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Planning of the talks

Lecture room Jean Prouvé 11.-1.V

9h00-9h50  Georges BastinBoundary control of open channels : Application to the Meuse River

Georges Bastin & Jean-Michel Coron

In this communication we emphasize the main features that may occur in real live applications of boundary feedback control of systems represented by 1-D 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 Saint-Venant 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 non-homogeneous densities.

The goal of this talk is to present several recent results on the local exact controllability of Navier-Stokes equations with non-homogeneous 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, Jean-Pierre Puel.
Enrique Fernández CaraSome recent control results for α-models

This talk is mainly devoted to present some internal and boundary controllability results for the Leray-α 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 Navier-Stokes system. The main aim of the talk is to prove that the local null controllability results for the Navier-Stokes equations hold true for the Leray-α system with controls that are uniformly bounded with respect to α. Accordingly, we can get sequences of control-state pairs that converge, in an appropriate sense, to null controls and associated states for the Navier-Stokes 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.
Andreï Fursikov SlidesManuel González-Burgos Slides
10h20-11h10  Jean-Pierre Raymond Eduardo CerpaControl of fourth-order parabolic control systems.

In this talk we address the boundary and internal controllability of some fourth-order 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 fluid-structure interactions.

We consider the mathematical model of a rigid structure moving in a viscous incompressible fluid occupying a bounded domain. We show that the fluid-solid 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 semi-discrete 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 1-d problems.
11h10-12h00 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 well-posedness and stability properties of the obtained closed loop system. This is a joint work with Jamal Daafouz and Marius Tucsnak.
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.
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 bang-bang 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.
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.
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 finite-dimensional, 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.
13h30-14h20   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 weak-coupling and on its consequences in term of attainable sets, including an extension of a celebrated result of Ball-Marsden-Slemrod.
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 well-posedness of both the open-loop and closed-loop system. Then using a Lyapunov approach, we obtain the exponential stabilization for the closed-loop system under natural feedbacks.
Jérôme Le RousseauCarleman estimates for high-order elliptic operators.

We consider elliptic operators of even order with complex coefficients and we derive microlocal and local Carleman estimates near a boundary, under sub-ellipticity and strong Lopatinskii conditions or near an interface under sub-ellipticity 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).
14h20-15h10 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 pseudo-random 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.
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 high-quality 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 single-atom 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.
Young researchers presentations Luzero de Teresa Slides
15h30-16h20 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 Bardos-Lebeau-Rauch 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).
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 Ginzburg-Landau 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.
16h20-17h10 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.
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 self-adjoint, infinite-dimensional operator associated with a nonlinear (possibly infinite-dimensional) dynamical system. I will discuss the connection between the finite-dimensional 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 off-unit circle eigenvalues. Appropriate (Hardy-type) spaces are defined for on and off-attractor 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 (off-attractor) 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.

Young researchers presentations

Lecture room 21.2.28Lecture room Jean Prouvé 11.-1.V
14h20Morgan Morancey Ivonne Rivas Slides
14h50Ivan 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 post-process 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
15h40Ying FuQuantum Hamiltonian identification in presence of large perturbationsGuillaume 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 space-dependent coefficients.
16h10 Landry Bretheau Mamadou GueyeOn Exact Boundary Controllability of 1-D Degenerate Equations. Slides
16h40Dario PrandiPierre LissyOn the uniform controllability of the unidimensional transport-diffusion equation Slides
17h10Laetitia GiraldiFrédéric 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 Cole-Hopf transform and maximum principles.

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, 19h00-20h30, 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.