### Generalized Secrecy Capacity

**Matthieu Bloch**

### On the Degrees of Freedom of MISO Broadcast Channels with Partial CSIT

**Dr. Hamdi Joudeh (Imperial College London)**

The multiple-input-single-output (MISO) broadcast channel (BC), in which a multi-antenna transmitter communicates with multiple uncoordinated single-antenna receivers, is an essential building block of modern wireless networks. In this channel, multiuser interference management is naturally carried out at the transmitter. This in turn requires highly accurate and up-to-date channel state information at the transmitter (CSIT), which is not always available in practice. While it is understood that the MISO BC is sensitive to CSIT inaccuracies, the capacity under such conditions remains largely a mystery. Hence, it is natural to resort to coarse approximations, e.g. the Degrees of Freedom (DoF), when studying such challenging problems. In this talk, I will review some recent (and not so recent) results in DoF studies of the MISO BC when only partial instantaneous CSIT is available. I will be focusing on tools used to derive achievability and converse result. I will also present some new DoF results for parallel MISO BCs (e.g. OFDM) with partial CSIT. Implications, insights and open problems are also discussed.

Bio: Hamdi Joudeh is a postdoctoral research associate in the Communications and Signal Processing Group, Department of Electrical and Electronic Engineering at Imperial College London. He received his PhD in Electrical Engineering and MSc in Communications and Signal Processing from Imperial College London, UK, in 2016 and 2011 respectively. His research interests are in the areas of wireless communications and multiuser information theory. He is currently serving as an associate editor for the EURASIP Journal on Wireless Communications and Networking.

### Séminaire d’Automatique du plateau de Saclay : Non-Markovian Quantum Feedback Networks

**John Gough (Institute of Mathematics and Physics, Aberystwyth University)**

We will recall the theory of Markovian Quantum feedback Networks, and explain some recent models with non-Markovian behaviour coming from physical requirements.

The concept of a controlled flow of a dynamical system, especially when the controlling process feeds information back about the system, is of central importance in control engineering, and we build on the ideas of by Bouten and van Handel to develop a general theory of quantum feedback. We elucidate the relationship between the controlling processes Z and the measured process Y, and to this end make a distinction between what we call the input picture and the output picture.

The theory is general enough to include a modulating filter which processes the measurement readout Y before returning to the system. This opens up the prospect of applying very general engineering feedback control techniques to open quantum systems in a systematic manner, and we consider a number of specific modulating filter problems.

Bio. John E. Gough was born in Drogheda, Ireland, in 1967. He received the B.Sc. and M.Sc. in Mathematical Sciences and the Ph.D. degree in Mathematical Physics from the National University of Ireland, Dublin, in 1987, 1988 and 1992 respectively. He was reader in Mathematical Physics at the Department of Mathematics and Computing, Nottingham-Trent University, up until 2007. He then joined the Institute of Mathematics and Physics at Aberystwyth University as established chair of Mathematics. He has held visiting positions at the University of Rome Tor Vergata, EPFL Lausanne, UC Santa Barbara and the Hong Kong Polytechnic University. His research interests include quantum probability, measurement and control of open quantum dynamical systems, and quantum feedback networks.

### Séminaire d'Automatique du Plateau de Saclay : Quantum reservoir engineering to control light with atoms.

**Alain Sarlette (QUANTIC Lab, INRIA Paris & SYSTeMS research group, Ghent University)**

This talk will give a simple introduction to a quantum stabilization technique called "reservoir engineering", which builds on the dissipation induced on a target system by its interaction with an open auxiliary system. We will introduce the technique, recall some older results obtained in our group and finally present our latest results in which we study the effect on the target system, of entanglement "in time" in the auxiliary system. This is joint work with my postdoc Zibo Miao.

Bio. Alain Sarlette has an engineering degree (applied physics) and a PhD (systems and control theory) from the University of Liège, Belgium. He has been a visiting researcher at Princeton University, Mines Paris-Tech, IIT Bombay among others. He is currently assistant professor at Ghent University (Belgium) and Senior Researcher (CR1) at INRIA Paris in the QUANTIC lab. His research interests include nonlinear and geometric control, coordination algorithms, and mainly algorithms and control for quantum technologies.

### Séminaire d'Automatique du plateau de Saclay : Some Mathematical and Numerical questions on the Lindblad equation. Application to Quantum Control.

**Claude Le Bris (Ecole des Ponts & Inria)**

We overview a series of joint works with P. Rouchon (Mines de Paris) and other collaborators devoted to the mathematical analysis and the numerical simulation of high-dimensional Lindblad equations. These equations rule the time evolution of density matrices of open quantum systems. The numerical techniques we present aim

at adaptively constructing a low-rank approximation of the density matrices, deriving an evolution equation for this reduced model, and using it as a surrogate model for the original evolution. Alternately, using that reduced model, we also consider and improve advanced Monte-Carlo type techniques that simulate the stochastic system of equations equivalent to the Lindblad equation. The practically relevant setting where we test our approaches arises in stabilization/control problems for quantum optics and circuits. We believe that, interestingly, our approaches may be readily adapted to problems involving the simulation and control of the evolution of density matrices in other contexts.

Bio. Claude Le Bris is a civil engineer in chief, HdR from University Paris Dauphine. His applied mathematics works have primarily been devoted to the design and analysis of numerical approaches for Physics and Mechanics. He holds a research position at Ecole des Ponts et Chaussées. He is the scientific leader of the project-team MATHERIALS at INRIA, the activity of which is focused on multiscale numerical simulation.

### S³ seminar : Recursive State Estimation for Nonlinear Stochastic Systems and Application to a Continuous Glucose Monitoring System

**Alexandros Charalampidis (CentraleSupélec, Rennes)**

The talk will start with an introduction to recursive state estimation. It will be presented how the problem can be solved exactly in two important cases (systems with finite state space and linear Gaussian systems). The difficulties associated with nonlinear systems will be explained and the main techniques will be presented (Extended Kalman Filter, Unscented Kalman Filter, Gauss-Hermite Kalman Filter, Particle Filtering, Gaussian Sums). Then the talk will focus on systems that consist of linear dynamical systems interconnected through static nonlinear characteristics. It will be explained that for them, it is possible to avoid integration on the space space, which may be of high order, reducing it to the solution of some linear systems and low-order integration. This way, more accurate calculations can be made. Additionally, a novel quadrature technique, alternative to the Gauss-Hermite quadrature, specially designed for nonlinear filters using norm minimization concepts will be presented. The proposed techniques are applied to an example and it is shown that they can lead to a significant improvement. The final part of the talk will deal with the application of filters to data from a Continuous Glucose Monitoring System (CGMS). The importance of the CGMS to the construction of an artificial pancreas will be explained. It will be shown that, using simple models of the system dynamics, the application of Kalman and Particle Filtering to experimental data from ICU patients leads to an important reduction of the glucose estimation error.

### S³ seminar : Inversion de données en traitement du signal et des images : régularisation parcimonieuse et algorithmes de minimisation L0.

**Charles SOUSSEN, (Centre de Recherche en Automatique de Nancy (CRAN, UMR CNRS 7039), Université de Lorraine)**

Dans la première partie de l'exposé, je présenterai différents problèmes inverses auxquels je me suis intéressé ces dernières années et les contextes applicatifs associés : reconstruction d'images en tomographie, analyse d'images biologiques et d'images hyperspectrales en microscopie, problèmes d'inversion de données en spectroscopie optique avec applications biomédicales. Lorsque les données disponibles sont en nombre limité et partiellement informatives sur la quantité à estimer (problèmes inverses mal posés), la prise en compte d’informations a priori sur les inconnues est indispensable, et s’effectue par le biais des techniques de régularisation. Dans la seconde partie de l'exposé, je présenterai plus particulièrement la régularisation parcimonieuse de problèmes inverses, basée sur la minimisation de la "norme" l0. Les algorithmes heuristiques proposés sont conçus pour minimiser des critères mixtes L2-L0 du type

min_x J(x;lambda) = || y - Ax ||_2^2 + lambda || x ||_0.

Ce problème d'optimisation est connu pour être fortement non-convexe et NP-difficile. Les heuristiques proposées (appelées algorithmes "gloutons") sont définies en tant qu'extensions d'Orthogonal Least Squares (OLS). Leur développement est motivé par le très bon comportement empirique d'OLS et de ses versions dérivées lorsque la matrice A est mal conditionnée. Je présenterai deux types d'algorithmes pour minimiser J(x;lambda) à lambda fixé et pour un continuum de valeurs de lambda. Finalement, je présenterai quelques résultats théoriques visant à garantir que les algorithmes gloutons permettent de reconstruire exactement le support d'une représentation parcimonieuse y = Ax*, c'est-à-dire le support du vecteur x*.

Biographie : Charles Soussen est né en France en 1972. Il est diplômé de l'Ecole Nationale Supérieure en Informatique et Mathématiques Appliquées, Grenoble (ENSIMAG) en 1996. Il a obtenu sa thèse en traitement du signal et des images au Laboratoire des Signaux et Systèmes (L2S), Université de Paris-Sud, Orsay, en 2000, et son Habilitation à Diriger des Recherches à l'Université de Lorraine en 2013. Il est actuellement Maître de Conférences à l'Université de Lorraine, et au Centre de Recherche en Automatique de Nancy depuis 2005. Ses thématiques de recherche concernent les problèmes inverses et l'approximation parcimonieuse.

### S³ seminar : Deux trous noirs dans une meule de foin : analyse de données pour l'astronomie gravitationnelle

**Eric Chassande-Mottin, (CNRS, AstroParticule et Cosmologie, Université Paris Diderot)**

Le 14 septembre 2015, les deux détecteurs du Laser Interferometer Gravitational-wave Observatory (LIGO) inauguraient une nouvelle ère pour l'astrophysique en observant pour la première fois une onde gravitationnelle issue de la fusion de deux trous noirs faisant chacun trente fois la masse du soleil environ et situés à une distance supérieure à un milliard d'années-lumière. On donnera une vue d'ensemble de cette découverte majeure en insistant sur les méthodes d'analyse de données utilisées pour sortir le signal du bruit complexe rencontré dans ces expériences.

### Coded Caching in Wireless Networks

**Meixia Tao**

The global mobile data traffic has been shifting from voice and messages to rich content distributions, such as video streaming and application downloads. These contents are typically produced ahead of transmission and can be requested by multiple users though at possibly different times. By prefetching popular contents during off-peak times at the edge of wireless networks, such as small base stations, helper nodes, and user devices, wireless caching can alleviate peak-time network congestion and reduce user access latency. A fundamental question is what and how much gain can be leveraged by caching. In this talk, we shall investigate the gain of caching in two types of wireless networks. One is a general wireless interference network with arbitrary number of transmitters and arbitrary number of receives and with caches equipped at all the nodes. An information-theoretic study in terms of the storage-latency tradeoff will be presented. The other is a large-scale small-cell network where each small base station is equipped with a cache. We apply stochastic geometry to model, analyze, and optimize coded caching with performances characterized by average fractional offloaded traffic and average ergodic rate. Our study reveals several design insights of caching in practical wireless networks.

Bio: Meixia Tao received the B.S. degree from Fudan University, Shanghai, China, in 1999, and the Ph.D. degree from Hong Kong University of Science and Technology in 2003. She is currently a Professor with the Department of Electronic Engineering, Shanghai Jiao Tong University, China. Prior to that, she was a Member of Professional Staff at Hong Kong Applied Science and Technology Research Institute during 2003-2004, and a Teaching Fellow then an Assistant Professor at the Department of Electrical and Computer Engineering, National University of Singapore from 2004 to 2007. Her current research interests include content-centric wireless networks, wireless caching and multicasting, resource allocation, and interference coordination.

Dr. Tao is currently serving as a member of the Executive Editorial Committee of the IEEE Transactions on Wireless Communications and an Editor for the IEEE Transactions on Communications. Dr. Tao is the recipient of the IEEE Heinrich Hertz Award for Best Communications Letters in 2013 and the IEEE ComSoc Asia-Pacific Outstanding Young Researcher Award in 2009. She also receives the best paper awards from IEEE/CIC ICCC 2015 and IEEE WCSP 2012.

### Semantically-Secured Message-Key Trade-off over Wiretap Channels with Random Parameters

**Alexander Bunin, Faculty of Electrical Engineering at the Technion-Israel Institute of Technology, Israel.**

Modern communication systems usually present an architectural separation between error correction and data encryption. The former is typically realized at the physical layer by transforming the noisy communication channel into a reliable "bit pipe". The data encryption is implemented on top of that by applying cryptographic principles.

Physical layer security (PLS) rooted in information-theoretic principles, is an alternative approach to provably secure communication. This approach dates back to Wyner's celebrated 1975 paper on the wiretap channel (WTC). By harnessing randomness from the noisy communication channel and combining it with proper physical layer coding, PLS guarantees protection against computationally-unlimited eavesdroppers with no requirement that the legitimate parties share a secret key (SK) in advance. The eavesdroppers computational abilities are of no consequence here since the signal he/she observes from the channel carries only negligible information about the secret data.

Two fundamental questions in PLS are those of the best achievable transmission rate of a secret message (SM) over a noisy channel, and the highest attainable SK rate that distributed parties can agree upon. Our work studies the trade-off between SM and SK rates simultaneously achievable over a state-dependent wiretap channel WTC with non-causal channel state information (CSI) at the encoder. This model subsumes all other instances of CSI availability as special cases, and calls for an efficient utilization of the state sequence both for reliability and security purposes. We derive an inner bound on the SM-SK capacity region based on a novel superposition coding scheme. Our inner bound improves upon the previously best known SM-SK trade-off result by Prabhakaran et al., and to the best of our knowledge, upon all other existing lower bounds for either SM or SK for this setup. The results are derived under the strict semantic-security metric that requires negligible information leakage for all message-key distributions. The achievability proof uses the strong soft-covering lemma for superposition codes.

The talk is based on joint work with: Z. Goldfeld and H. H. Permuter (Ben-Gurion University of the Negev, Israel), S. Shamai (Technion - Israel Institute of Technology), P. W. Cuff (Princeton University) and P. Piantanida (CentralSupelec).

The work of A. Bunin and S. Shamai has been supported by the European Union's Horizon 2020 Research And Innovation Programme, grant agreement no. 694630.

### Séminaire d’Automatique du plateau de Saclay : Chance-constrained optimization with tight confidence bounds.

**Mark Cannon (Department of Engineering Science, University of Oxford)**

Optimization problems involving chance constraints, i.e. constraints on decision variables that are required to hold with given probability, occur in numerous engineering contexts, but have in particular contributed to developments in robust control design over the past decade. This talk will provide a new perspective on randomized methods for solving chance-constrained programming problems based on samples of uncertain parameters, and presents a theoretical framework for sampled convex programming that encompasses analyses of constraint discarding approaches and sequential sampling approaches. We show that tight bounds on the confidence of the solution of a sampled problem meeting chance constraints apply if a randomized sample discarding strategy is employed. This suggests a solution methodology which is both computationally convenient, being based on the solutions of convex sampled optimization problems, and efficient, requiring the solution of smaller numbers of problems than existing constraint discarding and sequential methods. We illustrate the method with examples from stochastic model predictive control design.

Bio. Mark Cannon obtained the degrees of MEng in Engineering Science in 1993 and D.Phil. in Control Engineering in 1998, both from Oxford University, and SM in Mechanical Engineering in 1995 from Massachusetts Institute of Technology. He is currently Associate Professor of Engineering Science, Oxford University, and an Official Fellow of St John's College. His research interests are in robust constrained control and stochastic model predictive control, specifically: issues relating to optimization and controller design, closed loop stability and constraint satisfaction, and applications to power management in electric vehicles.

### Séminaire d’Automatique du plateau de Saclay : On generalized homogeneity and time-constrained stabilization of evolution systems.

**Andrey polyakov (NON-A team, Inria-Lille-Nord Europe)**

Homogeneity is a symmetry of an object (e.g. function or operator) with respect to some transformations (dilations). Nonlinear homogeneous ODEs (ordinary differential equations) form an important class of models of control systems. They appear as local approximations of nonlinear plant and include models of process control, nonholonomic mechanical systems, models with frictions, etc. Being non-linear the homogeneous systems demonstrate properties typical for linear systems, for example, local stability implies the global one, stable homogeneous control system is ISS (input-to-state stable) with respect to measurement noises and additive exogenous disturbance, etc.

This talk is devoted to extension of ideas of homogeneity to evolution systems in Banach/Hilbert spaces. A lot of well-known partial differential equations are homogeneous in a generalized sense, (e.g. heat, wave, Navier-Stocks, Saint-Venant, Korteweg-de Vries, fast diffusion equations). They inherit many important properties of homogeneous ODEs such as scalability of trajectories or finite-time stability in the case of negative homogeneity degree. Homogeneity allows us to design a universal control for finite-time stabilization of evolution system.

Bio. Andrey Polyakov received PhD degree from Voronezh State University (Russia) in 2005.

He was lecturer (2004-2007) and associate professor (2008-2010) of this university.

In 2007 and 2008 he was a post-doctoral research associate with Automatic Control Department of CINVESTAV (Mexico). From 2010 till 2013 he was researcher with Institute of Control Sciences of Russian Academy of Sciences. Now Andrey Polyakovis Inria researcher with NON-A team of Inria Lille Nord Europe (France). His research interests include

different problems of robust nonlinear control and estimation. He is co-author of the book "Attractive Ellipsoids in Robust Control". He is editor of International Journal of Robust and Nonlinear Control, Journal of Optimization Theory and Applications (JOTA), Automation and Remote Control.

### S³ seminar : Extending Stationarity to Graph Signal Processing: a Model for Stochastic Graph Signals

**Benjamin Girault, (University of Southern California)**

During the past few years, graph signal processing has been extending the field of signal processing on Euclidean spaces to irregular spaces represented by graphs. We have seen successes ranging from the Fourier transform, to wavelets, vertex-frequency (time-frequency) decomposition, sampling theory, uncertainty principle, or convolutive filtering. One missing ingredient though are the tools to study stochastic graph signals for which the randomness introduces its own difficulties. Classical signal processing has introduced a very simple yet very rich class of stochastic signals that is at the core of the study of stochastic signals: the stationary signals. These are the signals statistically invariant through a shift of the origin of time. In this talk, we study two extensions of stationarity to graph signals, one that stems from a new translation operator for graph signals, and another one with a more sensible interpretation on the graph. In the course, we show that attempts of alternate definitions of stationarity on graphs in the recent literature are actually equivalent to our first definition. Finally, we look at a real weather dataset and show empirical evidence of stationarity.

Bio: Benjamin Girault received his License (B.Sc.) and his Master (M.Sc.) in France from École Normale Supérieure de Cachan, France, in 2009 and 2012 respectively in the field of theoretical computer science. He then received his PhD in computer science from École Normale Supérieure de Lyon, France, in December 2015. His dissertation entitled "Signal Processing on Graphs - Contributions to an Emerging Field" focused on extending the classical definition of stationary temporal signals to stationary graph signal. Currently, he is a postdoctoral scholar with Antonio Ortega and Shri Narayanan at the University of Southern California continuing his work on graph signal processing with a focus on applying these tools to understanding human behavior.

### S³ seminar : Novel Algorithms for Automated Diagnosis of Neurological and Psychiatric Disorders

**Hojjat ADELI, (The Ohio State University, Columbus, USA)**

Novel algorithms are presented for data mining of time-series data and automated electroencephalogram (EEG)-based diagnosis of neurological and psychiatric disorders based on adroit integration of three different computing technologies and problem solving paradigms: neural networks, wavelets, and the chaos theory. Examples of the research performed by the author and his associates for automated diagnosis of epilepsy, the Alzheimer’s Disease, Attention Deficit Hyperactivity Disorder (ADHD), autism spectrum disorder (ASD), and Parkinson’s disease (PD) are reviewed.

Biography: Hojjat Adeli received his Ph.D. from Stanford University in 1976 at the age of 26. He is Professor of Civil, Environmental, and Geodetic Engineering, and by courtesy Professor of Biomedical Informatics, Biomedical Engineering, Neuroscience, and Neurology at The Ohio State University. He has authored over 550 publications including 15 books. He is the Founder and Editor-in-Chief of international research journals Computer-Aided Civil and Infrastructure, now in 32nd year of publication, and Integrated Computer-Aided Engineering, now in 25th year of publication, and the Editor-in-Chief of International Journal of Neural Systems. In 1998 he received the Distinguished Scholar Award from OSU, “in recognition of extraordinary accomplishment in research and scholarship”. In 2005, he was elected Distinguished Member, ASCE: "for wide-ranging, exceptional, and pioneering contributions to computing in civil engineering and extraordinary leadership in advancing the use of computing and information technologies in many engineering disciplines throughout the world.” In 2010 he was profiled as an Engineering Legend in the ASCE journal of Leadership and Management in Engineering, and Wiley established the Hojjat Adeli Award for Innovation in Computing. In 2011 World Scientific established the Hojjat Adeli Award for Outstanding Contributions in Neural Systems. He is a Fellow of IEEE, the American Association for the Advancement of Science, American Neurological Society, and American Institute for Medical and Biomedical Engineering. Among his numerous awards and honors are a special medal from Polish Neural Network Society, the Eduardo Renato Caianiello Award for Excellence in Scientific Research from the Italian Society of Neural Networks, the Omar Khayyam Research Excellence Award from Scientia Iranica, an Honorary Doctorate from Vilnius Gediminas Technical University, and corresponding member of the Spanish Royal Engineering Society.

### S³ seminar : Stochastic proximal algorithms with applications to online image recovery

**Jean-Christophe PESQUET, CVN, CentraleSupélec**

Stochastic approximation techniques have been used in various contexts in machine learning and adaptive filtering. We investigate the asymptotic behavior of a stochastic version of the forward-backward splitting algorithm for finding a zero of the sum of a maximally monotone set-valued operator and a cocoercive operator in a Hilbert space. In our general setting, stochastic approximations of the cocoercive operator and perturbations in the evaluation of the resolvents of the set-valued operator are possible. In addition, relaxations and not necessarily vanishing proximal parameters are allowed. Weak almost sure convergence properties of the iterates are established under mild conditions on the underlying stochastic processes. Leveraging on these results, we propose a stochastic version of a popular primal-dual proximal optimization algorithm, and establish its convergence. We finally show the interest of these results in an online image restoration problem.

### Séminaire d'Automatique du plateau de Saclay : Controllability of a bent 3-link magnetic microswimmer

**Pierre Lissy (CEREMADE, Universite Paris-Dauphine)**

A recent promising technique for moving a robotic micro-swimmer (in view notably of medical applications) is to apply an external magnetic field. In this talk, I will focus on a 3-link magnetic microswimmer, which consists of three rigid magnetized segments connected by two torsional springs, one of the springs being twisted, so that the swimmer is not aligned at rest. By acting on it with

an external magnetic field, the swimmer twists and moves through the surrounding fluid. After explaining some specific difficulties coming from the Low Reynolds number regime, I will explain how to model the problem thanks to a system of non-linear ODEs. By considering the external magnetic field as a control function, I will state a local partial controllability result around the equilibrium states. Then, I will propose a constructive method to find a magnetic field that allows the swimmer to move along a prescribed trajectory (tracking) in view of obtaining global partial controllability results. Finally, I will show some numerical simulations that illustrate the practical difficulties of the tracking method due to the straight positions of the swimmer. This is a joint work with Laetitia Giraldi (INRIA Sophia), Jean-Baptiste Pomet (INRIA Sophia) and Clément Moreau (ENS Cachan).

Bio: Pierre Lissy received his Ph.D degree in Applied Mathematics in 2013 under the direction of Professor Jean-Michel Coron at Université Pierre et Marie Curie. He is now Assistant Professor in Applied Mathematics at University Paris-Dauphine since 2014. His research interests include the controllability properties of partial differential equations (PDEs), with a focus on the controllability of (linear and non-linear) coupled systems of PDEs and the estimations of the cost of the control near the minimal time of control and in singular limits. He began recently to work on the controllability properties of magnetized micro-swimmers governed by non-linear ODEs.

### Séminaire d'Automatique du plateau de Saclay : Time-extremal trajectories of generic control-affine systems have at most finite-order Fuller singularities

**Francesco Boarotto (CMAP, Ecole Polytechnique)**

In this talk we show that, in fact, for the generic choice of the pair $(f_0,f_1),$ there exists an integer $N>0$ such that the control $u$ associated to any time-extremal trajectory admits at most Fuller times of order $N$. In particular, $u$ is smooth out of a set of measure zero. This is a joint work with M. Sigalotti (CMAP, Ecole Polytechnique).

Bio: Francesco Boarotto was born in Verona, Italie, in 1988. He received the Master's degree in mathematics from the University of Padou, Italie, in 2012 and the Ph.D degree from SISSA, Trieste, Italie, in 2016. Since then he has been post-doc in CMAP - Ecole Polytechnique. His research interests include geometric control theory and sub-Riemannian geometry.

### S³ seminar : On Electromagnetic Modeling and Imaging of Defects in Periodic Fibered Laminates

**Zicheng LIU, (Inverse problems Group, Signals and Statistics Division, L2S Laboratory)**

Composite laminates are commonly utilized in industry due to advantages as high stiffness, light weight, versatility, etc. Multiple layers, each one involving periodically-positioned circular-cylindrical fibers in a given homogeneous matrix, are usually involved. However, defects can affect the structure and thereupon impact security and efficiency, and they call for nondestructive testing. By electromagnetic (EM) means, it requires fast and reliable computational modeling of both sound and damaged laminates if one wishes to better understand pluses and minuses of the testing, and derive efficient imaging algorithms for the end user. Both direct modeling and inverse imaging will be introduced in this presentation. For the former, since the periodicity of the structure is destroyed due to defects, methods based on the Floquet theorem are inapplicable. Two modeling approaches are then utilized: one is with supercell methodology where a fictitious periodic structure is fabricated, so as the EM field solution everywhere in space can be well approximately modeled, provided the supercell be large enough; the other is based on fictitious source superposition (FSS) where defects are treated as equivalent sources and the field solution is a summation of responses to the exterior source and equivalent ones. For imaging, with MUSIC and sparsity-based algorithm, missing fibers could be accurately located.

Biography: Zicheng LIU was born in Puyang, China, in October 1988. He received the M.S. degree in circuit and system from Xidian University, Xi’an, China in March 2014 and is currently pursuing the Ph.D. degree with the benefit of a Chinese Scholarship Council (CSC) grant at the Laboratoire des Signaux et Systèmes, jointly Centre National de la Recherche Scientifique (CNRS), CentraleSupélec, and Université Paris-Sud, Université Paris-Saclay, Paris, France. He will defend his Université Paris-Saclay Ph.D. early Fall 2017. His present work is on the electromagnetic modeling of damaged periodic fiber-based laminates and corresponding imaging algorithms and inversion. His research interests include computational electromagnetics, scattering theory on periodic structures, non-destructive testing, sparsity theory, and array signal processing.

### S³ seminar : On Imaging Methods of Material Structures with Different Boundary Conditions

**Xiuzhu YE, (Beihang University, Beijing, China)**

This talk is about the two-dimensional inverse scattering problems for different kinds of boundary conditions. Firstly, we propose a perfect electric conductor (PEC) inverse scattering approach, which is able to reconstruct PEC objects of arbitrary number and shape without requiring prior information on the approximate locations or the number of the unknown scatterers. Secondly, the modeling scheme of the T-matrix method is introduced to solve the challenging problem of reconstructing a mixture of both PEC and dielectric scatterers together. Then the method is further extended to the case of scatterers with four boundary conditions together. Last, we propose a method to solve the dielectric and mixed boundary through-wall imaging problem. Various numerical simulations and experiments are carried out to validate the proposed methods.

Biography: Xiuzhu YE was born in Heilongjiang, China, in December 1986. She received the Bachelor degree of Communication Engineering from Harbin Institute of Technology, China, in July 2008 and the Ph.D. degree from the National University of Singapore, Singapore, in April 2012. From February 2012 to January 2013, she worked in the Department E.C.E., National University of Singapore, as a Research Fellow. Currently, she is Assistant Professor in the School of Electronic and Information Engineering of the Beihang University. She has been and is engaged under various guises with Ecole Centrale de Pékin (ECPK) also. She is presently benefiting from an invited professorship position at University Paris-Sud and later this Summer 2017 she will be benefiting from an invited professorship position at CentraleSupélec, both within the Laboratoire des Signaux et Systèmes, jointly Centre National de la Recherche Scientifique (CNRS), CentraleSupélec, and Université Paris-Sud, Université Paris-Saclay, Gif-sur-Yvette, France. Her current research interest mainly includes fast algorithms in solving inverse scattering problems, near field imaging, biomedical imaging, and antenna designing.

### Séminaire d'Automatique du plateau de Saclay : Computation of Curvature Penalized Shortest Paths via the Fast Marching Algorithm

**Jean-Marie Mirebeau (Laboratoire de mathématique d'Orsay, Université Paris-Sud)**

Motivated by applications to motion planning and image segmentation, we consider shortest paths models with a curvature penalization, such as the Euler/Mumford elasticas, or the Reed-Shepp car with or without reverse gear. Our numerical strategy, for computing the path of minimal energy joining two given points, involves approximating these singular models using strongly anisotropic Riemannian or Finslerian metrics on the product space R^d x S^{d-1}. The associated eikonal equations are then solved via specialized variants of the Fast-Marching algorithm.

Bio. Jean-Marie Mirebeau est chargé de recherches au Laboratoire de mathématiques d'Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay. Ses travaux portent sur la résolution numérique des équations aux dérivées partielles, et en particulier sur les difficultés liées aux fortes anisotropies. C'est à dire à l'existence de directions privilégiées par le modèle, non alignées avec les axes de coordonnées. La conception de schémas pour ces modèles requiert des outils mathématiques peu communs en analyse, souvent issus de l'arithmétique et de la géométrie discrète. Son activité englobe l'étude théorique de la convergence et de la complexité des schémas numériques, leur implémentation et leur distribution en license libre, et le suivi de leur application via des collaborations académiques et industrielles. Jean-Marie Mirebeau a reçu le prix Popov 2016 pour ses contributions en théorie de l'approximation. Il était antérieurement affecté au laboratoire Ceremade de l'Université Paris-Dauphine, et a effectué sa thèse sous la direction d'Albert Cohen à l'Université Pierre et Marie Curie.