This talk is interested by delay differential inclusions in finite dimensional real space. The celebrated Filippov’s theorem is extended to this case. Then, this theorem is generalized to the case when the state variable is constrained to the closure of an open state subset. Under a new “inward pointing condition”, a relaxation result stating that the set of trajectories lying in the interior of the state constraint is dense in the set of constrained trajectories of the convexified inclusion is shown.

Bio. Ihab Haidar was born in Beirut, Lebanon, in 1983. He received the Master’s degree in mathematics from the University of Aix-Marseille 1, France, in 2008 and the Ph.D degree from the University of Montpellier 2, France, in 2011. Since then he has been post-doc in different places (Laboratoire des Signaux et Systèmes, Institut de Mathématiques de Jussieu, Laboratoire QUARTZ-ENSEA). His research interests include control theory, time delay systems and systems biology.

### Séminaire d'Automatique du plateau de Saclay : A relaxation result for state constrained delay differential inclusion

**Ihab Haidar (Laboratoire Quartz, ENSEA-CERGY)**

### S³ seminar : FastText: A library for efficient learning of word representations and sentence classification

**Piotr Bojanowski, (Facebook AI Research)**

In this talk, I will describe FastText, an open-source library that can be used to train word representations or text classifiers. This library is based on our generalization of the famous word2vec model, allowing to adapt it easily to various applications. I will go over the formulation of the skipgram and cbow models of word2vec and how these were extended to meet the needs of our model. I will describe in details the two applications of our model, namely document classification and building morphologically-rich word representations. In both applications, our model achieves very competitive performance while being very simple and fast.

### Séminaire d’Automatique du plateau de Saclay : Cooperative Control of Multi-Agents: On a Sphere Manifold and in the Euclidean Space

**Wei Li (Department of Control and Systems Engineering, Nanjing University)**

The talk will discuss cooperative control of multi-agents on a sphere and in the Euclidean space. We will first consider the control law design of agents on a sphere, and analyze the stability, scaling, and geometry properties, and discuss future directions. Then, for agents evolving in the Euclidean space, we will consider coupled agents with second-order dynamics. The state of a single agent includes both position and velocity, thus generally, the agents have both velocity coupling and position couplings (VCPC); and if we consider different VCPC, then interesting yet difficult problems arise. We then discuss two aspects of analysis on consensus convergence , and future directions.

Bio. Wei Li received the Ph.D. degree in Automatic Control from Shanghai Jiao Tong University, Shanghai, China, in 2008.

From 2009 to 2010, he was a Post-Doctoral Research Associate with the Department of Electrical Engineering, The University of Texas at Dallas, Dallas, TX, USA. Since 2010, he has been an Associate Professor with the Department of Control and Systems Engineering, Nanjing University, Nanjing, China. His current research interests include robotics, autonomous mobile robots, decentralized control, cooperative control of mobile robotic agents, and wireless sensor networks. Dr. Li is an Associate Editor of Asian Journal of Control. He is a Senior Member of IEEE.

### Séminaire d’Automatique du plateau de Saclay : Observer synthesis under time-varying sampling for Lipschitz nonlinear systems

**Lucien Etienne (L2S, CentraleSupelec)**

The problem of observation of continuous-time nonlinear Lipschitz systems under time-varying discrete measurements is studied. This class of systems naturally occurs when continuous processes are observed through digital sensors and information is sent via a network to a computer for state estimation. Since network introduces uncertainties in the sampling time, the observer must be designed so to take these uncertainties into account. Here two classes of observation scheme are studied. First an impulsive observers, which make instantaneous correction when information is received, is considered. Then a Luenberger-like observer with a piece wise constant correction term is studied. For both classes of observer, generic conditions are provided. Then a restriction of the generic conditions is used to establish tractable conditions that allows the synthesis of an observer gain.

Bio. Lucien Etienne received a M.Sc. Degree in Applied Mathematics at the INSA Rouen in 2012 and a joint Ph.D. in Automatic Control from the university of L'Aquila and the university of Cergy-Pontoise in 2016. After a Post-doc at INRIA Lille on observer synthesis for sampled data system, he is currently Post-doc at L2S CentralSupéléc working on switched systems for embedded control under mixed stochastic/deterministic timing uncertainty.

His research interests include switched and hybrid systems, Observer synthesis and sampled data systems.

### S³ seminar : Stochastic Quasi-Newton Langevin Monte Carlo

**Umut Şimşekli, (LTCI, Télécom ParisTech)**

Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC might suffer from poor mixing rates when random variables exhibit strong couplings under the target densities or big scale differences. In this talk, I will present a novel SG-MCMC method that takes the local geometry into account by using ideas from Quasi-Newton optimization methods. These second order methods directly approximate the inverse Hessian by using a limited history of samples and their gradients. Our method uses dense approximations of the inverse Hessian while keeping the time and memory complexities linear with the dimension of the problem. I will provide formal theoretical analysis where it is shown that the proposed method is asymptotically unbiased and consistent with the posterior expectations. I will finally illustrate the effectiveness of the approach on both synthetic and real datasets. This is a joint work with Roland Badeau, Taylan Cemgil and Gaël Richard. arXiv: https://arxiv.org/abs/1602.03442

### S³-PASADENA seminar : Detecting confounding in multivariate linear models via spectral analysis

**Dominik Janzing, Max Planck Institute for Intelligent Systems, Tuebingen, Germany**

We study a model where one target variable Y is correlated

with a vector X:=(X_1,...,X_d) of predictor variables being potential causes of Y.

We describe a method that infers to what extent the statistical dependences between X and Y

are due to the influence of X on Y and to what extent due to a hidden common cause

(confounder) of X and Y. The method is based on an independence assumption stating that, in the absence of confounding,

the vector of regression coefficients describing the influence of each X on Y has 'generic orientation'

relative to the eigenspaces of the covariance matrix of X. For the special case of a scalar confounder we show that confounding typically spoils this generic orientation in a characteristic way that can be used to quantitatively estimate the amount of confounding.

I also show some encouraging experiments with real data, but the method is work in progress and critical comments are highly appreciated.

Postulating 'generic orientation' is inspired by a more general postulate stating that

P(cause) and P(effect|cause) are independent objects of Nature and therefore don't contain information about each other [1,2,3],

an idea that inspired several causal inference methods already, e.g. [4,5].

[1] Janzing, Schoelkopf: Causal inference using the algorithmic Markov condition, IEEE TIT 2010.

[2] Lemeire, Janzing: Replacing causal faithfulness with the algorithmic independence of conditionals, Minds and Machines, 2012.

[3] Schoelkopf et al: On causal and anticausal learning, ICML 2012.

[4] Janzing et al: Telling cause frome effect based on high-dimensional observations, ICML 2010.

[5] Shajarisales et al: Telling cause from effect in deterministic linear dynamical systems, ICML 2015.

### Feedback transformations of underactuated mechanical systems for trajectory planning: case studies in non-prehensile manipulation

**Anton SHIRIAEV (Department of Engineering Cybernetics, NTNU, Norway)**

The talk is aimed at discussion of challenges present in developing model based trajectory planning algorithms for underactuated mechanical systems. Nonlinearity of system’s dynamics and presence of one or several passive degrees of freedom are among several structural properties that are difficult to handle in a trajectory search. Other challenges are related to different formats of representation of feasible trajectories, where some choices can be better suited for further stabilization or advantageous in sensitivity analysis with respect to uncertainty in system parameters. The author is interested to emphasize the attention on two relatively new points in the problem that have recently helped in solving a series of longstanding manipulation problems in robotics: change of coordinates and feedback transformation for mechanical systems are useful to formulate as dependent on an individual trajectory even though such a feasible behavior is not found yet. The arguments are illustrated by new analytical results and the case study in non-prehensile manipulation.

### Feedback transformations of underactuated mechanical systems for trajectory planning: case studies in non-prehensile manipulation

**Anton SHIRIAEV (Department of Engineering Cybernetics, NTNU, Norway)**

The talk is aimed at discussion of challenges present in developing model based trajectory planning algorithms for underactuated mechanical systems. Nonlinearity of system’s dynamics and presence of one or several passive degrees of freedom are among several structural properties that are difficult to handle in a trajectory search. Other challenges are related to different formats of representation of feasible trajectories, where some choices can be better suited for further stabilization or advantageous in sensitivity analysis with respect to uncertainty in system parameters. The author is interested to emphasize the attention on two relatively new points in the problem that have recently helped in solving a series of longstanding manipulation problems in robotics: change of coordinates and feedback transformation for mechanical systems are useful to formulate as dependent on an individual trajectory even though such a feasible behavior is not found yet. The arguments are illustrated by new analytical results and the case study in non-prehensile manipulation.

### Séminaire d’Automatique du plateau de Saclay : What drives the quality of local public goods in Africa? Disentangling social capital and ethnic divisions

**Guillaume Hollard (Département d’Economie, Ecole polytechnique)**

Two important lines of research shaped our understanding of the ability of communities to engage in collective action. The first line proposes ethnic division as a key determinant, with more ethnically heterogeneous countries having lower economic performances and levels of public goods. Thus, we expect to find better schools where ethnic fractionalization is low. The second line of research focuses on social capital as a major determinant of the ability to engage in collective action.We expect that trust among community members, a widely-used measure of social capital, is an important and positive determinant of school quality. The present work aims to disentangle the relative effects of ethnic fractionalization and social capital on school quality. We use instrumental variable estimations to address reverse causality and other endogeneity issues. We instrument both social capital and ethnic fractionalization by using historical information on the settlement patterns of ethnic groups in Sub-Saharan Africa. Our empirical strategy is implemented by combining four datasets, including Afrobarometer, covering 16 Sub-Saharan countries. We run our analysis at the district level, with more than 1000 districts covered. We find an important and positive effect of trust on the practical aspects of schooling, such as maintaining buildings or providing textbooks. A one percent increase in the level of trust increases the quality of local public goods by 0.18 to 1.05 percent, depending on the measure of school quality under consideration. In sharp contrast, ethnic fractionalization is found to have a very limited effect, if any. We propose a simple model of public good provision that explores a channel by which social capital and ethnic division may (or may not) have an impact on the provision of local public goods such as schools. Our results suggest that policies designed to enhance social capital are likely to have a positive effect on schools and local public goods in general.

Bio. Directeur de recherche au CNRS et professeur associé à l'école polytechnique. Spécialisé dans l'analyse de la décision et du comportement. Responsable du laboratoire d'économie expérimentale.

### Séminaire d’Automatique du plateau de Saclay : Moral hazard with mean field type interactions

**Thibault Mastrolia (CMAP, Ecole Polytechnique)**

We investigate a moral hazard problem in finite time with lump-sum and continuous payments, involving infinitely many Agents, with mean field type interactions, hired by one Principal. By reinterpreting the mean-field game faced by each Agent in terms of a mean field FBSDE, we are able to rewrite the Principal’s problem as a control problem for McKean-Vlasov SDEs. We solve completely and explicitly the problem in special cases, going beyond the usual linear-quadratic framework.

Bio. Après avoir effectué un magistère de mathématiques à l'université de Strasbourg puis le M2 MASEF de l'université Paris-Dauphine, j'ai poursuivi mes études par un doctorat au sein de cette université sous la direction d'Anthony Réveillac et de Dylan Possamaï autour du calcul de Malliavin, des EDSR et de leurs applications en finance. J'ai ensuite été recruté comme Maître de conférences en probabilités et mathématiques financières à l'Ecole Polytechnique. Actuellement, je travaille autour de problèmes de théorie des contrats et de leurs applications.

### S³ seminar : Inverse problems for speech production

**Benjamin Elie (LORIA, IADI)**

Studies on speech production are based on the extraction and the analysis of the acoustic features of human speech, and also on their relationships with the articulatory and phonatory configurations realized by the speaker. An interesting tool, which will be the topic of the talk, to make such researches is the articulatory synthesis, which consists in the numerical simulation of the mechanical and acoustical phenomena that are involved in speech production. The aim is to numerically reproduce a speech signal that contains the observed acoustic features with regards to the actual articulatory and phonatory gestures of the speaker. Using the articulatory approach may lead to a few problems that will be tackled in this talk, and to which possible solutions will be discussed. Firstly, the different articulatory gestures realized in natural speech should be precisely observed. For that purpose, the first part of the talk focuses on methods to acquire articulatory films of the vocal tract by MRI techniques with a fast acquisition rate via sparse techniques (Compressed Sensing). The aim is, in fine, to build an articulatory and a coarticulation model. The investigation of the acoustical phenomena involved in natural speech require to separate the contributions of the different acoustic sources in the speech signal. The periodic/aperiodic decomposition of the speech signal is the subject of the second part of the talk. The challenge is to be able to study the acoustic properties of the frication noise that is generated during the production of fricatives, and also to quantify the amount of voicing produced during fricatives. Finally, in order to directly use the analysis by synthesis methods, it is interesting to estimate the articulatory configurations of the speaker from the acoustic signal. This is the aim of the acoustic-articulatory inversion for copy synthesis, which is the third part of the talk. Direct applications of these problems for the study of speech production and phonetics will be presented.

### S³ Seminar: Adapting to unknown noise level in super-resolution

**Claire Boyer (LSTA, UPMC)**

We study sparse spikes deconvolution over the space of complex-valued measures when the input measure is a finite sum of Dirac masses. We introduce a new procedure to handle the spike deconvolution when the noise level is unknown. Prediction and localization results will be presented for this approach. An insight on the probabilistic tools used in the proofs could be briefly given as well.

### Séminaire d’Automatique du plateau de Saclay : Fokker-Planck optimal control for stochastic processes

**Mario Annunziato (Università degli Studi di Salerno)**

An innovative framework for the control of stochastic process by means of an optimization problem on the Fokker-Planck equation is presented. The time dependent probability density function (PDF) as representative of the dynamical state of a stochastic system is used, hence the governing Kolmogorov-Fokker-Planck-type (KFP) equation is employed as a constraint for the minimization of a cost function. The problem to find a controller that minimizes the cost function can be solved by solving an optimality system of time dependent forward and backward partial differential equations. A short review of control objectives, KFP equations and numerical techniques to tackle the optimization problem, is shown by using models from biology, physics, and finance.

Bio. Mario Annunziato is a researcher in Mathematics, in the field of Numerical analysis at "Università degli Studi di Salerno" since 2004. He is also a member of "Gruppo Nazionale di Calcolo Scientifico, Instituto Nazionale di Alta Mathemaica". He has received his Ph.D. degree in Physics at " Università degli Studi di Pisa" in 2000. He obtained a degree of laurea in Physics at "Rome University - La Sapienza" in 1995.

His research interests focus on numerical solutions of time dependent Partial Differential Equations (PDE) and Integral Equations, related to stochastic processes and stochastic optimal control.

### S³ seminar: High dimensional sampling with the Unadjusted Langevin Algorithm

**Alain Durmus (LTCI, Telecom ParisTech)**

Recently, the problem of designing MCMC sampler adapted to high-dimensional distributions and with sensible theoretical guarantees has received a lot of interest. The applications are numerous, including large-scale inference in machine learning, Bayesian nonparametrics, Bayesian inverse problem, aggregation of experts among others. When the density is L-smooth (the log-density is continuously differentiable and its derivative is Lipshitz), we will advocate the use of a “rejection-free” algorithm, based on the discretization of the Euler diffusion with either constant or decreasing stepsizes. We will present several new results allowing convergence to stationarity under different conditions for the log-density (from the weakest, bounded oscillations on a compact set and super-exponential in the tails to the log concave).

When the density is strongly log-concave, the convergence of an appropriately weighted empirical measure is also investigated and bounds for the mean square error and exponential deviation inequality for Lipschitz functions will be reported.

Finally, based on optimzation techniques we will propose new methods to sample from high dimensional distributions. In particular, we will be interested in densities which are not continuously differentiable. Some Monte Carlo experiments will be presented to support our findings.

### Séminaire d'Automatique du Plateau de Saclay : Extending spacecraft operational life: Challenges and opportunities for control

**Prof. Ilya Kolmanovsky (University of Michigan)**

To extend spacecraft operational life, control techniques that can accommodate actuator failures, reduce the use of fuel and avoid collisions with debris are of interest. Such techniques may need to exploit “higher order” physical effects, such as forces and torques normally considered as disturbances, approaches that can take advantage of nonlinearities in spacecraft kinematics and dynamics, and handle stationary and moving obstacle avoidance requirements. Hence spacecraft operational life extension problems create many potential opportunities for the application of nonlinear, optimal and constrained/predictive control.

After general remarks on control challenges and opportunities in spacecraft operational life extension problems, the presentation will focus on related recent case studies.

In particular, it will be shown that for a spacecraft with only two functioning reaction wheels linear controllability of attitude dynamics can be regained, under appropriate assumptions, if solar radiation pressure torques are included in the analysis. This conclusion can be exploited for handling reaction wheel failures based on conventional linear controllers. Alternative approaches that do not rely on the solar radiation pressure torques but exploit nonlinearities in the spacecraft kinematics and dynamics will also be discussed. Furthermore, an intriguing capability of model predictive controllers to achieve discontinuous stabilization in underactuated spacecraft attitude control problems will be highlighted. We will also touch upon coupled translational and rotational relative motion dynamics of a rigid spacecraft in central gravity field and potential opportunities to move translationally in space by employing attitude control only. In the final part of the presentation, drift counteraction optimal control problems for systems with drift and/or large disturbances will be introduced, in which the objective is to maximize the time for a system to violate prescribed constraints. Potential applications of drift counteraction optimal control, including for geostationary satellite orbit maintenance and drag induced orbit decay compensation, will be discussed.

### Gaussian Channels: I-MMSE at Every SNR

**Prof. Shlomo Shamai, The Andrew and Erna Viterbi Faculty of Electrical Engineering at the Technion-Israel Institute of Technology**

Multi-user information theory presents many open problems, even in the simple Gaussian regime. One such prominent problem is the two-user Gaussian interference channel which has been a long standing open problem for over 30 years. We distinguish between two families of multi-user scalar Gaussian settings; a single transmitter (one dimension) and two transmitters (two dimensions), not restricting the number and nature of the receivers. Our first goal is to fully depict the behavior of asymptotically optimal, capacity

achieving, codes in one dimensional settings for every SNR. Such an understanding provides important insight to capacity achieving schemes and also gives an exact measure of the disturbance such codes have on unintended receivers.

We first discuss the Gaussian point-to-point channel and enhance some known results. We then consider the Gaussian wiretap channel and the Gaussian Broadcast channel (with and without secrecy demands) and reveal MMSE properties that confirm "rules of thumb" used in the achievability proofs of the capacity region of these channels and provide insights to the design of such codes.

We also include some recent observations that give a graphical interpretation to rate and equivocation in this one dimensional setting.

Our second goal is to employ these observations to the analysis of the two dimensional setting. Specifically, we analyze the two-user Gaussian interference channel, where simultaneous transmissions from two users interfere with each other. We employ our understanding of asymptotically point-to-point optimal code sequences to the analysis of this channel. Our results also resolve the "Costa Conjecture"

(a.k.a the "missing corner points" conjecture), as has been recently proved by Polyanskiy-Wu, applying Wasserstein Continuity of Entopy.

The talk is based on joint studies with R. Bustin, H. V. Poor and R. F. Schaefer.

### Scalable Techniques for Quantum Network Engineering

**Dr. Nikolas Tezak (Stanford University)**

In the quest for creating "quantum enhanced" systems for information processing currently pursued design strategies are unlikely to scale significantly beyond a few dozen qubits. The dominant design paradigm relies on a vast overhead of external classical control. In this talk we argue for an integrated framework that treats quantum and hybrid quantum-classical systems on equal footing.

We have recently defined a Quantum Hardware Description Language (QHDL) capable of describing networks of such interconnected quantum systems. QHDL is compiled to symbolic system models by a recently developed symbolic software tool suite named QNET. We discuss an example of a recently proposed autonomous Quantum Error Correction circuit with coherently embedded control systems.

Finally, we present a model transformation capable of dividing the description of quantum states into quasi-classical coordinates living on a low-dimensional manifold coupled to a lower complexity quantum state. This approach (QMANIFOLD) is in principle exact and naturally tailored to simulating coupled quantum systems with varying degrees of dissipation.

Bio. Nikolas Tezak is a post-doc in Stanford University's Applied Physics Department, where he works with Hideo Mabuchi. He recently completed his PhD under Professor Mabuchi’s supervision. He also works part-time at Hewlett Packard Laboratories in the Large Scale Integrated Photonics group led by Ray Beausoleil. In November 2016, he will join Rigetti Computing (Berkeley, California) in their quest to build a quantum computer.

### S³: Material-by-Design for Synthesis, Modeling, and Simulation of Innovative Systems and Devices

**Giacomo Oliveri (ELEDIA, University of Trento)**

Several new devices and architectures have been proposed in the last decade to exploit the unique features of innovative artificially-engineered materials (such as metamaterials, nanomaterials, biomaterials) with important applications in science and engineering. In such a framework, a new set of techniques belonging to the Material-by-Design (MbD) framework [1]-[5] have been recently introduced to synthesize innovative devices comprising task-oriented artificial materials. MbD is an instance of the System-by-Design paradigm [6][7] defined in short as “How to deal with complexity”. More specifically, MbD considers the problem of designing artificial-material enhanced-devices from a completely new perspective, that is "The application-oriented synthesis of advanced systems comprising artificial materials whose constituent properties are driven by the device functional requirements". The aim of this seminar will be to review the fundamentals, features, and potentialities of the MbD paradigm, as well as to illustrate selected state-of-the-art applications of this design framework in sensing and communications scenarios.

Bio: Giacomo Oliveri received the B.S. and M.S. degrees in Telecommunications Engineering and the PhD degree in Space Sciences and Engineering from the University of Genoa, Italy, in 2003, 2005, and 2009 respectively. He is currently an Tenure Track Associate Professor at the Department of Information Engineering and Computer Science (University of Trento), Professor at CentraleSupélec, member of the Laboratoire des signaux et systèmes (L2S)@CentraleSupélec, and member of the ELEDIA Research Center. He has been a visiting researcher at L2S, Gif-sur-Yvette, France, in 2012, 2013, and 2015, and he has been an Invited Associate Professor at the University of Paris Sud, France, in 2014. In 2016, he has been awarded the "Jean d'Alembert" Scholarship by the IDEX Université Paris-Saclay. He is author/co-author of over 250 peer-reviewed papers on international journals and conferences, which have been cited above 2200 times, and his H-Index is 26 (source: Scopus). His research work is mainly focused on electromagnetic direct and inverse problems, system-by-design and metamaterials, compressive sensing techniques and applications to electromagnetics, and antenna array synthesis. Dr. Oliveri serves as an Associate Editor of the International Journal of Antennas and Propagation, of the Microwave Processing journal, and of the International Journal of Distributed Sensor Networks. He is the Chair of the IEEE AP/ED/MTT North Italy Chapter.

### Some results on the existence of equilibria and stability of dc linear networks with constant power loads.

**Prof. Robert Griñó, Polytechnic University of Catalonia**

The presentation will show some results on the existence of equilibria in dc electrical networks that supply to constant power loads (CPLs). Specifically, a necessary condition for the existence, which is also sufficient for the case one and two CPLs, will be presented. Besides, a sufficient condition, based on the negative imaginary systems concept, that assures local stability for all the range of possible equilibria will be shown for the case of a dc linear network with a single ideal or finite-bandwidth CPL.

### Singular perturbations for hyperbolic port-Hamiltonian and non-hyperbolic systems

**Prof. Jacquelien Scherpen, University of Groningen**

In this talk we explore the methodology of model order reduction based on singular perturbations for a fexible-joint robot within the port-Hamiltonian framework. We show that a fexible-joint robot has a port-Hamiltonian representation which is also a singularly perturbed ordinary differential equation. Moreover, the associated reduced slow subsystem corresponds to a port-Hamiltonian model of a rigid-joint robot. To exploit the usefulness of the reduced models, we provide a numerical example where an existing controller for a rigid robot is implemented. In addition, we provide ideas on how to expand this to planar slow-fast systems at a non-hyperbolic point. At these type of points, the classical theory of singular perturbations is not applicable and new techniques need to be introduced in order to design a controller that stabilizes such a point. We show for some class of nonlinear systems that using geometric desingularization (also known as blow up), it is possible to design, in a simple way, controllers that stabilize non-hyperbolic equilibrium points of slow-fast systems. The results are exemplified on the Van der Pol oscillator.

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