The project-team is particularly active in the following areas:

classical theory of dynamical systems

optimal deterministic, stochastic and robust control

failure detection in dynamical systems (both passive and active)

network control and monitoring for transportation systems

hybrid systems, in particular the development of Scicos

maxplus linear systems: applications to transportation systems

numerical matrix algebra and implementation in Scilab

The objectives of the project-team are the design, analysis and development of new methods and algorithms for detection, identification, simulation and control of dynamical systems and their software implementations.

These methods and algorithms are usually implemented in Scilab which is an open-source scientific software package originally developed in the project-team. This task has been facilitated thanks to the creation of the new development project-team SCILAB which has taken over the engineering tasks such as maintenance, porting, testing, etc.

The project-team is actively involved in the development of control, signal processing, optimization and simulation tools in Scilab, in particular Scicos, a modeler and simulator for dynamical systems which is based on research on hybrid systems. Encouraged by the interest in Scicos, expressed both by the academia and industry, developing a robust user-friendly Scicos has become an important objective of the project-team. A lot of effort is put on the development of Scicos within the project-team.

As theory and applications enrich mutually, many of the objectives of the project-team can be seen through the applications:

modeling and simulation of physical systems (mechanical, electrical, fluids, thermodynamics,...) based on the theory of implicit systems

modeling, simulation and code generation of control systems based on the theory of hybrid systems

modeling, analysis and control of transportation systems using the maxplus algebra

using robust control theory, and finite element models for identification purposes in the framework of failure detection and default localization for space systems, civil structures and other dynamical systems.

Systems, control and signal processing constitute the main foundations of the research work of the project-team. We have been particularly interested in numerical and algorithmic aspects. This research which has been the driving force behind the creation of Scilab has nourished this software over the years thanks to which, today, Scilab contains most of the modern tools in control and signal processing. Scilab has been a vehicle by which theoretical results of the project-team concerning areas such as classical, modern and robust control, signal processing and optimization, have been made available to industry and academia.

Ties between this fundamental research and Scilab are very strong. Indeed, even the design of the software itself, elementary functions and data structures are heavily influenced by the results of this research. For example, even elementary operations such as basic manipulation of polynomial fractions have been implemented using a generalization of the the state-space theory developed as part of our research on implicit systems. These ties are of course normal since Scilab has been primarily developed for applications in automatics.

Scilab has created for our research team new contacts with engineers in industry and other research groups. Being used in real applications, it has provided a guide for choosing new research directions. For example, robust control tools in Scilab have been developed in cooperation with industrial users. Similarly, Scilab's LMI toolbox has been developed with the help of other research groups. It should also be noted that most of the basic systems and control functions in Scilab are based on algorithms developed in the European research project Slicot in which METALAU has taken part.

Implicit systems are a natural framework for modeling physical phenomena. We work on theoretical and practical problems associated with such systems in particular in applications such as failure detection and dynamical system modeling and simulation.

Constructing complex models of dynamical systems by interconnecting elementary components leads very often to implicit systems. An implicit dynamical system is one where the equations representing the behavior of the system are of the algebraic-differential type. If represent the ``state'' of the system, an implicit system is often described as follows:

where
is the time derivative of
,
tis the time and the vector
zcontains the external variables (inputs and outputs) of the system. Indeed it is an important property of implicit systems that outside variables interacting with the system need not be characterized a priori as inputs or outputs, as it is the case with explicit
dynamical systems. For example if we model a capacitor in an electrical circuit as a dynamical system, it would not be possible to label a-priori the external variables, in this case the currents and voltages associated with the capacitor, as inputs and outputs. The physical laws governing
the capacitor simply impose dynamical constraints on these variables. Depending on the configuration of the circuit, it is sometimes possible to specify some external variables as inputs and the rest as outputs (and thus make the system explicit) however in doing so system structure and
modularity is often lost. That is why, usually, even if an implicit system can be converted into an explicit system, it is more advantages to keep the implicit model.

It turns out that many of the methods developed for the analysis and synthesis of control systems modeled as explicit systems can be extended to implicit systems. In fact, in many cases, these methods are more naturally derived in this more general setting and allows for a deeper understanding of the existing theory. In the past few years, we have studied a number of systems and control problems in the implicit framework.

For example in the linear discrete time case, we have revisited classical problems such as observer design, Kalman filtering, residual generation to extend them to the implicit case or have used techniques from implicit system theory to derive more direct and efficient design methods. Another area where implicit system theory has been used is failure detection. In particular in the mutli-model approach where implicit systems arise naturally from combining multiple explicit models.

We have also done work on nonlinear implicit systems. For example nonlinear implicit system theory has been used to develop a predictive control system and a novel nonlinear observer design methodology. Research on nonlinear implicit systems continues in particular because of the development of the ``implicit'' version of Scicos.

Failure detection has been the subject of many studies in the past. Most of these works are concerned with the problem of
*passive failure detection*. In the passive approach, for material or security reasons, the detector has no way of acting upon the system; the detector can only monitor the inputs and the outputs of the system and then decides whether, and if possible what kind of, a failure has
occurred. This is done by comparing the measured input-output behavior of the system with the ``normal'' behavior of the system. The passive approach is often used to continuously monitor the system although it can also be used to make periodic checks.

In some situations however failures can be masked by the operation of the system. This often happens in controlled systems. The reason for this is that the purpose of controllers, in general, is to keep the system at some equilibrium point even if the behavior of the system changes. This robustness property, desired in control systems, tends to mask abnormal behaviors of the systems. This makes the task of failure detection difficult. An example of this effect is the well known fact that it is harder for a driver to detect an under-inflated or flat front tire in a car which is equipped with power steering. This tradeoff between detection performance and controller robustness has been noted in the literature and has lead to the study of the integrated design of controller and detector.

But the problem of failures being masked by system operation is not limited to controlled systems. Some failures may simply remain hidden under certain operating conditions and show up only under special circumstances. For example, a failure in the brake system of a truck is very difficult to detect as long as the truck is cruising down the road on level ground. It is for this reason that on many roads, just before steep downhill stretches, there are signs asking truck drivers to test their brakes. A driver who ignores these signs would find out about a brake failure only when he needs to brake going down hill, i.e., too late.

An alternative to passive detection which could avoid the problem of failures being masked by system operation is
*active detection*. The active approach to failure detection consists in acting upon the system on a periodic basis or at critical times using a test signal in order to detect abnormal behaviors which would otherwise remain undetected during normal operation. The detector in an active
approach can act either by taking over the usual inputs of the system or through a special input channel. An example of using the existing input channels is testing the brakes by stepping on the brake pedal.

The active detection problem has been less studied than the passive detection problem. The idea of injecting a signal into the system for identification purposes has been widely used. But the use of extra input signals in the context of failure detection has only been recently introduced.

The specificity of our approach for solving the problem of auxiliary signal design is that we have adopted a deterministic point of view in which we model uncertainty using newly developed techniques from
control theory. In doing so, we can deal efficiently with the robustness issue which is in general not properly dealt with in stochastic approaches to this problem. This has allowed us in particular to introduce the notion of
*guaranteed failure detection*.

In the active failure detection method considered an auxiliary signal
vis injected into the system to facilitate detection; it can be part or all of the system inputs. The signal
udenotes the remaining inputs measured on-line just as the outputs
yare measured online. In some applications the time trajectory of
umay be known in advance but in general the information regarding
uis obtained through sensor data in the same way that it is done for the output
y.

Suppose we have only one possible type of failure. Then we have two sets of input-output behaviors to consider and hence two models. The set
is the set of normal input-outputs
{
u,
y}from Model 0 and the set
is the set of input-outputs when failure occurs. That is,
is from Model 1. These sets represent possible/likely input-output trajectories for each model. Note that Model 0 and Model 1 can differ greatly in size and complexity but they have in common
uand
y.

The problem of auxiliary signal design for guaranteed failure detection is to find a ``reasonable''
vsuch that

That is, any observed pair
{
u,
y}must come only from one of the two models. Here reasonable
vmeans a
vthat does not perturb the normal operation of the system too much during the test period. This means, in general, a
vof small energy applied over a short test period. However, depending on the application, ``reasonable" can imply more complicated criteria.

Depending on how uncertainties are accounted for in the models, the mathematics needed to solve the problem can be very different. For example guaranteed failure detection has been first introduced in the case where unknown bounded parameters were used to model uncertainties. This lead to solution techniques based on linear programming algorithms. But in most of our works, we consider the types of uncertainties used in robust control theory. This has allowed us to develop a methodology based on established tools such as Riccati equations that allow us to handle very large multivariable systems. The methodology we develop for the construction of the optimal auxiliary signal and its associated test can be implemented easily in computational environments such as Scilab. Moreover, the online detection test that we obtain is similar to some existing tests based on Kalman filters and is easy to implement in real-time. The results of our research can be found in a book published in 2004.

We consider mechanical systems with the corresponding stochastic state-space models of automatic control.

The mechanical system is assumed to be a time-invariant linear dynamical system:

where the variables are :
: displacements of the degrees of freedom,
M,
C,
K: mass, damping, stiffness matrices,
t: continuous time;
: vector of external (non measured) forces modeled as a non-stationary white noise;
L: observation matrix giving the observation
Y(corresponding to the locations of the sensors on the structure).

The modal characteristics are: the vibration modes or eigen-frequencies and the modal shapes or eigenvectors. They satisfy:

By stacking
Zand
and sampling at rate
1/
, i.e.,

we get the following equivalent state-space model:

with

The mechanical systems under consideration are vibrating structures and the numerical simulation is done by the finite element model.

The objectives are the analysis and the implementation of statistical model-based algorithms, for modal identification, monitoring and (modal and physical) diagnosis of such structures.

For modal analysis and monitoring, the approach is based on subspace methods using the covariances of the observations: that means that all the algorithms are designed for in-operation situation, i.e., without any measurement or control on the input (the situation where both input and output are measured is a simple special case).

The identification procedure is realized on the healthy structure.

The second part of the work is to determine, given new data after an operating period with the structure, if some changes have occurred on the modal characteristics.

In case there are changes, we want to find the most likely localization of the defaults on the structure. For this purpose we have to do the matching of the identified modal characteristics of the healthy structure with those of the finite element model. By use of the different Jacobian matrices and clustering algorithms we try to get clusters on the elements with the corresponding value of the "default criterion".

This work is done in collaboration with the INRIA-IRISA project-team SISTHEM (see the web-site of this project-team for a complete presentation and bibliography) and with the project-team MACS for the physical diagnosis (on civil structures).

Originally motivated by problems encountered in modeling and simulation of failure detection systems, the objective of this research is the development of a solid formalism for efficient modeling of hybrid dynamical systems.

A hybrid dynamical system is obtained by the interconnection of continuous time, discrete time and event driven models. Such systems are common in most control system design problems where a continuous time model of the plant is hooked up to a discrete time digital controller.

The formalism we develop here tries to extend methodologies from Synchronous languages to the hybrid context. Motivated by the work on the extension of Signal language to continuous time, we develop a formalism in which through a generalization of the notion of event to what we call
*activation signal*, continuous time activations and event triggered activations can co-exist and interact harmoniously. This means in particular that standard operations on events such as subsampling and conditioning are also extended and operate on activation signals in general
paving the way for a uniform theory.

The theoretical formalism developed here is the backbone of the modeling and simulation software Scicos. Scicos is the place where the theory is implemented, tested and validated. But Scicos has become more than just an experimental tool for testing the theory. Scicos has been successfully used in a number of industrial projects and has shown to be a valuable tool for modeling and simulation of dynamical systems.

Encouraged by the interest in Scicos, expressed both by the academia and industry, beyond the theoretical studies necessary to ensure that the bases of the tool are solid, the project-team has started to invest considerable effort on improving its usability for real world applications. Developing a robust user-friendly Scicos has become one of the objectives of the project-team.

In the modeling of human activities, in contrast to natural phenomena, quite frequently only the operations max (respectively min) and +are needed (this is the case in particular of some queuing or storage systems, synchronized processes encountered in manufacturing, traffic systems, when optimizing deterministic dynamic processes, etc.).

The set of real numbers endowed with the operation max (respectively min) denoted
and the operation
+denoted
is a nice mathematical structure that we may call an idempotent semi-field. The operation
is idempotent and has the neutral element
= -
but it is not invertible. The operation
has its usual properties and is distributive with respect to
. Based on this set of scalars we can build the counterpart of a module and write the general
(
n,
n)system of linear maxplus equations:

A
x
b
C
x
d

using matrix notation where we have made the natural substitution of for +and of for ×in the definition of the matrix product.

A complete theory of such linear system is still not completely achieved. In recent development we try to have a better understanding of image and kernel of maxplus matrices.

System theory is concerned with the input (
u)-output (
y) relation of a dynamical system (
) denoted
y=
S(
u)and by the improvement of this input-output relation (based on some engineering criterium) by altering the system through a feedback control law
u=
F(
y,
v). Then the new input (
v)-output (
y) relation is defined implicitly by
y=
S(
F(
y,
v)). Not surprisingly, system theory is well developed in the particular case of linear shift-invariant systems. Similarly, a min-plus version of this theory can also be developed.

In the case of SISO (single-input-single-output) systems,
uand
yare functions of time. In the particular case of a shift-invariant linear system,
Sbecomes an inf-convolution:

where
his a function of time called the impulse response of system
. Therefore such a system is completely defined by its impulse response. Elementary systems are combined by arranging them in parallel, series and feedback. These three engineering operations correspond to adding systems pointwise (
), making inf-convolutions (
) and solving special linear equations (
y=
h(
f_{1}yf_{2}v)) over the set of impulse responses. Mathematically we have to study the algebra of functions endowed with the two operations
and
and to solve special classes of linear equations in this set.

An important class of shift-invariant min-plus linear systems is the process of counting events versus time in timed event graphs (a subclass of Petri nets frequently used to represent manufacturing systems). A dual theory based on the maxplus algebra allows the timing of events identified by their numbering.

The Fourier and Laplace transforms are important tools in automatic control and signal processing because the exponentials diagonalize simultaneously all the convolution operators. The convolutions are converted into multiplications by the Fourier transform. The Fenchel transform ( ) defined by:

plays the same role in the min-plus algebra context. The affine functions diagonalize the inf-convolution operators and we have:

A general inf-convolution is an operation too complicated to be used in practice since it involves an infinite number of operations. We have to restrict ourselves to convolutions that can be computed with finite memory. We would like that there exists a finite state
xrepresenting the memory necessary to compute the convolution recursively. In the discrete-time case, given some
h, we have to find
(
C,
A,
B)such that
h_{n}=
CA^{n}B, and
is then `realized' as

x
_{n+ 1}
A
x
_{
n
}
B
u
_{
n
}
y
_{
n
}
C
x
_{
n
}

SISO systems (with increasing h) which are realizable in the min-plus algebra are characterized by the existence of some
and
csuch that for
nlarge enough:

h
_{n+
c}
c
h
_{
n
}

If
hsatisfies this property, it is easy to find a 3-tuple
(
A,
B,
C).

This beautiful theory is difficult to be applied because the class of linear systems is not large enough for realistic applications. Generalization to nonlinear maxplus system able to model general Petri nets is under development.

Dynamic Programming in the discrete state and time case amounts to finding the shortest path in a graph. If we denote generically by
nthe number of arcs of paths, the dynamic programming equation can be written linearly in the min-plus algebra:

X
_{
n
}
A
X
_{n-1}

where the entries of
Aare the lengths of the arcs of the graph and
X_{n}denotes the matrix of the shortest lengths of paths with
n arcs joining any pair of nodes. We can consider normalized matrices defined by the fact that the infimum in each row is equal to 0. Such kind of matrices can be viewed as the min-plus counterpart of transition matrices of a Markov chain.

The problem

may be called dynamic programming with independent instantaneous costs (
depends only on
uand not on
x). Clearly
vsatisfies the linear min-plus equation:

(the Hamilton-Jacobi equation is a continuous version of this problem).

The Cramer transform ( ), where denotes the Laplace transform, maps probability measures to convex functions and transform convolutions into inf-convolutions:

Therefore it converts the problem of adding independent random variables into a dynamic programming problem with independent costs. These remarks suggest the existence of a formalism analogous to probability calculus adapted to optimization that we have developed.

The theoretical research in this domain is currently done in the MAXPLUS project-team. In the METALAU project-team we are more concerned with applications to traffic systems of this theory.

Traffic modeling is a domain where maxplus algebra appears naturally : – at microscopic level where we follow the vehicles in a network of streets, – at macroscopic level where assignment are based on computing smallest length paths in a graph, – in the algebraic duality between stochastic and deterministic assignments.

We develop free computing tools and models of traffic implementing our experience on optimization and discrete event system modeling based on maxplus algebra.

Let us consider a circular road with places occupied or not by a car symbolized by a 1. The dynamic is defined by the rule
10
01that we apply simultaneously to all the parts of the word
mrepresenting the system. For example, starting with
m_{1}= 1010100101we obtain the sequence of works
(
m
_{i}):

For such a system we can call density
dthe number of cars divided by the number of places called
pthat is
d=
n/
p. We call flow
f(
t)at time
tthe number of cars at this time period divided by the place number. The fundamental traffic law gives the relation between
f(
t)and
d.

If the density is smaller than
1/2, after a transient period of time all the cars are separated and can go without interaction with the other cars. Then
f(
t) =
n/
pthat can be written as function of the density as
f(
t) =
d

On the other hand if the density is larger than
1/2, all the free places are separated after a finite amount of time and go backward freely. Then we have
p-
ncar which can go forward. Then the relation between flow and density becomes

f
t
p
n
p
d

This can be stated formally: it exists a time
Tsuch that for all
tT,
f(
t)stays equal to a constant that we call
fwith

The fundamental traffic law linking the density of vehicles and the flow of vehicles can be also derived easily from maxplus modeling : – in the deterministic case by computing the eigenvalue of a maxplus matrix, – in the stochastic case by computing a Lyapounov exponent of stochastic maxplus matrices.

The main research consists in developing extensions to systems of roads with crossings. In this case, we leave maxplus linear modeling and have to study more general dynamical systems. Nevertheless these systems can still be defined in matrix form using standard and maxplus linear algebra simultaneously.

With this point of view efficient microscopic traffic simulator can be developed in Scilab.

Given a transportation network
and a set
of transportation demands from an origin
to a destination
, the
*traffic assignment*problem consists in determining the flows
f_{a}on the arcs
of the network when the times
t_{a}spent on the arcs
aare given functions of the flows
f_{a}.

We can distinguish the deterministic case — when all the travel times are known by the users — from the stochastic cases — when the users perceive travel times different from the actual ones.

When the travel times are deterministic and do not depend on the link flows, the assignment can be reduced to compute the routes with shortest travel times for each origin-destination pair.

When the travel times are deterministic and depend on the link flows, Wardrop equilibriums are defined and computed by iterative methods based on the previous case.

When the perceived travel times do not depend on the link flows but are stochastic with error distribution — between the perceived time and the actual time — satisfying a Gumbel distribution, the probability that a user choose a particular route can be computed explicitly. This probability has a Gibbs distribution called logit in transportation literature. From this distribution the arc flows — supposed to be deterministic — can be computed using a matrix calculus which can be seen as the counterpart of the shortest path computation (of the case 1) up to the substitution of the minplus semiring by the Gibbs-Maslov semiring, where we call Gibbs-Maslov semiring the set of real numbers endowed with the following two operations :

When the perceived travel times are stochastic and depend on the link flows — supposed to be deterministic quantities — stochastic equilibriums are defined and can be computed using iterative methods based on the logit assignments discussed in the case 3.

The purpose of this research is double :

To study an engineering example of quantization. By quantization we mean the application of a morphism changing a deterministic optimization problem into a linear system of equations for modeling improvement by analogy with the way we obtain the Quantum Mechanics Equation from the Hamilton-Jacobi Equation of a system. This quantization can be seen as an application of what we have called previously ``the duality between probability and optimization'' introduced in the section

To develop a toolbox in Scilab dedicated to traffic assignment indeed it does not exist any free toolbox for this kind of application.

We have used the techniques developed for modal analysis and diagnosis in many different applications: rotating machines, aircrafts, parts of cars, space launcher, civil structures. The most recent examples are:

Eureka (FLITE) project: exploitation of flight test data under natural excitation conditions.

Ariane 5 launcher: application to a ground experiment (contract with CNES and EADS Space Transportation)

Steelquake: a European benchmark for a civil structure.

Scilab scientific software package (open source software available from Scilab)

Scicos object oriented modeler, simulator and code generator included in Scilab ( Scicos)

CiudadSim Scilab Traffic Assignment toolboxes

COSMAD Output modal analysis and diagnosis

MAXPLUS Maxplus arithmetic and linear systems toolbox by the Maxplus Working Group

SLICOT Interface with SLICOT library for computations in systems and control theory

LIPSOL Linear-programming Interior-Point SOlvers for Scilab

FSQP Interface Scilab-FSQP optimization tool

CUTEr testing environment for optimization and linear algebra solvers

LMI optimization for robust control applications (included in Scilab)

The above software packages are all available freely from Scilab.

Implicit Scicos: new extension of Scicos for modeling more naturally physical systems based on Modelica language

Digiplant extension of Greenlab with new modeling techniques

The development of Scicos continues. This work is financed mainly through the RNTL projects Simpa, Eclipse and Metisse. A new more efficient compiler has been developed. This work was done by C. Bourcier, an intern supported through the Eclipse project in collaboration with the AOSTE project team.

The extension of Scicos to allow for ``implicit blocks'' in the framework of the RNTL Simpa project has been pursued. It is now possible to define implicit blocks in Scicos using (a subset) of Modelica language. This new extension is being tested using application examples from EDF.

In the context of the Metisse project, work has been done to allow the import of Amesim diagrams into Scicos. Closer integration between Scilab/Scicos and Amesim is being considered.

Scilab code generator has been extended and can now accept continuous-time blocks. The stand-alone usage of the generated code however requires the implementation of a fixed step size solver which is not yet available. This latter is also needed in the context of the Eclipse project and in particular the test examples from PSA.

A book on modeling and simulation in the Scilab/Scicos environment has been published. This book contains a complete documentation for Scicos.

Metalau project continues to support the development of Scilab through both fundamental research and specific developments. The team has been working on defining the future extensions of the Scilab language and their implementations. These extensions which must be in line with applications in sytems and control, will be developed to facilitate the use of Scilab. These extensions include in particular new types of objects.

The work on the development of Matlab compatible mexfiles utilities has been pursued and is now pratically complete. This utility facilitates the work of the Matlab-Scilab translator which is being developed by the Scilab project team. The main purpose of this utility however is to make possible simultaneous development of toolboxes for Matlab and Scilab. To make these mexfiles operational in Scilab a number of new functionalities have been added to Scilab kernel, in particular those concerning the cells and structure objects. These objects can now be manipulated in Scilab similarly to Matlab.

The Metalau project continues to support and maintain the toolboxes it has developed in the past: LMITOOL, control, signal processing, etc.

We develop a novel theory of robust active failure detection based on multi-model formulation of failures. The results of years of research have been published in a book in 2004.

We have continued also to work on the extension of our approach to more general situations. We started the study of active failure detection in continuous-time dynamical systems with sampled observations and obtained some interesting results last year. We have pursued this work and we now have a complete and efficient solution which is a subject of a journal paper accpeted for publication.

We have also examined numerical aspects of the implementation of our technique. This work is done in close collaboration with a PhD student of S.L. Campbell at NCSU.

A comprehensive and consistent methodology in terms of covariance driven subspace for identification and modal detection of changes in case of output only measurement leading to a Scilab toolbox COSMAD has been developed. This toolbox is currently in an industrial evaluation process at EADS Space Launchers and CNES.

Significant results obtained for the physical diagnosis and defect isolation. The COSMAD toolbox includes a prototype version for this purpose.

The work on maxplus algebra has been continued this year on three directions.

Scilab Maxplus toolbox has been upgraded to work with scilab 3.1.1 on Apple MacOSX and on Windows with the microsoft compiler. For MacOSX, the dynamic linking with Fortran interface containing common being not available, a version of Scilab including the maxplus toolbox has been done and is available at Maxplus.org. A presentation of the toolbox has been given during a Scilab course at Blida.

The study of the different characterizations of the regular maxplus matrices (matrices
Asuch that it exists
A^{g}satisfying
AA^{g}A=
A) has been continued by the writing an article containing geometric, combinatorial and order characterizations. A preliminary version of this article is now written.

An attempt is currently done to develop a maxplus differential calculus based on separation theorem developed previously.

Some articles , , written previously has appeared this year.

The work done in 2004 on numerical solution of dynamic programming equation in incomplete observation has been presented in the colloquium in the honor of P. Bernhard (Avril 2005).

The interface of the scilab toolbox dedicated to traffic assignment (CiudadSim) has been rewritten to work with the new scilab graph editor. CiudadSim for scilab 3.1.1 is now available on the web.

An article on the link beetween stochastic traffic assignment and maxplus algebra has appeared.

The thesis of N. Farhi is dedicated to maxplus modeling of traffic. The fundamental traffic law giving the relation between the average flow and the density of vehicles is studied in different cases. The case of a circular road with stochastic speeds studied previously has appeared in . The result obtained in case of two circular roads with a crossing has is now available in but the mathematical justification of the existence of an average flow observed empirically is in progress but is still not completed. The case of two circular roads has been also studied numerically. The numerical study show the existence of different phases interesting to analyze.

A new problem has been also studied par N. Farhi concerning the optimization of traffic light in the case of two modes (bus and cars) using a distributed standard linear model. The aim is to improve the bus traffic. This work has been achieved during an internship at INRETS of N. Farhi. A report on this work will be soon available.

The cooperation on this subject, organized by E. Rofman, with P. Lotito and E. Mancinelli, who has returned now in Argentina, continue on the ciudadsim toolbox. Contact to apply these techniques in Argentina has been established by E. Rofman.

A work making the link between the stochastic modeling of plant used in Greenlab and branching processes has started. Indeed it is useful to study tree populations according to the GreenLab model, in the stochastic case (for example when stochastic number of buds appearing at each cycle) for agronomical reasons. Up to now, in this situation, formulae has been derived for computing the mean and correlation between the number of organs but the distribution is only computed approximatively. In this new work, using the theory of branching processes, we derive the generating function of the distribution law of the organ numbers. Routines in Matlab and Scilab have be written to compute these generating function. A report is in preparation on this subject.

Eureka (FLITE2) project: exploitation of flight test data under natural excitation conditions (Dassault Aviation, Airbus France and SOPEMEA are the French industrial partners)

RNTL Project SIMPA2. Main objective: development of a complete, Open Source, Modelica compiler and its integration in Scilab/Scicos (labelling in November 2005).

RNTL Project ECLIPSE. Objective: provide Scicos with real-time multiprocessor code generation capabilities through an interface with the SynDEx software. Examples from PSA.

RNTL Project METISSE. Objective: provide Scicos with the capability to import models constructed using the software AmeSim. Partner : the company Imagine.

ACI Constructif: the ACI is leaded by the project-team SISTHEM and the partners are the project-team MACS, the MSSMat laboratory from ECP and the LCPC.

F. Delebecque, M. Goursat, R. Nikoukhah, J.-P. Quadrat, S. Steer.

Organization of a Scilab Workshop at the University of Blida (Algeria). The attendees of this workshop were 30 teachers from different universities of the country. This workshop (12-17 November 2005) was funded by the European and International Affairs Department of our institute and the Blida Saad Dahlab University.

F. Delebecque, M. Goursat, R. Nikoukhah

Organization of a Scilab-Scicos session at IEEE- Conference on Control Applications Toronto, Canada (August 2005).

R. Nikoukhah, S. Steer

ITEA europeen project GENE-AUTO. Main objective: specification and development of an automatic software code generation for real-time embedded systems (labeling in December 2005)

Serge Steer: ``Elements de comparaison de Scilab/Scicos et Matlab/Simulink'', Journées Scilab/Scicos SNECMA, April 2005.

Serge Steer: ``Scilab : un enjeu pour le calcul scientifique'', Journée ingénieurs de développement, INRIA, April 2005.

Serge Steer: ``Présentation de Scicos et Scicos Implicite'', Siemens VDO, April 2005.

Serge Steer: ``Eléments de comparaison de Scilab/Scicos et Matlab/Simulink'', Journées Scilab IFP, June 2005.

Serge Steer: ``Scicos : modélisation et simulation de systèmes dynamiques'', Journées Scilab IFP, June 2005.

University of Rosario (Argentina): on optimal control problems and application with the research team of R. Gonzales under the coordination of E. Rofman.

North Carolina State University (USA): on failure detection and numerical solution of hybrid DAEs under the coordination of R. Nikoukhah.

ENPC Cermics: on maxplus algebra under the coordination of G. Cohen, and on future of Scilab with J. Ph. Chancelier.

R. Nikoukhah.

- Member of the International Program Committee of the Meditteranean Control and Automation Conference 2004 and 2005.

- Member of IFAC Technical Committee on Fault Detection, Supervision and Safety in Technical Processes (SAFEPROCESS TC).

- Member of International Program Committee for SAFEPROCESS 2006.

- Senior Member of IEEE.

F. Delebecque

- Member of the French national board of ``Agrégation de Mathématique''.

R. Nikoukhah

- Ensta: Systems and Control, 2nd year, Dynamic Programming, 3rd year.

- Pulv: Systems and Control, fifth year, Stochastic processes, forth year.

J.P. Quadrat

- Paris 1 : Introduction to optimal stochastic control: DEA.

F. Delebecque

- Ensta: Systems and Control, 2nd year.

- Essi: Financial Math, DESS.

M. Najafi, supervised by R. Nikoukhah.

A. Azil, supervised by R. Nikoukhah.

N. Farhi, supervised by J.P. Quadrat and M. Goursat.