Planning of the talks
Lecture room Jean Prouvé 11.1.V
 Monday  Tuesday  Wednesday  Thursday  Friday 
9h009h50 
Georges BastinBoundary control of open channels : Application to the Meuse River
Georges Bastin & JeanMichel Coron
In this communication we emphasize the main features that may occur in real live applications of boundary feedback control of systems represented by 1D hyperbolic partial differential equations. The issue is presented through the specific case study of the control of navigable rivers with a particular focus on the Meuse river in Wallonia (south of Belgium). The system is described by SaintVenant equations and an important challenge is to regulate the water level while mitigating the flow rate variations. 
Sylvain ErvedozaOn the controllability of fluid flows with nonhomogeneous densities.
The goal of this talk is to present several recent results on the local exact controllability of NavierStokes equations with nonhomogeneous data for both incompressible and compressible cases. Especially, we will explain how to develop Carleman weights to deal simultaneously with the transport equation satisfied by the density together with the equation of the velocity.
This talk is based on joint works with Mehdi Badra, Olivier Glass, Sergio Guerrero, JeanPierre Puel.
Slides

Enrique Fernández CaraSome recent control results for αmodels
This talk is mainly devoted to present some internal and boundary controllability results for the Lerayα model of turbulence. In the equations, the usual transport term is regularized with the help of an operator that depends on a small parameter α. In the limit α tending to 0+, we find the classical NavierStokes system. The main aim of the talk is to prove that the local null controllability results for the NavierStokes equations hold true for the Lerayα system with controls that are uniformly bounded with respect to α. Accordingly, we can get sequences of controlstate pairs that converge, in an appropriate sense, to null controls and associated states for the NavierStokes equations. Some additional results and open questions will also be presented. This research has been performed in collaboration with F.D. Araruna and D.A. Souza. Slides 
Andreï Fursikov Slides  Manuel GonzálezBurgos Slides 
10h2011h10 
JeanPierre Raymond 
Eduardo CerpaControl of fourthorder parabolic control systems.
In this talk we address the boundary and internal controllability of some fourthorder parabolic control systems posed on a finite interval. We deal with the null controllability of single and coupled equations by applying the moment theory and a Carleman estimate approach 
Marius TucsnakScanning control of viscous fluids and fluidstructure interactions.
We consider the mathematical model of a rigid structure moving in a viscous
incompressible fluid occupying a bounded domain. We show that the fluidsolid system can be stabilized, globally in 2D and locally in 3D, using a feedback force
acting on the solid. For a toy model coupling the viscous Burgers equation we obtain the a finite time controllability result. In this case we explain why our result can be interpreted as a scanning controllability property of the viscous Burgers equation. 
Fatiha Alabau Slides 
Lucie BaudouinInverse problem for the waves : stability and convergence matters.
This talk aims to present some recent works in collaboration with Maya de Buhan, Sylvain Ervedoza and Axel Osses regarding an inverse problem for the wave equation. More specifically, we study the determination of the potential in a wave equation with given Dirichlet boundary data from a measurement of the flux of the solution on a part of the boundary. On the one hand, we will focus on the question of convergence of the space semidiscrete inverse problems toward their continuous counterpart. Several uniqueness and stability results are available in the literature about the continuous setting of the inverse problem of determination of a potential in the wave equation. In particular, we can mention a Lipschitz stability result under a classical geometric condition obtained by Imanuvilov and Yamamoto, and a logarithmic stability result obtained by Bellassoued when the observation measurement is made on an arbitrary part of the boundary. In both situations, we can design a numerical process for which convergence results are proved. The analysis we conduct is based on discrete Carleman estimates, either for the hyperbolic or for the elliptic operator, in which case we shall use a result of Boyer, Hubert and Le Rousseau. On the other hand, still considering the same inverse problem, we will present a new reconstruction algorithm of the potential. The design and convergence of the algorithm are based on the Carleman estimates for the waves previously used to prove the Lipschitz stability. We will finally give some simple illustrative numerical simulations for 1d problems. Slides 

11h1012h00  Julie ValeinNonlinear control of a coupled PDE/ODE system modelling a switched power converter with a transmission line
We consider an infinite dimensional system modelling a boost converter connected to a load via a transmission line. The governing equations form a system coupling the telegraph partial differential equation with the ordinary differential equations modeling the converter. The coupling is given by the boundary conditions and the nonlinear controller we introduce.
We design a nonlinear saturating control law using a Lyapunov function for the averaged model of the system.
The main results give the wellposedness and stability properties of the obtained closed loop system.
This is a joint work with Jamal Daafouz and Marius Tucsnak. Slides 
Benjamin HuardControl of superconducting circuits by quantum feedback
The macroscopic variables of electrical circuits, such as voltages and currents, obey quantum mechanics as long as they are protected enough from their environment. Since the first qubit based on a superconducting circuit was realized 15 years ago, the coherence time has already increased by 5 orders of magnitude. In this talk, I will present recent experiments on these circuits where quantum feedback enables the time control of quantum trajectories. Autonomous feedback and measurement based feedback are implemented.
Slides 
Wang GengshengTIME OPTIMAL CONTROL OF HEAT EQUATIONS. Progress and comments
This talk presents some progress and comments on time optimal control problems of heat equations. It focuses on the bangbang property. Several methods deriving this property from different cases, and some of its applications are introduced. In the studies of this property, the null controllability from measurable sets plays a key role. Several ways approaching such controllability from different cases are presented. Slides 
Sorin Micu
Approximation of periodic solutions for a dissipative hyperbolic equation.
We study the numerical approximation of periodic solutions for an exponentially stable linear hyperbolic equation in the presence of a periodic external force f. These approximations are obtained by combining a fixed point algorithm with the Galerkin method. It is known that the energy of the usual discrete models does not decay uniformly with respect to the mesh
size. Our aim is to analyze this phenomenon's consequences on the convergence of the approximation method and its error estimates. We prove that, under appropriate regularity assumptions on f, the approximation method is always convergent. However, our error estimates show that the convergence's properties are improved if a numerically vanishing viscosity is added to the system. The same is true if the nonhomogeneous term $f$ is monochromatic. Slides 
Enrique ZuazuaAverage control.
This lecture is devoted to address the problem of controlling uncertain systems submitted to parametrized perturbations.
First, we introduce the notion of averaged control according to which the average of the states with respect to the uncertainty parameter is the quantity of interest. We observe that this property is equivalent to a suitable averaged observability one. We discuss this property in the context of finitedimensional, wave and parabolic equations.
We then address the issue of observability of a given PDE in presence of an additive perturbation given by the solutions of another PDE.
We will also present some open problems and perspectives of future developments. Slides 
13h3014h20 
Fabio Ancona Slides 
Thomas ChambrionRegularity of propagators of the bilinear Schrödinger equations.
The bilinear Schrödinger equation models the action of an external field (e.g., a laser) on a quantum system. In many applications (quantum chemistry or NMR), one chooses a suitable time varying external field in order to steer the system to a given target. The structure of the Schrödinger equation implies some regularity of the solutions, which prevents to reach ``irregular'' states. This talks focuses on the recently introduced notion of weakcoupling and on its consequences in term of attainable sets, including an extension of a celebrated result of BallMarsdenSlemrod. Slides 
Wang ZhiqiangStabilization of extrusion process modeled by hyperbolic systems coupled
through a moving interface.
In this talk, we consider a physical model of the extrusion process,
which is described by two systems of conservation laws coupled through a
moving interface. We first study the wellposedness of both the
openloop and closedloop system. Then using a Lyapunov approach, we
obtain the exponential stabilization for the closedloop system under
natural feedbacks. Slides 
Jérôme Le RousseauCarleman estimates for highorder elliptic operators.
We consider elliptic operators of even order with complex coefficients and we derive microlocal and local Carleman estimates near a boundary, under subellipticity and strong Lopatinskii conditions or near an interface under subellipticity and proper transmission conditions. Carleman estimates are weighted a priori estimates for the solutions of the associated elliptic problem. The weight is of exponential form, exp(τφ), where τ is meant to be taken as large as desired. Such estimates have numerous applications in unique continuation, inverse problems, and control theory. This is joint work with Mourad Bellassoued (Fac. Sciences Bizerte).
Slides 
14h2015h10 
Alain SarletteFrom consensus to robust algorithms: symmetrization.
We show how an abstract viewpoint on consensus algorithms, as performing symmetrization with respect to a group, allows to connect consensus to various algorithmic procedures. The latter include reaching agreement on probability distributions, generating pseudorandom numbers and quantum control strategies. We prove how the robust convergence of the consensus algorithm guarantees robustness to these algorithmic procedures.
This is joint work with F.Ticozzi and L.Mazzarella from the University of Padova. Slides 
Igor DotsenkoQuantum control of light in a cavity
We present experimental results on quantum control of photon number states of microwave field stored in a highquality cavity. Rydberg atoms crossing the cavity mode one by one perform a series of weak measurements of the field photon number. A sequence of many atoms realizes a complete quantum nondemolition photon counting. Adapting the measurement settings for each atom using information on the field obtained so far allows us to speed up the information acquisition rate and thus to faster project the initial coherent field into a random photon number state. In order to realize deterministic preparation and stabilization of these states against decoherence we have implemented quantum feedback schemes: After each singleatom weak measurement the state is slightly modified by injecting a small coherent field or by sending resonant atoms (depending on a chosen scheme) in order to steer it towards a desired state. Slides 
Young researchers presentations 
Luzero de Teresa Slides  

15h3016h20 
Gilles Lebeau Some new results for the controllability of waves equations.
I will present two results on the controllability of waves.
The first one is a generalization of the classical result of BardosLebeauRauch
adapted to the case where the control region is moving in time. The second one
is an exact controllability result for a system of waves with different speed.
These works are in collaboration with J. Le Rousseau (Orléans), P. Terpolilli (Total)
et E. Trélat (Paris 6). Slides 
Bing Yu Zhang 
Young researchers presentations 
Xu ZhangRecent Progress on Controllability of Multidimensional Quasilinear Parabolic Systems.
The purpose of this talk is to overview our recent controllability results (jointly with Xiaoyu Fu and/or Xu Liu) on multidimensional quasilinear parabolic equations, quasilinear complex GinzburgLandau equations, and coupled quasilinear parabolic systems by one control. The main tools that we employed are some new and delicate Carleman estimates for suitable linear parabolic equations/systems. The key points of our approach are to formulate the controllability problems in the frame of classical solutions and to seek the control functions in the Hölder spaces for given data with certain regularity. Slides 

16h2017h10 
Lionel RosierNull controllability of the heat equation by the flatness approach
We revisit the null controllability of the heat equation by the
flatness approach, which provides explicitly the trajectory and the control as series
in some Gevrey class. This approach gives good numerical approximations of the solution
and the control with explicit error estimates. Finally, we show how to adapt the method to
deal with Schrodinger equation. This is a joint work with Philippe Martin and Pierre Rouchon.

Dominique SugnyOptimal control of spin systems with applications in Magnetic Resonance Imaging
We analyze the optimal control of spin systems in Nuclear Magnetic Resonance. We consider the non unitary case where the spins are in interaction with their environment, their dynamics being governed by the Bloch equation. In the ideal situation where all the spins have the same dynamics, geometric control theory gives a complete geometrical description of the control problem. In a more realistic experimental setup, we have to deal with the simultaneous control of an ensemble of spins with different parameters, and only numerical optimal control algorithms can be used to solve the control problem. The validity and the accuracy of the different methods are tested on key control targets. Finally, experimental results using techniques of Nuclear Magnetic Resonance and Magnetic Resonance Imaging will illustrate this theoretical work. Slides 
Young researchers presentations 
Igor Mezić (to be confirmed)Koopman Operator Methods in Control
I will present a technique and framework for spectral decomposition of solutions of evolution equations and its applications in control. The framework is based on spectral properties of Koopman (composition) operator, a linear, non selfadjoint, infinitedimensional operator associated with a nonlinear (possibly infinitedimensional) dynamical system. I will discuss the connection between the finitedimensional nature of attractors of evolution equations and the Koopman Mode Decomposition (KMD) of the solution of such an evolution equation. KMD leads to evolution modes (spatial shapes) that have simple dynamics. Koopman modes are defined via projections of evolution dynamics onto eigenspaces of the Koopman operator. They split into those representing asymptotic behavior on the attractor whose associated eigenvalues of the Koopman operator reside on the unit circle in the complex plane and the transient modes that are associated with offunit circle eigenvalues. Appropriate (Hardytype) spaces are defined for on and offattractor behavior. Due to possibility of continuous spectrum, care must be taken with projections. Generalized Laplace Analysis technique is presented to provide the technique for capturing transient (offattractor) behavior. Spectral considerations coupled with the aforementioned decomposition then lead to a new point of view on global stability analysis in dynamical systems, and an associated framework for control. Applications of the methodology in fluid mechanics are presented.
Slides 

Young researchers presentations
 Lecture room 21.2.28  Lecture room Jean Prouvé 11.1.V 
14h20  Morgan Morancey 
Ivonne Rivas Slides 
14h50  Ivan MaximovApplication of optimal control theory to MRI/NMR experiments
Magnetic resonance is very interesting and exciting subject for research
due to a complex web entangling and incorporating such fundamental
disciplines as physics, math, chemistry and
medicine. In turn, it demands consider a multidisciplinary approach in
all aspects of MR studies such as appropriate
selection of patients/volunteers, adequately organized/performed
measurements, sophisticated postprocess methods etc.
In my talk I would like to concentrate an attention on topic: optimal
control theory and its application for rf pulse design and diffusion
weighted imaging. Modern MR machines require design of more and more
compound pulse sequences using numerous technical achievements such as
ultra high fields and related field inhomogeneity
suppression/insensitivity, novel gradient systems and accessible field
strength and slew rates, parallel transmit coils and rf pulse excitation
profiles, adequate local and global special absorption rates and many
others. The OCT allows one to operate with all these constraints and to
produce reasonable high quality images. As a result,
we can apply these achievements to clinical studies such as diffusion
weighted imaging and obtained excellent improved biomarkers for check
and diagnostics.  Nicolas Carreño Slides 
15h40  Ying FuQuantum Hamiltonian identification in presence of large perturbations  Guillaume OliveInfluence of the geometry on the controllability of parabolic systems
In this talk we will focus on how the geometry of the control domain can change the controllability properties of some linear parabolic systems. We will discuss two situations, namely a boundary controllability problem in dimension 2 on a rectangular domain, and a distributed controllability problem in dimension 1 with spacedependent coefficients. Slides 

16h10 
Landry Bretheau 
Mamadou GueyeOn Exact Boundary Controllability of 1D Degenerate Equations. Slides 
16h40  Dario Prandi  Pierre LissyOn the uniform controllability of the unidimensional transportdiffusion equation
Slides 

17h10  Laetitia Giraldi  Frédéric Marbach
Controllability and boundary layers for a Burgers equation
In order to establish small time controllability results for viscous fluid systems, a natural method is to study their inviscid counterparts. When the inviscid limit system is controllable (like Euler's system), one can recover results of small time controllability for the initial viscous system, by means of an appropriate scaling. However, if the controls don't act over the whole boundary of the physical domain, boundary layers can arise near the uncontrolled parts of the boundary and make the analysis harder.
In this talk, I will expose a simple setting, namely the 1D viscous Burger's equation for which a precise computation of the boundary layer is possible. I will show that global small time null controllability still holds with only two scalar controls (dropping a control on the right end of the domain with respect to the previous known controllability result). Methods used will include Fourier analysis, the ColeHopf transform and maximum principles.
Slides 
Coffee breaks and lunch time
Coffee breaks are planned at 9h50 and 15h10. Lunch time is from 12h00 to 13h30. The CNAM has got its own food facility, rue Conté, the price of one meal is about 10 euros. Many small restaurants around the CNAM are also a good option (rue au maire, passage brady, rue meslay....). In the main building of the CNAM stands the "Café des techniques" where it is also possible to eat. Besides, organizers recommand visiting the CNAM museum.
Social Event
Wednesday, april 2nd, 19h0020h30, in the Zamansky room, at the very last floor of the Jussieu tower of the Paris 6 university, 4, place Jussieu, Paris 5e. The regular bus 47 passes in front of the CNAM and stops at Jussieu and takes about 30 mn for the route. Metro 4 and then 7 are also possible if not better, particularly in case of heavy traffic.