address the problem of eye blink artifacts detection in such systems. The occurrence of an artifact is modeled as an irregularity which appears explicitly in the time (generalized) derivative of the EEG signal as a delay. Manipulating such delay is easy with the operational calculus and it leads to a simple joint detection and localization algorithm. Comparison of the results on artificially created and real signal leads to conclusions that with detection techniques based on derivative estimation we are able to detect not only eye blink artifacts, but also any spike shaped artifact, even if it is very low in amplitude;
Algebraic parametric differentiation technique is presented in , where the approximation error for this derivative estimation is analyzed, which contains two sources of error: the bias term error and the noise error. The analysis for the noise error of a known noise is given. Especially, the bias term errors are bounded for the minimal estimators and the affine estimators. It was shown that these estimators are more efficient than some improved classical ones;
Algebraic method is adopted to identify the time delay involved in timedelay systems. Identifiability and algebraic identification of time delay systems are investigated in , where online algorithms were proposed for both parameters and delay estimation. Based on a distributional technique, these algorithms enable an algebraic and simultaneous estimation by solving a generalized eigenvalue problem. Simulation studies with noisy data and experimental results show the performance of the proposed approach.
Automobile manufacturers have dedicated enormous efforts on developing intelligent systems for the dynamic performance of road vehicles in the last years. Thus, many systems have been deeply studied in order to increase safety and improve handling characteristics. Most of these systems are based on an efficient transmission of the forces from vehicle wheels to the road surface. Friction is the major mechanism for generating these forces on the vehicle. Unfortunately the road maximum adherence cannot be measured directly. In and , the algebraic method is used to estimate it. Instantaneous friction is first computed within this framework. Then, extended braking stiffness concept is exploited to detect which braking efforts allow to distinguish a road type from another. A weighted Dugoff model is used during these "distinguishable" intervals to estimate the maximum friction coefficient. Promising results have been obtained in noisy simulations and real experimentations.
Compressive Sensing (CS) is a new sampling theory which allows signals to be sampled at subNyquist rate without loss of information. The following gives a brief description of our recent results:
To guarantee exact recovery from compressed measurements, one should choose specific matrix, which satisfies the Restricted Isometry Property (RIP), to implement the sensing procedure. In , we proposed to construct the sensing matrix with chaotic sequence following a trivial method and proved that with overwhelming probability, the RIP of this kind of matrix is guaranteed. Meanwhile, its experimental comparisons with Gaussian random matrix, Bernoulli random matrix and sparse matrix are carried out and show that the performances among these sensing matrix are almost equal;
Ordinarily, the compressive sensing matrix is constructed by the Gaussian random one or Bernoulli random one. In , we have proved that the typical chaotic sequence  logistic map can be adopted to generate the sensing matrix for CS. In , we showed that Toeplitzstructured matrix constructed by chaotic sequence is sufficient to satisfy RIP with high probability. With the Toeplitzstructured Chaotic Sensing Matrix (TsCSM), we can easily build a filter with small number of taps. Meanwhile, we implement the TsCSM in compressive sensing of images.
Observability analysis and observer design are important issues in the field of control theory. Some recent results are listed below:
A global finitetime observer was proposed in for nonlinear systems which are uniformly observable and globally Lipschitz. The parameters of the proposed observer can be set once and then will provide finite time convergence whatever the initial conditions. This result is based on a highgain approach combined with recent advances on finitetime stability using Lyapunov function and homogeneity concepts;
Concerning the problem of the design sliding mode observers for nonlinear systems subject to unknown inputs, in most approaches, sliding mode observers can be designed under the assumption that the system can be transformed into a specific canonical observable form. Then, the state and the unknown input of the system can be recovered in finite time. In , the class of systems for which unknown input sliding mode observers can be designed is enlarged by introducing an extended triangular observable form and a higher order sliding mode observers for which finite time convergence can be shown using Lyapunov stability arguments;
Roughly speaking, two types of observers exist: full order observer and reduced order one. It is well known that the existence of a full order observer with linear error dynamics implies the existence of a reduced order observer with linear error dynamics, however the reverse is not valid. Moreover, there are no results available for nonlinear systems to provide conditions, under which via a transformation, a reduced order observer with linear error dynamics may be found. In and , we presented a new nonlinear canonical form which allows us to design reduced order observers, just like the linear case. Necessary and sufficient conditions are given to guarantee the existence of the proposed nonlinear canonical form;
The problem of loss of observability at low frequency range for the Permanent Magnet Synchronous Motor is always recognized in experimental settings. analyzed the observability for sensorless control design. Moreover, an Estimator/Observer Swapping system is designed for the surface Permanent Magnet Synchronous Motor to overcome position observability problems at zero speed, which becomes unobservable at this point;
Using the second order sliding mode observer for the induction motor without mechanical sensor was presented in and . This observer converges in finite time and is robust to the variation of parameters. The simulation results show the performance of the proposed observer. Furthermore, an industrial application is presented in order to highlight the technological interest of the proposed method and also show the difficulties due to real time computation constraints;
By tacking the hybrid behavior of the multicellular converter into account, proposed a nonlinear finite time observer to estimate the capacitor's voltages. The stability and properties of the proposed homogeneous finite time observer are studied using Lyapunov theory. Our approach enables the stabilization of the observation errors in spite of the presence of perturbations. Simulations highlight the efficiency of the proposed strategy;
A robust control for a stepper motor with no position nor velocity sensors and only needing current and voltage measurements was designed in and . Second order sliding mode observers are realized to estimate both rotor angular position and velocity. Moreover, a robust control law, which is also based on second order sliding modes and which uses the estimates of the observer, is designed. The stability of the observer based control loop is discussed. The results obtained in simulations indicate the usefulness and the robustness of the method.
Causal and noncausal observability were discussed in for nonlinear timedelay systems. By extending the Lie derivative for timedelay systems in the algebraic framework introduced by , we present a canonical form and give sufficient condition in order to deal with causal and noncausal observations of state and unknown inputs of timedelay systems. The problem of causal observability of the states and unknown inputs of nonlinear timedelay systems is investigated in . Algorithms are provided to check the possibility of obtaining causal estimations of the states and unknown inputs for the studied systems;
Identification problem for systems with delayed inputs was studied in , where a fast identification algorithm is proposed. It is based on a nonasymptotic distributional estimation technique initiated in the framework of systems without delay. Such technique leads to simple realization schemes, involving integrators, multipliers and piecewise polynomial or exponential time functions. Thus, it allows for a real time implementation.
In relation with the framework of embedded and networked systems, the sampleddata stabilization of linear timeinvariant systems with feedback delay was considered in , where the delay is assumed to be timevarying and that its value is approximatively known. Interval timevarying delay systems was studied in , where the timedelay interval is divided into several zones and the systems switch among the different zones. An additional result on the stabilization of neutral systems in the presence of timevarying delays and control saturation was presented in .
Multivariate signals are abundant in various branches of physics, in telecommunication, geology, econometrics as well as digital images and videos. Online differentiation of multivariate signals in a noisy environment was developed in and by extending further the monodimensional differentiation method of and its multidimensional extension . The multivariate estimators enjoy the same properties of their monovariable counterpart. Namely:
pointwise estimation,
orthogonal projection in the orthogonal set of multivariate Jacobi polynomials.
In fact those estimators correspond to orthogonal projection in a Jacobi basis i.e., a least squares minimization. In addition they can be implemented as finite impulse digital filters. We combine somehow optimization and fast computation.
A " fast" practical implementation through a discrete convolution was also developed. The utility of our estimators in image and video processing will be investigated in the future project. We plan to develop new low level image analysis tools for features extraction (edges, motion detection and estimation...).
Concerning hybrid dynamical systems, we obtained the following results:
The observability of a class of switched systems with Zeno phenomenon or high switching frequency was discussed in , where three observability forms are proposed and the observability for each form with knowledge of filtered switching signal is analyzed. Meanwhile, sufficient and necessary conditions for the existence of a diffeomorphism to transform a class of switched systems into one of such forms are presented. Examples and simulations are given at the end to highlight the theoretical results;
A method for the finite time estimation of the switching times in linear switched systems was proposed in . This approach is based on algebraic tools and distribution theory. Switching time estimates are given by explicit algebraic formulae that can be implemented in a straightforward manner using standard tools from computational mathematics. Simulations illustrate the efficiency of the proposed techniques;
Online identification of nonlinear continuoustime systems subject to impulsive terms was studied in . Using a distribution framework, a scheme is proposed in order to annihilate singular terms in differential equations representing a class of impulsive systems. As a result, an online estimation of unknown parameters is provided, regardless of the switching times nor of the impulse rules. Numerical simulations of physical processes with noisy data are illustrating our methodology and results;
Traditional method to design a controller for each subsystem of switched systems will increase the complexity of the controller's realization. Sufficient conditions for designing a uniform output feedback controller for linear switched systems was given in , and this common controller can be used for all subsystems of the switched systems. Then the output stabilization problem for a particular class of linear switched systems under this uniform output feedback controller has been studied. An illustrative example is given in order to highlight the proposed method.
An Atomic Force Microscope (AFM) is a threeaxis
(
x,
y,
z)system used to capture images or
to manufacture at micro and nano scale. The main features of
this work is to improve the abilities of an AFM to capture
image at fast speed and at the same time to improve the
accuracy of trajectory tracking.
By using the modelfree control method and the algebraic estimation approach, we have obtained the following results:
Modelisation of AFM has been studied, based on which the modelfree control method has been tested and compared to the classical PID method. The simulation showed that the proposed method with iPID is better than the one with PID.
In practice, the modelfree control approach has been applied, with success, to control a piezoelectric actuator of AFM in LNE ("Laboratoire National de métrologie et d'Essais"), located at Trappes. Future experiments would be realized in Lille.
The collaboration with the MEC (Manufacturing Engineering
Center) of Cardiff University is established on AFM
probebased nano mechanical machining. Moreover, a nano
positioning system is now available at Arts et Metiers
ParisTech center of Lille, and we have begun to develop new
planning method by programming path planning trajectory on
this
(
x,
y)nano positioning system of
75
mrange of motion.
Contract with EDFCIH (Centre d'Ingénierie Hydraulique) to study control and estimation problems in hydroelectrical dams;
Contract with DIRIF (Direction Interdépartementale des Routes d'ÎledeFrance) to control the highway access problem.
Grant from GRAISyHM (Groupement de Recherche en Automatisation Intégrée et Systèmes HommeMachine, governmental Federation and Regional Council) on networked control (results connected with delay systems), with LAGIS and LAMIH (CNRSUVHC Valenciennes).
We are involved in several technical
groups of the GDR MACS (CNRS, "Modélisation, Analyse de
Conduite des Systèmes dynamiques", see
http://
Modelfree control: collaborations with Professor Brigitte D'AndréaNovel at Mines ParisTech and Professor Emmanuel Delaleau at ENIB.
Atomic Force Microscope (AFM): application of new algebraic methods in tapping mode for AFM, collaboration with the National Laboratory of Metrology (LNE) located at Trappes.
Thierry Floquet and Joachim Rudolph, from Saarland University (Germany), cosupervised a Master student in spring 2009. Since October 2009, they have been cosupervising a PhD student on the problem of fast identification and closedloop control for magnetic shaft.
Collaboration with Emmanuel Brousseau of Cardiff University for the project: "on nano mechanical machining of 3D nano structures by AFM".
Collaboration with Emilia Fridman (Tel Aviv University, Israel) and Joao Manoel Gomes da Silva (UFRGS, Porto Alegre, Brazil) on timedelay systems.
Cosupervision (French "cotutelle") of the PhD thesis of Kaouther Ibn Taarit with Mekki Ksouri, ENIT Tunis, Tunisia, on pseudospetra for delay identification.
Collaboration with Hong Sun (Whuan University, China) for cosupervising the PhD thesis of Lei Yu on Compressive sensing.
Collaborations with Guiseppe Fedele from University of Calabria, Italy, on "Modelfree control".
Programme Hubert Curien VOLUBILIS (Maroc, Integrated Action MA/09/211) between LAGIS (Université Lille1), ALIEN INRIA and Laboratory of Electronic, Information and Biotechnology of Department of Science at University Moulay Ismail of Meknès.
Michel Fliess is currently Associate Editor of Forum Mathematicumand Journal of Dynamical and Control Systems.
JeanPierre Richard is currently Associate Editor of Int. J. of Systems Science.
Mamadou Mboup is currently Managing Editor of African Diaspora Journal of Mathematics.
Thierry Floquet is currently Associate Editor of esta.
IFAC Technical Committees: The
members of ALIEN are participating to several technical
committees of the IFAC (International Federation of
Automatic Control, see the TC list on
http://
CIFA 2010: JeanPierre Richard is the president of international program committee and the chairman of session "emergent domains". Wilfrid Perruquetti is the chairman of session "hybrid dynamic systems". Michel Fliess, JeanPierre Barbot, Mamadou Mboup, Lotfi Belkoura and Thierry Floquet are involved in the international program committee.
JeanPierre Richard was in the International Program Committee of several IEEE and IFAC conferences: IEEE International Conference on Communications, 2011; IEEE International Workshop Towards Smart Communications and Network technologies applied on Autonomous Systems, 2010; IFAC Workshop on Distributed Estimation and Control of Networked Systems, 2010; IEEE Mediterranean Conference on Control and Automation, 2010; IFAC Symposium on System Structure and Control, 2010;
JeanPierre Barbot was in the committee of IEEE International Workshop on Variable Structure Systems, 2010.
Mamadou Mboup was in the committee of IEEE International Workshop on Machine Learning for Signal Processing, 2010, and in committee of IEEE International Telecommunication Symposium, 2010.
Gang Zheng was in the committee of IEEE International Conference on Intelligent Control and Information Processing, 2010.
JeanPierre Richard is president of the GRAISyHM, federation from the French government. He is an expert for the evaluation of projects submitted to ANR, CNRS, DGRI and AERES, and heading the 3rd year professional training "Research" of the École Centrale de Lille.
Wilfrid Perruquetti is an expert for the evaluation of ANR program Blanc SIMI (20092010). From 2010, he is the scientific head of this ANR program.
Mamadou Mboup is heading the group SYSCOM  CReSTIC, University of Reims ChampagneArdenne.
Lotfi Belkoura is heading the Master
"AG2i: Automatique, Génie Informatique et Image",
University of Lille 1 and École Centrale de Lille. This
Master, after a national evaluation (A), is presently
"SMaRT: Systèmes, Machines autonomes et Réseaux de
Terrain" (see
http://
Thierry Floquet is an expert for the evaluation of projects submitted to Israel Science Foundation.
The team members are also involved in numerous examination committees of theses and Habilitations, in France and abroad.
From February to July 2010, Mamadou Mboup was Guest Professor at Saarland University, InnoLecture program, Germany.
From June to July 2010, Stéphane Thiery was at Cardiff University, UnitedKingdom.
Yuri Orlov, Research director at CISES, Ensenada, Mexico, June 2010, invited by École Centrale de Lille.
Emilia Fridman, Professor, Tel Aviv University, Israel, June 2010, invited by École Centrale de Lille.
IEEE Conférence Internationale Francophone d'Automatique, Nancy, France, June 0204, 2010. (Most members of ALIEN).
IEEE, IET International Symposium on Communication Systems, Networks and Digital Signal Processing, Newcastle, UnitedKingdom, July 2123, 2010. (JeanPierre Barbot, Gang Zheng).
IEEE International Workshop on Variable Structure Systems, Mexico City, Mexico, June 2628, 2010. (JeanPierre Barbot, Wilfrid Perruquetti).
IFAC Symposium on Nonlinear Control Systems, Bologna, Italy, September 0103, 2010. (Michel Fliess, JeanPierre Barbot, Thierry Floquet).
IFAC Symposium on System, Structure and Control, Ancona, Italy, September 1517, 2010. (Michel Fliess).
IEEE Conference on Decision and Control, Atlanta, USA, December 1517, 2010. (JeanPierre Barbot).
IFAC Workshop on Time Delay Systems, Prague, Czech Republic, June 79, 2010. (Lotfi Belkoura).
JeanPierre Richard was a guest lecturer and presented surveys on Time Delay Systems and Networked Control Systems: in Besançon, by the GDR DYCOEC: A delay, what does it change? Seminar of the GDR DYCOEC, FEMTO LAB Besançon, France, 9 November 2010; and in Tunis, by ENSI and ENIT: Contrôle à travers le réseau : questions générales, résultats récents, Seminar ENSIENIT, École Nat. des Sciences de d'Informatique, École Nat. d'Ingénieurs de Tunis, Tunisia, 10 February 2010.
The members of ALIEN are reviewers for most of the journal of the control and signal communities: IEEE Transactions on Automatic Control, IEEE Transactions on Systems and Control Technologies, IEEE Transactions on Industrial Electronics, IEEE Transactions on Signal Processing, Automatica, Systems & Control Letters, International Journal of Control, International Journal of Robust and Nonlinear Control, International Journal of Systems Science, Journal Européen des Systèmes Automatisés, IET Control Theory & Applications, Fuzzy Sets and Systems, Mathematics and Computers in Simulation, International Journal of Modeling and Simulation, Journal of the Franklin Institute, ...
Yang Tian, "Contribution on observation and estimation of linear systems", December 8, 2010.
Kaouther Ibn Taarit, "Contribution on identification of timedelay systems", December 17, 2010.
The members of the team teach at different level in universities and engineering schools and, in particular, at Master Thesis level:
Name  Course title  Level  Institution 
Barbot  Process Control  Master  Univ. Tlemcen, Algeria 
Fliess  Advanced control  Master  École polytechnique, Tunis 
Gibaru  Applied Mathematics  Master  USTLUVHCULCO 
Mboup  Advanced Signal Processing  Master  Univ.Paris 5, ENITTunis 
Perruquetti  Nonlinear control  SMART  EC Lille  USTL 
Richard  Mathematical tools for nonlinear systems  Master AG2i  EC Lille  USTL 
Richard  Dynamical systems  Research training  EC Lille 
Belkoura  An introduction to distributions  Master AG2i  EC Lille  USTL 
JeanPierre Richard is in charge of
the professional training "Research" of École Centrale de
Lille since 2003 (training for lastyear students of EC
Lille who are preparing a research career). (
http://
Lotfi Belkoura is in charge of the SMART Master Thesis training in control of University of Lille 1 and École Centrale de Lille.
JeanPierre Barbot is in charge of the Master Thesis training in control of the University of Tlemcen, Algeria.