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)**

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### A Delay-Based Sustained Oscillator : Oregonator Based Model

**Hakki Ulas UNAL (L2S, Anadolu University)**

Many metabolic and physiological processes occur in some periodic fashion. The phenomena has been known for a long time, however, the underlying mechanism of such oscillatory behaviour has not been fully understood. Belousov-Zhabotinskii reaction, which exhibits oscillatory behaviour that are analogous to ones observed in certain biological systems, is often utilized to better understand the oscillatory mechanism in these systems. The reaction is very complicated, however, its oscillatory behaviour is described by a simple model, called Oregonator. By the mass-action kinetics, the model can be described by three variables, which correspond to concentration of some chemical reactants. In this talk, delay-based Oregonator model obtained by the use of delay-mass-action kinetics will be discussed. Some qualitative analysis on the model will also be presented.

### Mass-Action Kinetic Models

**VijaySekhar Chellaboina, (Mahindra Ecole Centrale)**

In this talk, we present a general construction of the mass-action kinetic equations in a state-space form. Next, we discuss the nonnegativity of solutions to the kinetic equations and the inverse problem of constructing a reaction network having specified essentially non- negative dynamics. The problem of reducibility of the kinetic equations is next considered as well as the stability of the equilibria of the kinetic equations. Specifically, Lyapunov methods are employed to show boundedness and convergence of solutions. Finally, the zero deficiency result for mass-action kinetics in standard matrix terminology is presented.

### Séminaire d'Automatique du Plateau de Saclay : Robust perfomance by a stable controller for infinite-dimensional plants

**Hakki Ulas Unal (Anadolu University)**

In a feedback system, besides the stabilization, the controllers are often designed to meet some performance specifications defined by H∞ norm minimization of corresponding sensitivity functions. From the practical point of view, if it is possible, it is desired the controller to be designed is stable. In this work, stable controller design to minimize the H∞ norm of the corresponding sensitivity function in a feedback system with a single-input single-output biproper infinite-dimensional real plant is considered. The plant may have infinitely many poles and simple zeros in the right-half-plane, however, its zeros are assumed to satisfy some growth condition. Interpolation-based approach will be used to design such a controller and a numerical example will be presented.

### Séminaire d'Automatique du Plateau de Saclay :On Control Lyapunov-Krasovskii Functionals and Stabilization in the Sample-and-Hold Sense of Nonlinear Time-Delay Systems

**Pierdomenico Pepe (Università degli Studi dell'Aquila)**

This talk deals with the stabilization in the sample-and-hold sense of nonlinear systems described by retarded functional differential equations. The notion of stabilization in the sample-and-hold sense has been introduced in 1997 by Clarke, Ledyaev, Sontag and Subbotin, for nonlinear delay-free systems. Roughly speaking, a state feedback (continuous or not) is said to be a stabilizer in the sample-and-hold sense if, for any given large ball and small ball of the origin, there exists a suitable small sampling period such that the feedback control law obtained by sampling and holding the above state feedback, with the given sampling period, keeps uniformly bounded all the trajectories starting in any point of the large ball and, moreover, drives all such trajectories into the small ball, uniformly in a maximum finite time, keeping them in, thereafter. In this talk suitable control Lyapunov-Krasovski functionals will be introduced and suitable induced state feedbacks (continuous or not), and it will be shown that these state feedbacks are stabilizers in the sample-and- hold sense, for fully nonlinear time-delay systems. Moreover, in the case of time-delay systems, implementation by means of digital devices often requires some further approximation due to non availability in the buffer of the value of the system variables at some past times, as it can be frequently required by the proposed state feedback. In order to cope with this problem, well known approximation schemes based on first order splines are used. It is shown, for fully nonlinear retarded systems, that, by sampling at suitable high frequency the system (finite dimensional) variable, stabilization in the sample-and-hold sense is still guaranteed, when the holden input is obtained as a feedback of the (first order) spline approximation of the (infinite dimensional) system state, whose entries are available at sampling times, and the state feedback is Lipschitz on any bounded subset of the Banach state space

### Séminaire d'Automatique du Plateau de Saclay : Optimal control and Lyapunov functions applied to the satellite attitude control

**Nadjim Horri (Coventry University)**

The use of Lyapunov functions is generally limited to proving the stability of a system with a given control law. In this presentation, Lyapunov functions are used to formulate optimal control problems as pointwise nonlinear programmes. These optimisation problems are equivalent to inverse optimal control problems. This approach is applied to satellite attitude control. The optimal attitude control problems under consideration will be the minimisation of the norm of the control torque subject to constraints on the convergence rate of a Lyapunov function. This approach improves the tradeoff between rapidity and energy consumption compared to a benchmark controller, which is taken to be a PD type controller without loss of generality. The phase space trajectories show that the solutions to some fundamental open loop optimization problems are particular cases of optimal control problem formulations based on the convergence rates of Lyapunov functions. This is the case of the minimum time single axis attitude control problem, which is a special case of the problem of maximizing the convergence rate of a Lyapunov function under maximum torque limitations. It is also the case of the problem of minimising toque for fixed manoeuvre time. The solution to this problem is a particular case of the problem of minimizing the norm of the control torque under a Lyapunov convergence rate constraint.

### Séminaire d'Automatique du Plateau de Saclay : Inverse optimal control: the sub-Riemannian case

**Frédéric Jean (ENSTA)**

An inverse control problem is formulated as follows: given a set of trajectories and a control system, find a cost such that these paths are optimal. The first question to ask is the uniqueness of the solution of such a problem. For general classes of costs the problem appears to be very difficult, even with a trivial dynamics. We are therefore interested in this issue for the class of costs which are quadratic in the control, when the dynamics depend linearly in the control (Riemannian and sub-Riemannian case). In this case we can reduce the problem to the question of the existence of geodesically equivalent metrics and the existing results will be described, from the theorem of Levi-Civita (1890) to those we obtained recently with Sofya Maslovskaya and Igor Zelenko.

### Control of Fuel Cell Hybrid Power Systems

**Prof. Jian Chen, College of Control Science and Engineering, Zhejiang University, Hangzhou, China**

with the environment and energy crisis worsening, fuel cells have shown signiﬁcant potential as an alternative energy conversion device with high efﬁciency and low environmental impact. In particular, Fuel cells are promising for new energy automotive applications. Fuel cell hybrid power systems usually include fuel cells and lithium-Ion batteries. In this presentation, I will talk about control of fuel cell systems, SOC Estimation of Lithium-Ion Batteries, and adaptive control strategies of fuel cell/battery hybrid power systems.

Biography: Jian Chen (M’06-SM’10) received the B.E. and M.E. degrees from Zhejiang University, Hangzhou, China, in 1998 and 2001, respectively, and the Ph.D. degree from Clemson University, South Carolina, USA, in 2005. From 2006 to 2008, he was as a research fellow working on fuel cell modeling and control at the University of Michigan, Ann Arbor, MI, USA. He joined IdaTech LLC, Oregen, USA, working on fuel cell back power systems and Proterra Inc., South Carolina, USA, working on the National Fuel Cell Bus Program, in 2008 and 2012, respectively. In 2013, he joined the Department of Control Science and Engineering, Zhejiang University, Hangzhou, China. Dr. Chen is currently a professor with the College of Control Science and Engineering, Zhejiang University, Hangzhou, China. He has been supported by the Chinese Recruitment Program of Global Youth Experts since 2012 and received the Major Program of National Natural Science Foundation of China on Modeling and Control of Fuel Cell vehicles in 2014. His research interests include fuel cell modeling and control, battery management, visual servo techniques, and nonlinear control.

### Séminaire d'Automatique du Plateau de Saclay: Virtual Inertia Emulation and Placement in Power Grids

**Florian Dörfler (ETH Zurich)**

A major transition in the operation of electric power grids is the replacement of bulk generation based on synchronous machines by distributed generation based on low-inertia power electronic sources. The accompanying "loss of rotational inertia" and the fluctuations by renewable sources jeopardize the system stability, as testified by the ever-growing number of frequency incidents. As a remedy, numerous studies demonstrate how virtual inertia can be emulated through various devices, but few of them address the question of "where" to place this inertia. It is however strongly believed that the placement of virtual inertia hugely impacts system efficiency, as demonstrated by recent case studies. We carry out a comprehensive analysis in an attempt to address the optimal inertia placement problem, considering a linear network-reduced power system model along with an H2 performance metric accounting for the network coherency. The optimal inertia placement problem turns out to be non-convex, yet we provide a set of closed-form global optimality results for particular problem instances as well as a computational approach resulting in locally optimal solutions. We illustrate our results with a three-region power grid case study and compare our locally optimal solution with different placement heuristics in terms of different performance metrics.

### Séminaire d'Automatique du Plateau de Saclay: A modular design of incremental Lyapunov functions for microgrid control

**Claudio De Persis (Groningen University)**

In this talk we propose a Lyapunov based analysis of microgrids. The starting point is an energy function comprising the kinetic energy associated with the elements that emulate the rotating machinery and terms taking into account the reactive power stored in the lines and dissipated on shunt elements. We then shape this energy function with the addition of an adjustable voltage-dependent term, and construct incremental storage functions satisfying suitable dissipation inequalities. The choice of the voltage-dependent term depends on the voltage dynamics/controller under investigation. Several microgrids dynamics that have similarities or coincide with dynamics already considered in the literature are captured in this incremental energy analysis framework. These incremental storage functions allow for a complete analysis of the coupled microgrid obviating the need for simplifying linearization techniques and for the restrictive decoupling assumption in which the frequency dynamics is fully separated from the voltage one.