The goal of this project is to develop and promote methods for automatic control, in particular for modelling and analysis of complex controlled systems. The main application fields are Health, with diagnosis in cardiology and ovulation control, and Automobile, with low-emission vehicles. The project is being reorganized: a new project is in preparation, based on the following present themes.
Research themes
Mathematical modelling, identification and control of:
Nonlinear systems with hysteresis or delays. Applications include control of friction-intensive mechanical systems and cardiac mechanics.
Reaction-diffusion systems with applications in automobile-emission reduction and cardiac electrophysiology.
Hybrid dynamical systems with applications in Automobile (transmission systems) and Health (genetic regulatory networks).
Multiscale dynamical systems with applications in cardiac mechanics and ovulation control.
Model-based signal processing with applications in cardiological diagnosis.
LARY_CR is a software package dedicated to the study of cardiovascular and respiratory rhythms, developed in the SCILAB_SCICOS scientific environment
We pursued this year the study of the methods previously developed.
First, we proved a result on existence of polynomial solutions for LMIs depending continuously upon scalar parameters lying in a compact set. This result generalizes some partial results of the same type, which were based on analyticity.
Moreover, this offers e.g. a general framework to study systems stabilization by gain-scheduling, by nonconservative methods. Indeed, state-feedback stabilization of usual may be solved by a standard LMI. Consequently, the issue of state-feedback stabilization for parameter-dependent systems amounts to solve a parameter-dependent LMI. By use of the preceding result, no loss of generality is introduced if assuming that the solution of the latter is polynomial. As a consequence, we proved that, when the system depend polynomially upon the parameters, a countable family of LMIs of increasing precision may be constructed (indexed by the degree of the polynomial parameter-dependent solution), and whose solution provides parameter-dependent stabilizing gain.
Backstepping is one of the most popular synthesis techniques
for the nonlinear systems.
Among its many advantages, it provides large family of globally asymptotically stabilizing
control laws, permits to ensure a certain amount of robustness to the control
and to solve adaptative problems.
We began the generalization of this technique to delay systems. As an example, we look for stabilizing feedback fot the system
which has the particularity of not being locally exponentially stabilizable.
We have considered this year the
where
As is well-known, such systems possess poles which lie in a band centred on the imaginary axis and are more delicate to analyse than retarded delay systems which possess only finitely many poles in the right half-plane.
Here it has been possible to analyse precisely the asymptotic location of the poles of
Those results were then applied to discuss the stabilizability of such systems by finite-dimensional controllers or
controllers possessing a coprime factorization over
We are now considering the use of these stability conditions of neutral systems to evaluate the stabilizing properties of a PID for a dead-time
system
Another project running in this area is the robust stabilization of systems with multiple transmission delays.
This research focuses on data-based modelling of hybrid systems. More specifically, we consider the problem of reconstructing Piece-Wise Affine (PWA) systems from a finite number of noisy data.
A PWA functions is defined by the equations
where modes defined
by the pairs
where
Note that, for
The main difficulty of PWA regression, with respect to standard linear regression, is that the data points must be classified,
i.e. attributed to the mode that generated them. Since mode regions are unknown, this task cannot be decoupled from the problem of
estimating the model parameters.
An efficient algorithm for solving PWA regression problems has been proposed in
The main drawback of supervised clustering algorithms, like K-means, is that the number of clusters to be found must be specified a
priori. In PWA regression, this is equivalent to knowing the number
We conducted an experimental study in the identification of the electronic component placement process in pick-and-place machines. Pick-and-place machines are used to automatically place electronic components on printed circuit boards (PCBs), and form a key part of an automated PCB assembly line. A pick-and-place machine works as follows: the PCB is placed in the working area of the mounting head; the mounting head, carrying an electronic component (using, for instance, a vacuum pipette), is navigated to the position where the component should be placed on the PCB; the component is placed, released, and the process is repeated with the next component
We focus our attention on the subtask of the component placement on the PCB. Assuming that the mounting head, carrying the component, is in the right position above the PCB, the component is pushed down until it comes in contact with the PCB and then released. The PCB is not rigid, but, depending on the material, has certain elasticity properties. In order to study the placement process, an experimental setup was made at the TU Heindoven. It consists of the mounting head, from an actual pick-and-place machine, which is fixed above an impacting surface in contact with the ground via a spring. The chosen design of the impacting surface simulates the elasticity properties of the PCB as well as hard mechanical constraints due to saturations. It also account for realistic linear and dry friction phenomena.
Saturations, impacts and dry frictions introduce hybrid dynamics and the hybrid systems identification algorithm, discussed in section , has been applied.
The results demonstrate that the PWARX models are flexible enough to describe the dynamics of the experimental setup. Despite the fact that the models are optimized for one-step-ahead prediction their performance in simulation is satisfactory, which makes them adequate for computer simulation, model-based control synthesis, and verification. Physical insights about the experimental setup allow also to isolate specific model features that are not well reconstructed. This information may be used to design the targeted identification experiments where unsatisfactory modes are better excited in order to refine the results.
The interest in hybrid systems goes beyond their use for simulation. In fact, each class of hybrid models
provides a mathematical framework for addressing analysis and synthesis problems. Concerning analysis, a large stream of research
focused on the development of methods for verifying structural properties such as stability, controllability and observability
A fairly complete study of observability for Mixed Logic Dynamical (MLD) systems is reported in
The main drawback of these algorithms is that the region to be tested must be specified a priori. Therefore, if it contains a
large set of observable states and a small set of unobservable states such tests give a negative answer without revealing the
presence of the observable subregion. This problem is critical in view of the fact that the computational cost of trial-and-error
procedures for finding observable regions is usually prohibitive.
We focus on the automatic computation of the maximal observability region (i.e. the maximal set of observable
states) for an MLD systems. The rationale underlying our procedure can be summarized in the following steps.
First, we show that the set of states indistinguishable from a given state
The function of the circulation is to supply tissues with oxygen, nutrients and to remove carbon dioxide and other catabolits. Variables involved in cardiovascular regulation, such as blood flow, blood pressure level, oxygen blood concentration, are kept around their reference point by several feedback control mechanisms. These control mechanisms have different dynamics and we are interested only in the short term control of blood flow and pressure which is assumed by the autonomic nervous system through baroreceptor control loops. The aim of this research is to relate classical discrete-time cardiovascular signal analysis to models of the cardiovascular and control systems taking into account its multiple feedback loop organisation. Cardiovascular modelling leads us to the definition of several discrete-time feedback loop sensitivities of pratical interest and to an approach for the estimation of the classical blood-pressure/heart-beating-period baroreflex sensitivity.
Models of the electro-mechanical activity of the cardiac muscle are very useful at the scale of the cardiovascular system as well as at the organ scale. In this later case, they are used for computing stress, strain and action potential fields from three-dimensional image processing. We present a chemically-controlled constitutive law of cardiac myofibre mechanics devoted to be embedded into macroscopic models. This law ensues from the modelling of the collective behaviour of actin-myosin molecular motors converting chemical into mechanical energy. The resulting dynamics of sarcomeres is consistent with the ``sliding filament hypothesis'' of A. F. Huxley.
This work has been undertaken within the framework of the ARC ICEMA-2.
We use ideas originating from the kinetic equation theory to model, on the molecular scale, the controlled collective behaviour of actin-myosin nanomotors at the root of muscle contraction. The classical Huxley's model is recovered on the sarcomere scale by using moment equations. A controlled constitutive law on the tissue scale is obtained using the same type of scaling techniques. This multi-scale description of controlled muscle contraction may be useful in studying modelling and control problems associated to the heart considered as a multi-scaled system. The control viewpoint is useful in accounting for macroscopic properties (such as the Starling law or the Hill force-velocity relation) on lower scales and defining performance indexes of the electro-mechanical coupling on each scale.
This work has been undertaken within the framework of the ACI SCARAMOCO.
The function of the circulation is to supply tissues with oxygen, nutrients and to remove carbon dioxide and other catabolits. The organs involved in this function are: the lungs which allow gas exchanges, the heart which pumps blood and the vascular system which carries molecules to the tissues, see fig. ().
The regulation of these exchanges is under hemodynamic mechanisms, which tend to keep physiological variables around a control level; these
mechanisms have to adapt the cardiovascular system to changes (orthostatisme as well as exercise).
A strict homeostasis point of view reduces the complexity of the living systems regulation.
Variables involved in cardiovascular regulation, such as blood flow, blood pressure level,
oxygen blood concentration, are kept around their reference point by feedback control mechanisms.
These control mechanisms have different dynamics and we are interested only in the short term control, about a few minutes, of the
cardiovascular system, which is assumed by the nervous system, more precisely by its autonomic part (ANS)
Models of the electro-mechanical activity of the cardiac muscle are very useful at the scale of the cardiovascular system as well as at the organ scale. In this later case, they are used for computing stress, strain and action potential fields from three-dimensional image processing. We have developped a chemically-controlled constitutive law of cardiac myofibre mechanics devoted to be embedded into macroscopic models. This law ensues from the modelling of the collective behaviour of actin-myosin molecular motors converting chemical into mechanical energy. Here this model is embedded into a lumped parameter model of the heart and used into a simulator of the cardiovascular system.
A new model of vascular compartments is currently developped. Compared to classical Windkessel models, it will be able to take into account some nonlinear phenomena like the dependence of the Pulse Transit Time (PTT) upon the pressure. Model-based analysis of PTT and distal arterial pressure may be useful for the non-invasive determination of arterial wall properties.
The general framework of this study is mathematical modelling in cardiac electrophysiology.
Mathematical non-linear analysis methods are used to study the different response patterns of
a system of a coupled, normal cell and a pathological one, depolarized by an added steady current
We found three possible levels for the resting potential of the system, with complex multistability phenomena
between these levels. In the low level zone, we evidenced Unidirectional Block (UB) patterns in a window of
depolarization thresholds or above a unique threshold depending of the value of the coupling resistance.
Periodic branches of solutions emerge from the two Hopf bifurcation points corresponding to Ectopic Foci (EF)
patterns coexisting with medium or high levels of stationary solutions. In these zones, we found again UB
phenomena but, with locking of the system to a rhythmic solution, when the action potential propagates.
This study presents a system where we met, in a single framework, eigher UB or EF by only changing
Groups of cells evidencing UB phenomena, are then included in a ring-shaped, one-dimensional, system of cardiac fibers. We are thus able to study reentreis phenomena (movement), and complex fibrillation behaviors corresponding to their interplay with EF.
Time-frequency distributions, such as smoothed pseudo Wigner-Ville distribution (SPWVD), and complex demodulation (CDM), provide useful
time-varying spectral parameter estimators. However, each of these methods has limitations that a joint utilization could largely reduce,
due to their interesting complementary features. The aim of this research is to validate the joint SPWVD-CDM method on synthetic and real
cardiovascular time series with normal and reduced variability such as in autonomic blockade or autonomic deficiency
Collaboration with the LIGE
Purpose. To examine if differences in heart rate variability (HRV) could distinguish sub- from supra-ventilatory-threshold exercise and whether the
exercise duration at supra-threshold intensity alters the cardio- respiratory synchronization.
Methods. Beat-to-beat RR interval, VO2, VCO2, VE and blood lactate concentration of eleven healthy well-trained pubertal subjects were
collected during two exercise bouts: 1) Moderate : fifteen minutes performed below the power at ventilatory threshold (pVT). 2) Heavy : above
pVT until exhaustion. Fast Fourier Transform, Smoothed Pseudo Wigner-Ville Distribution and Complex Demodulation were applied to RR time series.
Results. 1) Moderate exercise shows a prevalence of the LF spectral energy compared to the HF one (80
Conclusion. 1) heart rate variability (HRV) allows to distinguish sub- from supra-ventilatory-threshold exercise 2) exercise duration at supra-
threshold intensity does not alter the cardio-respiratory synchronization as evidenced by constant CR phase
Collaboration with the LIGE.
At the onset of a moderate aerobic exercise (i.e. under the
ventilatory anaerobic threshold - VAT), VO2 rises mono-exponentially until a VO2 steady
state is reached. Instead, if work rate is likely to elicit a submaximal
VO2 above VAT, VO2 first rises mono-exponentially during a phase (fast
component - FC) and then increases more progressively (slow component - SC)
until VO2max is reached or exhaustion occurs. Height men performed a cycle
ergometer exercise at the work rate corresponding to the midway between
pVAT and pVO2max (Pdelta50). RR kinetics was fitted by a bi-exponential
decreasing regression model and VO2 kinetics by a bi-exponential increasing
regression model with or without time delay (TD) for the SC. Adding the
delay did not improve VO2 data fit. The FC time constant of RR kinetics was
significantly lower than that of VO2 kinetics (22.2
Collaboration with the LIGE.
This study examines difference in horse's heart rate variability (HRV)
between three different trotting velocities (Warm-up, Heavy exercise,
Recovery) and between two heavy exercise repetitions respectively at the
beginning and the end of an interval training session. Beat-to-beat RR
interval of ten elite trotters were collected during two different training
sessions for each horse. From heavy exercise to recovery, HRV spectral
analysis revealed: first, a significant increase in total and in low
frequency energy whereas high frequency energy decreased and second, a
prevalence of HF energy compared to LF (LFn: 16
Hemodynamic alterations during balloon carotid angioplasty (BCA) and stenting have been ascribed to the consequences
of direct carotid baroreceptor stimulation during balloon inflation. BCA with stenting in patients with carotid atheromatous
stenoses offers a unique opportunity for elucidating the cardiovascular autonomic response to direct transient intravascular
stimulation of the baroreceptors. We analysed the consequences of BCA on the autonomic control of heart rate and on breathing
components in nine patients with atheromatous stenoses involving the bifurcation and the internal carotid. A time-frequency
domain method, the smoothed pseudo-Wigner-Ville transform (SPWVT), was used to evaluate the spectral parameters (i.e., the
instantaneous amplitude and centre frequency (ICF) of the cardiovascular and respiratory oscillations). Those parameters
and their dynamics (8 and 24 h later) were evaluated during and after the procedure. BCA stimulates baroreceptors in all
patients, which markedly reduces heart rate and blood pressure. Vagal baroreflex activation altered the respiratory
sinus arrhythmia in terms of amplitude and frequency (ICF HF RR shifted from 0.27 +/- 0.03 to 0.23 +/- 0.04 Hz pre-BCA vs.
BCA, respectively; p < 0.01). Both the high- and low-frequency amplitudes of heart rate oscillations were altered during
carotid baroreceptor stimulation, strongly supporting a contribution of the baroreflex to the generation of both oscillations
of heart rate. Carotid baroreceptors stimulation increased the inspiratory time (Ti) (1.5 +/- 0.5 to 2.3 +/- 0.6 s pre-BCA vs.
BCA, respectively; p < 0.01). In awake patients, BCA with stenting of atheromatous stenosis involving the bifurcation and internal
carotid causes marked changes in the cardiac autonomic and respiratory control systems
This work has been undertaken within the framework of the ACI RNTS REGLO: ``Ovulation control''. See
This work has been undertaken within the framework of a DEA (Automatique et Informatique industrielle, Lille 1)
training course and is currently the matter of a PhD thesis. By now, the mathematical models interested in follicular development
could be cast into two approaches.
One focuses on the mechanims underlying follicular development, on the molecular and cellular scales and considers separately either
ovulatory or atretic (degenerating) paths. The other focuses on the selection process by itself which is investigated in the sense of
population dynamics. Our work has consisted in merging the mechanistic and multi-scale features of the former approach with the ability
of the latter ``to make peaks arise'' within a distribution. Ovarian follicles are characterised by a density function describing the cell
population constituting the follicular granulosa tissue,
We have so far determined the relevant
This work has been undertaken within the framework of a DEA (Informatique Médicale et Technologies de la Communication, Paris 6) training course. Petri nets (in their extended sense including timed and stochastic Petri nets) constitute a powerful formalism for knowledge integration for which many implementation and analysis tools are available, and whose principles are easily accessible to non-specialists. The whole components of the female gonadotrope axis (hypothalamus, pituitary gland and ovaries with follicles and corpus luteum at different development stages) have been taken into account, thanks to a modular approach allowing to identify and describe subnets, while maintaining their ability to interact within the global net. The work steps have consisted, on the one hand, in formalising and writing-down the static nets, and, on the other hand, in simulating dynamically the firing of the net transitions. The main results have concerned the hypothalamo-pituitary part of the net, in which the features of the steroidal feedback on gonadotrophin and GnRH secretion have been introduced (range and frequency characteristics of LH pulsatility, conditions for the ovulatory surge).
Renault contract 1 02 D0667 00 21102 01 2. J.B. Millet is preparing his PhD in the framework of this CIFRE contract.
Homogeneous charge compression ignition (HCCI) is a new combustion technology that appears as a possible alternative to
diesel engines with high efficiency and low pollutant emissions (mainly
Renault contract 1 00 D0256 00 21102 012. K. Bencherif is preparing his PhD in the framework of this CIFRE contract.
The polymer electrolyte fuel cell (PEMFC) has a high energy conversion efficiency and zero pollutant emission when fueled with hydrogen.
It is then one of the most promising candidates for fuel cell powered vehicles.
Hydrogen can be stored or produced onboard the vehicle by reforming methanol or hydrocarbon fuels. Our research focuses on modelling
and control of fuel cell systems comprising a PEMFC with an hydrocarbon reformer that produces hydrogen when needed.
We have obtained reduced order models for this type of systems, that can be used for the control of
Renault contrat 1 04 D0004 00 21102 012. M. Gati is preparing his PhD in the framework of this CIFRE contract.
Gear trains are used to convert the high speed - low torque output of the engine into a lower speed - higher torque input to the wheels.
These transmissions systems have two main disadvantages: 1) contact between rotating parts may be lost somewhere along the kinematic chain during
some transients, this is the backlash effect; 2) some undesired compliance is introduced into the system.
Our objective is the suppression of the transient vibrations induced by the combined effect of backlash and compliance. The existence of
contact and non-contact phases leads us to adopt an hybrid-system point of view for modelling and backlash compensation.
Also we exploit the fact that backlash is a particular case of hysteresis
See
See
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and
See
The Nonlinear Control Network is funded by the European Commission's Training and Mobility of Researchrs (TMR) Programme. We participate to the Training Programme (M. Sorine: Lectures on friction modelling and control of systems with friction). P.A. Bliman is the coordinator for our participation.
G. Ferrari Trecate is the coordinator of the INRIA team participating to the Network of excellence HYCON (``Taming Heterogeneity and Complexity of Networked Embedded Systems'' - submitted in the context of the second IST call within the Sixth Framework Programme).
Simulation of the control of the cardio-vascular system by means of a neuron-like Autonomous Adaptive Control (AAC) system.
This is a joint Project between INRIA, and ISP RAS, Russia (
A PICS convention CNRS-NSF on systems with delays (2002/2004).
Participation to the research project ``Satellite communications and related laboratories project'' between the ``Institut Aéronautique et Spatial'' and the Yzmir University. In particular, G. Ferrari Trecate and Y. Sorel (Aoste project) supervised part of the Ph.D. activities of Tolga Ayav, focusing on the analysis and tuning of scheduling techniques for imprecise computation models.
Pierre-Alexandre Bliman and Catherine Bonnet participate at the GdR meetings on a regular basis.
Catherine Bonnet and Michel Sorine are members of this group.
See
Giancarlo Ferrari Trecate participates at the GdR meetings on a regular basis for all the project activities concerning hybrid systems.
See
P.A. Bliman:
- coordination of SCARAMOCO working group,
- Local organization of IFAC workshop on Time-Delay Systems TDS'03 with Catherine Bonnet, Frédérique Clément, Giancarlo Ferrari-Trecate, Martine Verneuille.
- Member of International Program Committee of IFAC TDS'04, to be held in Leuven, Belgium.
- Responsible for INRIA Rocquencourt Research center, of the activities of the Multi-partner Marie Curie Training Site entitled Control Training Site (beginning in 2002).
- Responsible for INRIA of the activities of the grant PICS CNRS-NSF ``Systèmes à retard'' (2002/2004).
- Participation to french-polish cooperation Polonium (2002-2003).
- Coordination, with Prof. J. Nekovář (Université Paris VI), of a collection of books and funds, organized by SMF and SMAI, in aid of Charles University Library in Prague (Czech Republic) after August 2002 flood.
C. Bonnet:
- is in the board of directors of the French Mathematical Society, of the GDR MACS (Research group on modelisation analysis and tracking of
systems of the CNRS) and of the association Femmes et mathématiques (Women and Mathematics). She is a member of the french piloting committee
of the Helsinki group on Women and Science of the European commission.
- Member of the national organizing committe of the IFAC Workshop on Time-Delay systems TDS'03.
F. Clément:
- coordination of ICEMA-2 consortium.
- coordination of REGLO working group.
- co-organisation of Iliatech day ``Modélisation et Simulation pour la Médecine'', October 21rd 2003, INRIA Rocquencourt.
G. Ferrari Trecate:
- Giancarlo Ferrari Trecate has been part of the International Program Committee for the IFAC Conference on Analysis and Design of Hybrid Systems, 16-18 June 2003, St. Malo. Within the same conference, he also organized the invited session ``modelling and identification of hybrid systems''.
See
- From November 2002, member of the IFAC Committee on Power Plants and Power Systems.
M. Sorine has been a member of the International Program Committees for the IFAC TDS03 and CIFA 2004 conferences. He is the Projects committee chairman of INRIA Rocquencourt Research Unit.
- P.A. Bliman: ``Linear Matrix Inequalities and Control Theory'' for 3rd year students at ENSTA.
- F. Clément: Educational training for the ``Modelling and control of biological systems'', module part of the "Master's Degree in BioInformatics and BioStatistics" (Paris 11 University), to be held during the second semester of the 2003-2004 academic year.
- G. Ferrari Trecate taught the courses ``Asservissements nonlinéaires'', (Maîtrise en Électronique, Électrotechnique, and ``Systèmes hybrides'' (DESS) at the Université Paris-Sud.
- M. Sorine: Lectures on ``The cardiovascular system and its short-term control: modelling and signal analysis'', Von Karman Institute, May 12-16, 2003.
Lecture on ``Le coeur : modélisation et traitement du signal'', Cours de l'Ecole Doctorale de Sciences Mathématiques de Paris Centre, September, 2003.
- P.A. Bliman, Lecture at LAAS, Toulouse – Juin 2003
- F. Clément, ``A control approach of the multi-scale modelling of excitation-contraction coupling''. Séminaire "Mathématiques, Biologie et Médecine" de l'Institut Henri Poincaré, February 25th 2003.
- M. Sorine, ``Problèmes de modélisation et de contrôle pour l'étude du système cardiovasculaire'', Colloquium Math Appli, IMAG, April 17th, 2003.
``Multiscale modelling of excitation-contraction coupling in striated muscles. Application to the cardiovascular system'', Séminaires du Collège de France, December 5th, 2003.
``Problèmes de modélisation et de contrôle pour l'étude du système cardiovasculaire'', Centre d'Automatique des Mines, Fontainebleau, June 23rd, 2003.