# Seminars - MAC

Seminars in Toulouse in which MAC team members are involved.

Retour à la page web de l'équipe MAC | Back to the english web page of MAC team |

Link to 2018 events | Main events before 2018 |

9 March 2019, 2pm, ENSEEIHT__Seminar SPOT__

14h - Augustin Cosse (ENS Paris)

3 March 2019, 9am, Salle du conseil**„Revisiting the Dual Iteration“ and „Controller Design via Experimental Exploration with Robustness Guarantees“**

by Tobias Holicki

Abstract: In this talk we consider two topics that recently caught my interest. The first one is the dual iteration as developed by Iwasaki which is a heuristic approach, e.g., for the challenging design of static output-feedback controllers. We reconsider the essential ingredients of the dual iteration and provide a novel control theoretic interpretation of the individual steps. The latter interpretation paves the way for an extension of the powerful scheme to situations where it was not used before. The second topic is on a systematic controller design approach for an unknown linear system with improved closed-loop performance if compared to a standard robust design. This is achieved by tuning the controller parameters based on closed-loop experiments while guaranteeing safe operation. We employ linear fractional representations in order to systematically incorporate prior knowledge on the unknown system and apply techniques from robust control with existing relaxations in order to cope with the emerging robust multi-objective synthesis problems. The approach is illustrated by means of several numerical examples.

3 February 2019, 2pm, ENSEEIHT__Seminar SPOT__

14h - Mateusz Skomra (ENS Lyon)

4 December 2019, 2pm, salle Europe**Almost Everywhere Conditions for Hybrid Lipschitz Lyapunov Functions**

by Matteo Della Rossa

CDC19-FRC18.1

Abstract: We introduce a class of locally Lipschitz continuous functions to establish stability of hybrid dynamical systems. We provide a set of assumptions on the system that permits us to propose sufficient conditions on the candidate Lyapunov function that need to be verified only on a dense set, using the gradient and without the necessity of relying on generalized gradients, in the sense of Clarke or otherwise. We discuss the relevance of the stated assumptions with the help of some counterexamples, underlining the subtlety of the proposed relaxation. As an application of our result, we study the stability of a classical example from the reset control literature: the Clegg integrator model, with almost everywhere differentiable convex and nonconvex Lyapunov functions.

**Magnetic Force Modelling and Nonlinear Switched Control of an Electromagnetic Actuator**

by Flavien Deschaux

CDC19-WEB14.1 -

Abstract: This paper presents the magnetic force modelling of a typical electromagnetic valve actuator system. In this work, the objective is to take into account two important features: the magnetic saturation phenomenon which is a physical problem and the positivity constraint of the magnetic force. Those issues are addressed with a switch modelling approach. The first proposed control law proves the stability in a limited set and the second one ensure the global stability of the closed loop system. For both controllers, the main part of the control consists of a two steps backstepping control, a first controller regulates the mechanical part depending on the expression of the magnetic force. And a second controller controls the coil current and the magnetic force implicitly. An illustrative example shows the effectiveness of the approach.

**Free-Matrices Min-Projection Control for High Frequency DC-DC Converters**

by Mathias Serieye

CDC19 - WEC19.3 -

Abstract: This paper deals with the stabilization of high frequency DC-DC converters. This kind of systems can be modeled as switched affine systems subject to a periodic sampled-data control implementation. The dynamics of these systems is expressed using the delta-operator in order to cope with high frequency switching control constraints. The novelties of this paper, first, relies on the formulation of a free-matrices based min-projection control law, that allows the selection of the mode to be activated, based on the knowledge of the state variables. Second, the stability theorem, expressed in terms of a tractable optimization problem, that guarantees a practical stability result to a set and delivers the optimal control law that minimizes the volume of this one. The method is then illustrated through the control of a high frequency boost converter.

**Inner Approximations of the Maximal Positively Invariant Set for Polynomial Dynamical Systems**

by Matteo Tacchi

CDC19 - THA16.1 -

Abstract: The Lasserre or moment-sum-of-square hierarchy of linear matrix inequality relaxations is used to compute inner approximations of the maximal positively invariant set for continuous-time dynamical systems with polynomial vector fields. Convergence in volume of the hierarchy is proved under a technical growth condition on the average exit time of trajectories. Our contribution is to deal with inner approximations in infinite time, while former work with volume convergence guarantees proposed either outer approximations of the maximal positively invariant set or inner approximations of the region of attraction in finite time.

29 November 2019, 2:00pm, Salle du conseil**Robust stabilizing controllers with avoidance properties (for linear systems with nontrivial drift)**

by Philipp Braun

Abstract: For linear and nonlinear dynamical systems, control problems such as feedback stabilization of target sets and feedback laws guaranteeing obstacle avoidance are topics of interest throughout the control literature. While the isolated problems (i.e., guaranteeing only stability or avoidance) are well understood, the combined control problem guaranteeing stability and avoidance simultaneously is leading to significant challenges even in the case of linear systems. In this talk we highlight difficulties in the controller design with conflicting objectives in terms of guaranteed avoidance of bounded sets and asymptotic stability of the origin. In addition, using the framework of hybrid systems, we propose a partial solution to the combined control problem for underactuated linear systems with nontrivial drift.

19 November 2019, 10:30am, Salle Tourmalet**Computational approach to property (T)**

by Marek Kaluba

Abstract: It has been a longstanding open question in Geometric Group Theory whether Aut(Fn), the group of automorphisms of free group has Kazhdan property (T). The property for this particular group (and the associated Kazhdan constant) has far reaching consequences including the efficiency of non-deterministic algorithms for finite groups. During the talk I will briefly discuss the the theoretical results of Ozawa which make the computational approach to the Kazhdan property (T) possible. It is known that property (T) is equivalent to positivity of certain operator in the full group *-algebra. Surprisingly, this positivity is equivalent to the existence of a sum of (hermitian) squares decomposition of the operator in the real group ring. This in turn is equivalent to the feasibility of a certain semi-definite optimisation problem. I will describe the algorithm encoding the optimisation problem, and how an (imprecise) numerical solution can be turned into a mathematical proof by using the order structure and the topology of cones in group rings. This leads to constructive computer-assisted proof that Aut(F5) has Kazhdan's property (T). An example computation can be seen here: https://nextjournal.com/kalmar/property-t-in-julia. The talk is based on our paper arXiv:1712.07167, which is a joint work with Piotr W. Nowak (IMPAN, Warsaw) and Narutaka Ozawa (RIMS, Kyoto).

4 November 2019, 2pm, ENSEEIHT__Seminar SPOT__

14h - Pierre-Antoine Absil (Université Catholique de Louvain) - Optimization on manifolds: methods and applications

15h - Victor Magron (LAAS-CNRS Toulouse) - The quest of efficiency and certification in polynomial optimization

19 September 2019, 9:30am, Salle Tourmalet**Output feedback stabilization of non-uniformly observable control systems**

by Lucas Brivadis

Abstract: When only part of the state of a control system is known, state stabilizing feedback cannot be directly implemented. One must achieve output feedback stabilization instead. A sufficient condition for a (globally) state feedback stabilizable control system to be (semi-globally) output feedback stabilizable is the uniform observability of the system, that is observability for all input. However, it is not generic for control systems to be uniformly observable. Investigating this issue, one can distinguish two cases of study: either the system is not uniformly observable, but the target point corresponds to an input that makes the system observable, either the control is singular at the target point. In the former case, we show how a smooth additive perturbation of the state stabilizing feedback allows to get observability along the trajectories of the closed-loop system. Also, if the system is dissipative, no perturbation is needed to achieve dynamic output feedback stabilization. In the latter case, we show on an example how to immerse the original system into a dissipative one, either finite or infinite dimensional. This strategy allows to achieve dynamic output feedback stabilization.**Synthèse d’un observateur de dimension finie pour un système de dimension infinie**

by Mathieu Bajodek

Abstract: Observer l’état de systèmes de dimension infinie consiste à reconstituer la solution d’une EDP sans connaître ses conditions initiales. De nombreux observateurs existent en dimension infinie mais ne peuvent pas être implémentés numériquement. Il est donc nécessaire de synthétiser des observateurs de dimension finie qui garantissent la convergence de la solution. Une nouvelle technique de synthèse d’observateurs, basée sur les polynômes de Legendre, est alors présentée. D’abord, nous détaillerons les étapes de cette méthode générique : la discrétisation en amont du système de dimension infinie sur la base orthogonale des polynômes de Legendre puis la construction d’un observateur de typre : e Luenberger sur le nouveau système à l’aide des outils de dimension finie. Ensuite, nous appliquerons cette synthèse d’observateur à une EDP linéaire du premier ordre : l’équation de transport. Nous montrerons que la synthèse du gain d’observation revient à résoudre une inégalité matricielle linéaire. Enfin, nous illustrerons à l’aide de quelques exemples les performances obtenues à l’aide de cet observateur.**Free-matrices min-projection control for high frequency DC-DC converters**

by Mathias Serieye

Abstract: This paper deals with the stabilization of high frequency DC-DC converters. This kind of systems can be modeled as switched affine systems subject to a periodic sampled-data control implementation. The dynamics of these systems is expressed using the $\delta$-operator in order to cope with high frequency switching control constraints. The novelties of this paper, first, relies on the formulation of a free-matrices based min-projection control law, that allows the selection of the mode to be activated, based on the knowledge of the state variables. Second, the stability theorem, expressed in terms of a tractable optimization problem, that guarantees a practical stability result to a set and delivers the optimal control law that minimizes the volume of this one. The method is then illustrated through the control of a high frequency boost converter.

16-18 September 2019, Institut de Mathématiques de Toulouse**Control and stabilization issues for PDE**

11 September 2019, 2pm, Salle Vignemale**L1-induced norm analysis of positive systems and its application**

by Yoshio Ebihara

Abstract: In this talk we start from the basics about linear copositive Lyapunov functions for positive systems, followed by the characterization of the L1-induced norm of

positive systems by means of linear inequalities (linear programming problems). We show that, a slightly generalized version, weighted L1-induced norm, is useful for the stability analysis of interconnected systems constructed from positive subsystems. More precisely, we show that the interconnected system is stable if and only if there exists a set of weighting vectors that renders the weighted L1-induced norm of each positive subsystem smaller than one. We show that this result can be applied to the stability margin analysis problem of the Foschini-Miljanic algorithm for power control in wireless networks.

9 September 2019, 2pm, ENSEEIHT__Seminar SPOT__

Simone Naldi (Université de Limoges) – Infeasibility certificates in conic programming

2 September 2019, 2:00pm, LAAS - Salle Vignemale**Periodic Event-Triggered Control for Extended Plants**

by Hiroyuki Ichihara

Abstract: This talk presents a method for output feedback control that guarantees asymptotic stability for extended plants of linear discrete-time systems with a periodic event-triggering condition based on the output error. The proposed formulation does not need any approximation while conventional methods of static feedback control design require some approximations in matrix inequality conditions. As a configuration of output feedback controllers without another triggering condition for the input signals, we introduce the extended plant that consists of the original plant and a filter that generates the input of the plant from an auxiliary input. Then the proposed static output feedback controller gives the auxiliary input from the triggered output signal of the plant. Numerical examples illustrate the effectiveness of the proposed event-triggered control.

23 July 2019, 10:00am, LAAS - Salle Europe**Advances in Autonomous Guidance, Navigation and Control for Miniaturized Distributed Space Systems**

by Simone D'Amico

Abstract: Two key trends are revolutionizing the way humans conduct spaceflight, namely, the miniaturization of satellites (e.g., micro- and nano-satellites) and the distribution of payload tasks among multiple coordinated units (e.g., formation-flying, on-orbit servicing, fractionation, swarms). The combination of these approaches promises breakthroughs in space science (e.g., imaging of earth-like planets, characterization of gravitational waves), remote sensing (e.g., synthetic aperture radar interferometry, aeronomy, gravimetry), and space exploration (e.g., lifetime extension, assembly of structures, space debris removal).

Irrespective of the specific application, future miniature distributed space missions require a high level of autonomy to maintain and reconfigure the relative motion of the participating vehicles within the prescribed accuracy and range of operations. Especially on small spacecraft, these requirements are hard to meet due to the limited resources, and the chief goal of current research and development is to pave the way for the autonomous Guidance, Navigation & Control (GN&C) of “self-driving nanosatellites”. Leveraging the author’s contributions to the most recent satellite formation-flying and rendezvous missions in low earth orbit (TanDEM-X, PRISMA, BIROS), this presentation addresses the astrodynamics and GN&C algorithms under developments to enable a new class of space instruments. A novel low-cost mission concept developed by the author is introduced, the so-called miniaturized Distributed Occulter/Telescope (mDOT). mDOT consists of two small formati! on-flying satellites precisely positioned in high elliptical orbit to directly image exozodiacal dust and exoplanets. Finally, the high-fidelity hardware-in-the-loop virtual reality and physical testbed under development at Stanford for the verification of the new GN&C algorithms is presented.

11 July 2019, 9:30am, LAAS - Salle de Conférences**Commande hybride pour des convertisseurs de puissance**

by Sabrina Hadjeras

Abstract: This thesis proposes the design of hybrid control laws for power electronics converters. These new type of control laws are based on some hybrid models which capture the macroscopic dynamical behaviors of such electronic devices, essentially its hybrid nature. In the context of the regulation of DC-DC or AC-DC converters, applying the hybrid dynamical theory, the proposed control laws are proved to ensure the stability of the closed loop as well as some LQ performances. For a half-bridge inverter (DC-AC converter), a hybrid control law is proposed in order that the output voltage tracks a desired sinusoidal reference. In the case of unknown load, an adaptive control law is coupled to the hybrid control allowing the estimation of the load and therefore leading to a more precise regulation or tracking. Notice that in order to achieve a perfect regulation or tracking, an infinite frequency is often mandatory for the proposed control laws, which is inappropriate in practice. To tackle this problem, a space- or time-regularization are added to the hybrid closed-loop ensuring a dwell time between two consecutive jumps and reducing thus drastically the switching frequency.

8 July 2019, 2:00pm, LAAS - Salle de Conférence**Stability analysis of coupled ordinary differential systems with a string equation - Application to a Drilling Mechanism**

by Matthieu Barreau

Abstract: This thesis is about the stability analysis of a coupled finite dimensional system and an infinite dimensional one. The generic analysis of such systems is complex, mainly because of their different nature. The analysis is conducted using a Lyapunov-based methodology and the more recent Quadratic Separation framework. Using the projections of the infinite dimensional state on a basis of polynomials, it is possible to take into account the coupling between the two systems. That results in tractable and reliable numerical tests with a moderate conservatism. Moreover, a hierarchy on the stability conditions is shown. The real application to a drilling mechanism is proposed to illustrate the efficiency of the method and it opens new perspectives.

3 July 2019, 10:30am, LAAS - Salle Europe**A Julia modeling layer for the Generalized Moment Problem**

by Tillmann Weisser

Abstract: Educational Background/Employment: since 2018 - Postdoc at T-5/CNLS, Los Alamos National Laboratory. 2015-2018 - Ph.D. at LAAS-CNRS and University Toulouse 3 Paul Sabatier, Toulouse, France. 2008-2016 - Staatsexamen (teaching degree), University of Konstanz, Germany. 2011-2015 - Diplom (M.S. Mathematics), University of Konstanz, Germany. Research Interests: My research interests are focussing around algorithms and applications of the Generarlized Moment Problem (GMP) and Positive Polynomials. The GMP is an infinite dimensional linear optimization problem on the space of (fintie, positive) Borel measures and has an incredible modelling power: to name only two recent applications, the GMP can describe solutions to hyperbolic PDEs as well as the probability of a semi-algebraic set. I love the flexibility of this problem formulation and am always keen on discovering new fields of application. Positive Polynomials and more precisely Certificates for Non-Negativity are key to numerically approximate solutions to the GMP. Currently computing these certificates is quite costly and usually involves solving Semi-Definite Programs (SDP). In order to push forward applications of the GMP to real world applications, I investigate possibilities to reduce this computational burden by proposing alternative certificates that usually exploit some feature of the particular instance of the GMP such as algebraic or geometric properties.

1 July 2019, 10:30am, LAAS - Salle Tourmalet**Extracting Information from Moments: Positivity Certification, Polynomial Systems Resolution and Generalized Christoffel-Darboux Kernels**

by Ngoc Hoang Mai

Abstract: In this talk, I will present the three main research results obtained during my Master’s internship. The first result provides a new representation of polynomials which are nonnegative on non-compact semialgebraic sets, together with applications to polynomial optimization. These representations generalize both Reznick’s decomposition of positive definite forms as sums of squares of rational functions with uniform denominators and Putinar’s representation of positive polynomials on compact semialgebraic sets. The second result is an algorithm to find at least one real solution of a given system of polynomial equations. This algorithm is built upon the difference rate of a function involving the polynomials of the system, the logarithm function and the exponential function, and it does not depend on the total degree of the system. We illustrate the efficiency of the algorithm via numerical benchmarks. The third result is the design of a new numerical method to extract information from the moments of a given signed atomic measure. The underlying algorithm relies on level sets of perturbed Christoffel functions combined with Newton’s method. We illustrate this method with numerical experiments in low-dimensional spaces and show how to apply this method to extract the solutions of polynomial optimization problems.

1 July 2019, 10:00am, LAAS - Salle Tourmalet**Stabilization of the KdV equation**

by Florent Koudohode

Abstract: The study of the Korteweg-de Vries equation, which models waves on shallow water surfaces, has known an increased interesed since decades. In this seminar, we will focus on a particular topic, which is the stabilization of the Korteweg-de Vries equation. We prove the small-time global stabilization of the Korteweg-de Vries equation with three controls. To achieve this, we split the proof into two steps : the global “approximate stabilization », which consists in using the nonlinear term together with the « Phantom tracking method » to build a time-varying feedback law yielding the state very close to 0, and the “small time local stabilization » obtained thanks to a feedback built with the backstepping method and applied to the linearized version of the Korteweg-de Vries equation.

1 July 2019, 2pm, ENSEEIHT__Seminar SPOT__

Bachir El Khadir – Princeton Univ, USA - Power and Limitations of Sum of Squares Programming for Stability Analysis of Dynamical Systems

Tillmann Weisser – Los Alamos Nat Lab, USA - Relaxations and Uncertainty Quantification for the Power Grid

27 June 2019, 2:30pm, LAAS - Salle Tourmalet**Sparse coding by spiking neural networks: Convergence theory and computational results**

by Ping Tak Peter Tang

Abstract: In a spiking neural network (SNN), individual neurons operate autonomously and only communicate with other neurons sparingly and asynchronously via spike signals. These characteristics render a massively parallel hardware implementation of SNN a potentially powerful computer, albeit a non von Neumann one. But can one guarantee that a SNN computer solves some important problems reliably? In this presentation, I formulate a mathematical model of one SNN that can be configured for a sparse coding problem for feature extraction. With a moderate but well-defined assumption, we prove that the SNN indeed solves sparse coding. To the best of our knowledge, this is the first rigorous result of this kind. This work is done jointly with Intel colleagues Tsung-han Lin and Mike Davies.

26 June 2019, 10:00am, LAAS - Salle de conférences**Algorithmes symboliques-numeriques validés et applications au domaine spatial**

by Mioara Joldes

Abstract: When computing with finite precision, one strives to achieve accurate and/or guaranteed results without compromising efficiency. For this, we combine symbolic and numerical computation, which leads to the development of specific new computer arithmetic and approximation algorithms. Firstly, at the arithmetics level, we focus on high-precision arithmetic operations, using as basic building blocks the available operators for floating-point arithmetic. We are also interested in problems related to the efficient and reliable implementation and evaluation in fixed-precision of elementary and special functions. Secondly, at the symbolic-numeric level, we focus on effective polynomial approximations together with validated error bounds expressed in Taylor or Chebyshev basis. We exploit approximation algorithms mainly related to D-finite functions i.e., solutions of linear differential equations with polynomial coefficients. The theoretical tools developed abov! e are then applied to problems coming from optimal control and aerospace. A first example consists of a new method to compute the orbital collision probability between two spherical objects involved in a short-term encounter, under Gaussian uncertainty. Another one discusses efficient and validated algorithms for impulsive spacecraft rendezvous. Finally, the obtained results are put in perspective: the goal is to bring more reliable computations in the field of optimal control theory and aerospace applications, by making further use of computer arithmetics, computer algebra and approximation theory tools.

19-21 June 2019, ISAE**FEANICSES 2019 Workshop**

18 June 2019, 2:00pm, LAAS - Salle de Europe**Learning to control: Data-driven stability analysis of switched systems**

by Raphaël Jungers

Abstract: With the upcoming Industry 4.0, we are facing an increasing complexification of the engineered control systems, and at the same time a need for firm guarantees on optimality and safety of their control loop. Think of a plant controlled with complex digital decentralized controllers, where resource constraints limit the amount of information available to the controllers, while disruptions (either malicious, or intrinsic to the communication media) may incur loss of information packets. With such nonstandard non-idealities, classical control theory is not able to provide exact algorithms with guarantees of performance. I will argue that even though these new systems are far more complex than classical textbook models, one may often recover firm guarantees on the good behaviour of the system with the help of advanced techniques from Mathematics, Optimization, or Computer Science. This may require to change one’s point of view on the nature of the guarantees we require. I will provide an example of such a result on data-driven stability analysis of switched systems.

3 June 2019, 2:30pm, LAAS - Salle Moore - Séminaire DO**New ways to multiply 3x3 matrices**

by Manuel Kauers

Abstract: The usual way of multiplying two 3x3 matrices requires 27 coefficient multiplications. It is known since 1976 that the product can also be computed with only 23 coefficient multiplications, and it is an open question whether 23 is optimal. For 23, several non-equivalent ways for computing the product are known. We extend the list by more than 13000 new matrix multiplication schemes. In the talk we will explain how we found them. This is joint work with Marijn Heule (Austin) and Martina Seidl (Linz).

10 April 2019, 2:00pm, LAAS - Salle Europe**Exploiting sparsity in certificates of nonnegativity and sparse polynomial optimization**

by Jie Wang

Abstract: Certifying nonnegativity of polynomials is a central problem in real algebraic geometry which has applications in polynomial optimization and many other fields. Polynomials arising from practice are usually sparse. Thus it is crucial to exploit sparsity in certificates of nonnegativity and related sparse polynomial optimization. We discuss two cases. In one case, we exploit term sparsity in the classic SOS method by introducing cross sparsity patterns and propose a new sparse SOS algorithm. In the other case, we study SONC decompositions which was introduced as a new certificate of nonnegativity of polynomials recently. We prove that SONC decompositions maintain sparsity of polynomials and give the conditions under which nonnegative polynomials admit SONC decompositions. We also give two approaches to compute SONC decompositions, via relative entropy programming or second order cone programming respectively.

28 March 2019, 2:00pm, LAAS - Salle Europe**Max-Min Lyapunov Functions for State-Dependent-Switched Systems**

by Matteo Della Rossa

Abstract: A class of locally Lipschitz continuous Lyapunov functions is studied in this talk to establish stability for differential inclusions obtained as the Filippov regularization of a non-continuous system arising from a switched systems with a state-dependent switching signal. Starting with a finite family of continuously differentiable positive definite functions, we study conditions under which a function obtained by max-min combinations over this family is a Lyapunov function. We investigate generalized notions of directional derivatives for these max-min of functions, and use them in deriving stability conditions with various degrees of conservatism, where the more conservative ones are numerically more tractable. The proposed constructions also provide nonconvex Lyapunov functions, which are shown to be useful for systems with state-dependent switching that do not admit a convex Lyapunov function.

**Stabilization of uncertain discrete-time systems subject to a time-varying state-delay and input saturation constraints**

by Michelle Castro Ferreira De Faria

Abstract: In this talk, I will present a study on the stabilization of uncertain discrete-time systems subject to a time-varying state-delay and input saturation constraints. These features are common in real processes and often cause undesired performance or even instability. The objectives are to establish synthesis conditions for a state feedback control law that guarantee the local asymptotic stability of the closed-loop system for a given set of initial conditions. We propose stability conditions obtained through two different approaches: a first method relies on Lyapunov-Krasovskii functionals while a second one is based on augmented systems formulation.

**Stabilizability of affine uncertain time-varying discrete-time systems**

by Ariadne Justi Bertolin

Abstract: This work investigates the stability and stabilizability of affine uncertain time-varying discrete-time systems by means of Linear Matrix Inequalities (LMIs) for arbitrary, limited and dynamic variations. As strategy, κ -1 redundant equations of the system is used to assure robust control and

stability by sufficient LMIs conditions with distinct complexities. In this way, as κ≥1 increases,

the conditions are progressively less conservatives. Numerical experiments, based on models borrowed from literature, will be performed, using computational tools available in Matlab to program the LMIs, together with parsers and solvers of public domain.

27 March 2019, 2:00pm, LAAS - Salle Moore**Generation and Verification for (Semi) Algebraic Invariant Sets for Polynomial ODEs**

by Khalil Ghorbal

Abstract: We will start by summarizing recent developments in the formal verification (or checking) of invariant semi-algebraic sets for polynomial ODEs, that is how a computer can formally check whether a candidate semi-algebraic set is an exact invariant for a given ODE.

The rest of the talk will be devoted to two particular generation procedures: (i) an entirely symbolic procedure to generate Darboux polynomial (which are closely related to rational invariant functions) and, (ii) the so-called vectorial barrier certificates, a high dimensional generalization of Prajna's original work on (scalar) Barrier certificates. The latter in particular relies on SDP solvers and thus suffers from the same plague: numerical inaccuracies, an open problem we are currently working on.

26 March 2019, 2:00pm, LAAS - Salle Feynman**A unifying framework for strong structural controllability for networked systems**

by Kanat Camlibel

Abstract: Motivated by various control synthesis problems for networked systems, this talk deals with strong structural controllability of linear structured systems. In contrast to existing work, the structured systems studied in this talk have a so-called zero/nonzero/arbitrary structure, which means that some of the entries are equal to zero, some of the entries are arbitrary but nonzero, and the remaining entries are arbitrary (zero or nonzero). We formalize this in terms of pattern matrices whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We establish necessary and sufficient algebraic conditions for strong structural controllability in terms of full rank tests on the pattern matrices associated with the structured system. We also give a necessary and sufficient graph theoretic condition for the full rank property of a given pattern matrix. Based on these two results, we then establish a necessary and sufficient graph theoretic! condition for strong structural controllability.

12-13 March 2019, Meeting__Seminar COMET-SCA & MACS-MOSAR__

Carsten Scherer (Univ. Stuttgart),

Yohei Hosoe (Univ. Kyoto),

Victor Magron (LAAS-CNRS),

Christelle Pittet (CNES),

Dimitri Peaucelle (LAAS-CNRS),

Charles Poussot-Vassal (ONERA)

28 February 2019, 2:00pm, LAAS - Salle Moore**Measure-valued solutions of Burgers’ equation and how to plot them**

by Quentin Vila

Abstract: The inverse design for Burgers’ equation is a difficult problem. Is it possible that the moment-sum-of-squares hierarchy gives resolution or information that the analytical techniques fail to obtain easily ? This question has not been given an answer yet, however, as a first step in that direction, we will see in this talk first how the notion of entropy measure-valued solution makes the Lasserre hierarchy applicable to the resolution of Burgers’ equation, then we will comment the reconstitution of some already known visual results, and only at the end shall we talk about some results obtained in the case of the inverse design. If the technique of the resolution by the GMP persents some advantages, it also introduces a certain number of parameters whose roles are still mysterious.

4 February 2019, 2pm, ENSEEIHT__Seminar SPOT__

Adrien Taylor (INRIA Paris)

Gersende Fort (IMT Toulouse)

24 January 2019, 2:00pm, LAAS - Salle Europe**Enjeux et techniques de l'approximation d'ensembles pour l'analyse de stabilité**

by Matteo Tacchi

Abstract: Avec la transition énergétique et les nouvelles technologies impliquées dans le transport de l'électricité, des incertitudes apparaissent quant à la prévision et la gestion des risques d'instabilité sur le réseau européen. Pour répondre à ce défi, nous cherchons une caractérisation géométrique des zones de stabilité associées aux équations du réseau. Une méthode prometteuse consiste à calculer des approximations conservatives de ces ensembles sous la forme de sous-solutions de problèmes de moments généralisés. La résolution approchée de ces problèmes implique l'utilisation des hiérarchies moments-SOS, et son application à grande échelle nécessite l'utilisation astucieuse de la structure "creuse" du réseau électrique.**Stabilité de systèmes de dimension infinie - Application au forage pétrolier**

by Matthieu Barreau

Abstract: Etudier la stabilité de systèmes de dimension infinie est un challenge théorique mais également combinatoire. Pour certains systèmes simples (système à retard, équation de transport...), il est possible de déterminer une fonction de Lyapunov permettant de statuer sur la stabilité du problème. Cependant, il n'existe pas de fonction de Lyapunov performante pour un système couplé, même simple, entre une équation aux dérivées ordinaires (EDO) et une autre aux dérivées partielles. Dans cet exposé, nous allons discuter le cas particulier d'un couplage entre une équation des ondes et une EDO. Une technique permettant d'approximer une fonction de Lyapunov est proposée utilisant des projections de l'état de dimension infinie. Après ce bref passage théorique, nous porterons notre attention sur l'étude d'un forage pétrolier.

7 January 2019, 2pm, ENSEEIHT__Seminar SPOT__

Hristo Sendov (University of Western Ontario) – Polar convexity and critical points of polynomials

Charles Dossal (INSA and IMT Toulouse) – Exact decay rate for Nesterov Acceleration

17 December 2018, IAS**COMET SCA - **Commande Tolérante aux Fautes

12 December 2018, 2:00pm, LAAS - Salle du Conseil**Control of complex systems through differential flatness and MPC**

by __Ionela Prodan__

Abstract: The first part of this presentation deals with the hierarchical optimization-based control of a meshed DC microgrid architecture supervised through a multi-layer optimization-based control. A multi-scale supervision scheduling is developed to handle the load balancing problem for the proper energy distribution within the transmission network. The control architecture considers three control layers. These are implemented via a combination of differential flatness and MPC (Model Predictive Control). Flat representations serve to define analytically profile, costs and constraints which are subsequently used in an MPC framework. Next some other applications involving the control and coordination of unmanned vehicles (aerial and aquatic drones) will be briefly enumerated to highlight the use of differential flatness and B-splines parametrizations.

11 December 2018, 11:00am, LAAS - Salle du Conseil**Networked Control Systems: The Signal-to-Noise Ratio Approach**

by Alejandro Rojas

Abstract: The background for the present project proposal is the research area of Networked Control Systems (NCS). The presentation focuses speciﬁcally on the Signal-to-Noise Ratio (SNR) approach, which studies LTI control feedback problems that explicitly include communication channel models subject to SNR constraints. The control feedback loop (either state feedback or output feedback) is closed over a communication channel model that highlights, through the SNR limitation, the unreliable nature of data transmission (as different from the classic control theory approach that assumes perfect availability of all signals in the loop). We can then, for example, characterize a lower limit on the channel SNR (between the channel input signal and the channel additive noise) necessary and sufﬁcient for stability of the control feedback loop. It is well known that such lower limit depends in general on the plant unstable poles, plant non minimum phase (NMP) zeros, plant time delay, channel bandwidth, coloring of the channel noise process, etcetera. We discuss results for stability, performance and robust LTI analysis, as well as connections to the algebraic Riccati equation.

10 December 2018, LAAS - Salle Europe**COMET ORB - Trajectoires faible énergie et propulsion électrique**

5 December 2018, LAAS - Salle Europe**LAAS-IMT Workshop**

3 December 2018, 2:00pm, LAAS - Salle Tourmalet**Lower Bounds via Circuit Polynomials**

by __Henning Seidler__

Abstract: Finding the minimum of a multivariate real polynomial is a well-known hard problem with various applications. We present a polynomial time algorithm to approximate such lower bounds via sums of nonnegative circuit polynomials (SONC). SONC yields bounds competitive to SOS in several cases, but using significantly less time and memory. Additionally, it provides a candidate for the global minimizer. By branching over the signs of the variables, we improve the bounds even further, with only a moderate increase in the running time.

3 December 2018, 2pm, ENSEEIHT__Seminar SPOT__

Gérard Dupont et Jayant Sen Gupta (AIRBUS) – Data science and AI at AIRBUS central research

Stéphane Canu (INSA Rouen) – Variable selection and outlier detection as a MIP

27 November 2018, LAAS - Salle du Conseil

in Workshop de l'axe Énergie - **Commande et contrôle avancé pour convertisseurs multicellulaires à base de semiconducteurs à grand gap GaN**

by Germain Garcia

21-23 November 2018__2nd DECOD Workshop - Delays and constraints in distributed parameter systems__

19 October 2018, 2:30pm, LAAS - Salle Europe**Control allocation, optimal output regulation and attack detection in cyber-physical systems**

by __Sergio Galeani__

Abstract: For a long time, the availability of more control inputs than regulated outputs in a controlled plant has been interpreted more as an obstacle rather than as an opportunity, essentially due to the fact that the "extra inputs" make the solution of the control problem non-unique. As a result, a classic approach consists in "squaring down" the plant, by combining some of the control inputs in order to obtain a model having as many inputs as outputs, to which standard theory can be applied and unique solutions arise. In this talk, a different perspective is taken, showing that the presence of more inputs than outputs ushers in the possibility of achieving better performance or extra features by exploiting the extra degrees of freedom through optimization. Examples will be given by showing performance improvement at non-trivial (not just constant) steady-state solutions, the interest for nonlinear solutions in otherwise linear output regulation problems, and the use of input reconfiguration to unveil otherwise stealthy attacks in cyber-physical systems.

18 October 2018, 10:00am, LAAS - Salle Tourmalet**Generation of Optimal Guidance Laws Under Epistemic Uncertainty and Imprecision**

by __Massimiliano Vasile__

Abstract: The preliminary design of interplanetary trajectories with low-thrust propulsion is subject to uncertainty that is generally epistemic. In particular the properties of the propulsion system and their variability during the operational life of the spacecraft have a degree of uncertainty that can affect the overall system design and the reliability of the design solution. This talk will present an approach to model this epistemic uncertainty with Dempster-Shafer theory of Evidence and to compute robust and reliable guidance laws that optimise a performance index and satisfy a number of constraints. The approach is applied to the case of a low-thrust transfer from the Earth to an asteroid. The talk will present also a method to compute optimal guidance laws in the case uncertainty is propagated with a generalised polynomial algebra based on Chebyshev expansions.

16 October 2018, 10:00am, LAAS - Salle Europe**Impulsive zone Model Predictive Control: a particular formulation and some applications.**

by __Alejandro H. Gonzalez__

Abstract: Many control problems - coming from very different areas that go from diseases treatments, to spacecraft guidance, passing through electronic and Nanoelectronic control- fell into the framework of what is called impulsive control: "a control paradigm based on impulsive differential equations in which a nonimpulsive plant has at least one impulsively changeable state variable". More precisely, we are interested in nonimpulsive plants (linear, time variant or invariant, continuous-time systems) controlled by impulsive actions, i.e., by manipulated actions producing a discontinuity of the trajectory solutions at certain time instants, and leaving the system free for the rest of the time.

Such systems have some particularities: they have no formal equilibriums out of the origin, they can be characterized by two discrete time sub-models describing the system just before and after the discontinuity (the jumps), their stability has to be defined in terms of two generalized equilibria, etc. Among the control strategies able to account for the impulsive schemes, model predictive control (MPC) is one of the most promising ones, because of its well-known benefits (constraint satisfaction, optimality, stability, etc.).

More important, MPC is able to account for the stability of equilibrium or invariant sets, instead of points, which means that once the closed-loop system reaches any point or trajectory in the target set, no further control actions are implemented (i.e., there are no preferences between points or trajectories inside the target set). In this talk, the details of a particular impulsive zone MPC formulation will be discussed. As a first step, a linear impulsive system characterization is made, which includes two discrete-time sub-systems and extended equilibrium and invariant sets, even in regions far from the origin. Then, an MPC formulation that takes advantage of the aforementioned characterization is presented. The main idea is to exploit the proper uses of artificial optimization variables and output target zones, which allows us to have an enlarged domain of attraction and preserves the stability and recursive feasibility of the closed loop. To motivate the potential application of the strategy, some simulation examples are proposed.

1 October 2018, 2pm, ENSEEIHT__Seminar SPOT__

Salma Kuhlmann (Constance) on moments and positive polynomials,

Jean-Claude Yakoubsohn (Toulouse) on certified computations for singular value decompositions.

18 September 2018, 2:00pm, LAAS - Salle Tourmalet**On the absence of spurious optimality**

by __Cédric Josz__

Abstract: We study the set of continuous functions that admit no spurious local optima (i.e. local minima that are not global minima) which we term global functions. They satisfy various properties for analyzing nonconvex and nonsmooth optimization problems. For instance, they satisfy a theorem akin to the uniform limit theorem in analysis regarding continuous functions. Global functions are also endowed with properties regarding the composition of functions and change of variables. Using these results, we show that a class of nonconvex and nonsmooth optimization problems arising in tensor decomposition applications are global functions. This provides a theoretical guarantee for the l1 norm to avoid outliers in nonconvex optimization.

3-7 September 2018__Ecole en contrôle optimal numérique__

Registrations online before 15 June 2018

30 August 2018, 2:00pm, LAAS - Salle Europe**Game-Theoretic Approach to Security and Resilience of Cyber-Physical Systems**

by __Quanyan Zhu__

Abstract: Game theory is an emerging modeling tool in engineering to capture complex interactions in large-scale intelligent systems such as autonomous systems, smart cities and the Internet of Things. Also, game theory is a quantitative method to understand conflicts and contentions among players or systems. These features make the theory an appropriate tool to model and design secure and resilient cyber-physical and human systems. In this talk, we will first give a short introduction to the theory and its applications. Then, we will present a meta-game approach to the multi-layer and multi-type cyber and physical interactions to provide a holistic analytical framework for assessing cyber risks of CPS under advanced persistent threats. We will leverage the theory as a guideline for developing security-hardening strategies for the network security and designing resilient controllers to respond to failures. We use the Internet of Controlled Things and the autonomous systems as case stu! dies to illustrate the design methodologies.

31 July 2018, 3:00pm, LAAS - Salle du Conseil**Discrete-Time Linear Systems with Stochastic Dynamics and LMI-Based Control**

by __Yohei Hosoe__

Abstract: This study is concerned with the development of a theoretical basis for controlling discrete-time linear systems with stochastic dynamics. Although the general class of such dynamics is difficult to deal with in numerical analysis and synthesis, some subclasses are relatively easy. The dynamics determined by a Markov chain is a solid example of such subclasses and has been extensively studied in the field of Markov jump systems. In this study, on the other hand, we focus on as another subclass the stochastic dynamics determined by a process that is i.i.d. (independently and identically distributed) with respect to the discrete time. We discuss equivalence of some stability notions for the systems with such dynamics, and show a Lyapunov inequality condition that is necessary and sufficient for their stability. Since our Lyapunov inequality will involve decision variables contained in the expectation operation, an idea is provided to solve it as a standard LMI (linear matrix inequality). The idea can be further exploited in stabilization state feedback synthesis for the systems.

31 July 2018, 2:00pm, LAAS - Salle du Conseil**Low-Power High-Gain Observers**

by __Daniele Astolfi__

Abstract: High-gain observers have been extensively used in nonlinear control since the end of the 80’s for their tunability property, namely the fact that the rate of convergence of the observer can be tuned by acting with one single high-gain parameter. This important feature is motivated by the use of observers in output feedback control and it has been proved that this tunability property plays a key role in establishing a nonlinear separation principle. Despite the evident benefits of this class of observers, their use in real applications is questionable due to some drawbacks. Mainly: numerical issues due to the fact that we need to implement coefficients which increases polynomially with the system dimension; the well-known peaking phenomenon; high sensitivity to measurement noise. Motivated by these considerations, we propose a new class of nonlinear high-gain observers, denoted as “low-power high-gain observers”, that preserves the same high-gain features but which s! ubstantially overtakes (or improves) the aforementioned drawbacks. The low-power high-gain observers are characterized by having coefficients which does not grow with the system dimension, by avoiding the peaking phenomenon and by improving the sensitivity to high-frequency measurement noise. The proposed observers can be used without loss of generality with respect to standard high-gain observers in frameworks of observations, output feedback or output regulation.

2 July 2018, 11:00am, LAAS - Salle Tourmalet**Numerical Computational Techniques for Nonlinear Optimal Control - Slides**

by __Yasuaki Oishi__

Abstract: In this talk, I present the stable-manifold method, an effective method for nonlinear optimal control introduced by Sakamoto and van der Schaft in 2008, and propose two numerical computational techniques for its improvement. The first technique is for generation of points on the stable manifold in a robust way against numerical errors. There, a special numerical method that preserves Hamiltonian is used to solve a differential equation sensitive to numerical errors. The second technique is a sort of shooting method to generate a point corresponding to the desired system state. These techniques are used for optimal swing-up of a pendulum and successfully give a swing-up trajectory with multiple swings. This is a joint work with Noboru Sakamoto and Takuto Nakamura.

27 June 2018, 2:00pm, LAAS - Salle du Conseil**Formal Verification of Convex Optimization Algorithms For Model Predictive Control**

by __Raphaël Cohen__

Abstract: The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. However, this cannot happen without addressing proper attention to the soundness of these algorithms. This work discusses the formal verification of convex optimization algorithms with a particular emphasis on receding-horizon controllers. Additionally, we demonstrate how theoretical proofs of real-time optimization algorithms can be used to describe functional properties at the code level, thereby making it accessible for the formal methods community. In seeking zero-bug software, we use the Credible Autocoding scheme. We focused our attention on the ellipsoid algorithm solving second-order cone programs (SOCP). In addition to this, we present a floating-point analysis of the algorithm and give a framework to numerically validate the method.

19 June 2018, 10:45am, LAAS - Salle Europe**Lp stability of networked control systems implemented on WirelessHART**

by __Dragan Nesic__

Abstract: Control systems in which sensor/actuator signals are sent via a communication network are increasingly important in various areas, such as X-by-wire technologies in the aerospace and automotive industries, smart grid, vehicle platoons, swarms of UAVs and control of large irrigation networks. Such networked control systems (NCS) are much harder to design and analyse because the communication network introduces a range of undesirable effects into the closed loop system, such as the sampling jitter, quantized signals, the need for signal scheduling, data dropouts, and so on. In the past decade, a large body of research addressed various issues in NCS via “generic” network models which are sometimes hard to apply to NCS with specific networks, such as CAN, Flexray or WirelessHART. In this talk I will concentrate on control oriented modelling of NCS with WirelessHART networks and then present results on an emulation oriented approach for achieving Lp stabilisation of such systems. We show that our results are less conservative (in an appropriate sense) than prior emulation results that do not exploit the specific network structure in the analysis.

19 June 2018, 9:30am, LAAS - Salle Europe**Glocal (Global/Local) Control towards Smart Cities**

by __Shinji Hara__

Abstract: There are many dynamical systems that can be regarded as hierarchical networked dynamical systems in a variety of fields related to smart cities. One of the ideas to treat those systems properly is "Glocal (Global/Local) Control," which means that the global purpose is achieved by only local actions of measurement and control. The background and idea of glocal control are explained by showing the control perspective of IoT (Internet of Things).

The key for realization of glocal control is hierarchical networked dynamical systems with multiple resolutions in time and space depending on the layer. After introducing a unified framework, its fundamental control theory such as stability and robust stability is provided. Then, we focus on how to design hierarchically decentralized controls with global/local objectives by aggregation. Through the talk we show the effectiveness of the theoretical results for applications to electric vehicle control and power network systems towards smart cities.

Slides GlocalControl_LAAS_June2018SH.pdf available in __MAC team Intranet__.

11 June 2018, 2pm, ENSEEIHT__Seminar SPOT__

28 May 2018, 2pm, ENSEEIHT__Seminar SPOT__

23 April 2018, 1:30pm, LAAS - Salle Tourmalet**Peak Effects in Stable Linear Difference Equations**

by __Pavel Shcherbakov__

Abstract: We consider homogenous, linear, asymptotically stable scalar difference equations with constant coefficients and unit-norm initial conditions. First, it is shown that the solution may happen to deviate far away from the equilibrium point at finite time instants prior to converging to zero. Second, for a number of root distributions and initial conditions, exact values of deviations or lower bounds are provided. Several specific difference equations known from the literature are also analyzed and estimates of deviations are proposed. Possible generalizations are discussed and directions for future research are outlined.

17 April 2018, ONERA__International Workshop on Robust LPV Control Techniques and Anti-Windup Design__

16 April 2018, 2pm, ENSEEIHT__Seminar SPOT__

5 April 2018, 2pm, LAAS - Salle du Conseil**Regulation of linear PDE's by P-I controller using a Lyapunov approach inspired by forwarding methods. Theory and application to the drilling case - Slides**

by

__Alexandre Terrand-Jeanne__

Abstract: Most of the existing results for the regulation of PDE's are based on semi-group and spectral theory. However, these results impose bounds on the control and the measurement operators. For instance, the boundary regulation of hyperbolic PDE employing control at the boundaries, can not be addressed. In order to deals with more general systems, we introduce a novel Lyapunov functionnal inspired by nonlinear forwarding technics. Our approach is then illustrated in the case of a drilling system.

3 April 2018, whole day, LAAS - Salle de Conférence

COMET-SCA Seminar - **Sloshing Modeling and Control **- __Program__

8 March 2018, 11am, LAAS - Salle de Conférence**Lyapunov-based analysis of TDSs and PDEs**

by __Anton Selivanov__

Abstract: I will briefly describe some resent results devoted to control and stability analysis of time-delay systems and PDEs. All results were obtained using Lyapunov(-Krasovskii) functionals whose properties are guaranteed by feasibility of certain linear matrix inequalities. First, I will talk about delay-induced stability – a phenomenon that occurs when a system cannot be stabilized using the output but can be stabilized using the output together with its delayed value. Then I’ll talk about the event-triggered control with a dwell time and predictor-based event-triggered control. A significant part of the talk will be devoted to control of PDEs. We will discuss event-triggered control of PDEs, relay control of PDEs, and input delay compensation using the idea of chain predictors. All the results were obtained jointly with Emilia Fridman.

## Main events organized in Toulouse by MAC team before 2018:

2017 - IFAC World Congress

2013 - IFAC NOLCOS

2006 - IFAC ROCOND