December 2019
4 décembre 2019 – 14h, salle Europe
Nota : Cette session est dédiée à la préparation des exposés pour la conférence CDC2019 à Nice. Le format est donc spécifique : 15 min de présentation et 15 min d’interaction avec le public (questions & conseils).
Speaker: Matteo Della Rossa
Title: Almost Everywhere Conditions for Hybrid Lipschitz Lyapunov Functions
Keywords: Stability of hybrid systems, Lyapunov methods
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.
Slides
Speaker: Flavien Deschaux
Title: Magnetic Force Modelling and Nonlinear Switched Control of an Electromagnetic Actuator
Keywords: Lyapunov methods, Aerospace, Hybrid systems
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.
Full text paper ; Slides
Speaker: Mathias Serieye
Title: Free-Matrices Min-Projection Control for High Frequency DC-DC Converters
Keywords: Switched systems, Lyapunov methods, Power electronics
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.
Full text paper ; Slides
Speaker: Matteo Tacchi
Title: Inner Approximations of the Maximal Positively Invariant Set for Polynomial Dynamical Systems
Keywords: Optimization, Stability of nonlinear systems, Computational methods
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.
Full text paper ; Slides