1,721,078 research outputs found
Set-Valued State Estimation of Linear Discrete-Time Systems with Linear Invariant
No full textInternational audienceThis note proposes the use of invariant relationships between the state variables of discrete-time systems to improve the tightness of a class of set-membership state estimators. Thanks to these relationships, contractor algorithms could be designed to discard almost all state vectors that are not compatible with the model-based predicted state enclosure.Moreover, this contribution introduces a less computational complexity algorithm to perform efficiently the prediction stage of the proposed set-valued state estimator
On the Local Stability of Irreversible and Reversible Linear Metabolic Pathways with Allosteric and Genetic Regulation
No full textInternational audienceThis work gives mathematical conditions that guarantee the local stability of the equilibrium regimen of two classes of cell metabolism. In fact, we have analyzed reversible and irreversible linear bacterial metabolic pathways that integrate both genetic and enzymatic control. Moreover, due to these conditions, we can state that: regardless the size of a doubly controlled linear metabolic pathway, the local stability of its steady state depends only on the dynamics of its input and output flux with respect to the concentration of its end product. These results are proved theoretically using some properties of the cooperative matrices
Set-membership state estimators based on cooperative output injections
No full textInternational audienceTo estimate validated bounds on the actual state vector of uncertain non-linear systems, cooperative output injectionsmethods are proposed in this contribution. The aim of the output injections is to design set-membership state estimatorsthat ensure the order-preserving property between the lower, actual and upper state trajectories. Based on a specialsensors placement, continuous-time and event-triggered output injections are proposed to cope with theconservatism of the classical bounding system methods. Furthermore, based on some properties of monotone dynamicalsystems, the convergence of the proposed set-membership state estimators is shown. It is worth pointing out that theproposed set-membership state estimation method allows one: on one hand, to avoid the conservatism related to theuse of similarity transformations usually required in the framework of interval observer design approaches, and on theother hand, to circumvent the pessimism accumulation related to the wrapping effect of set-valued iterative numericalschemes
On the Local Stability of Irreversible and Reversible Linear Metabolic Pathways with Allosteric and Genetic Regulation
No full textInternational audienceThis work gives mathematical conditions that guarantee the local stability of the equilibrium regimen of two classes of cell metabolism. In fact, we have analyzed reversible and irreversible linear bacterial metabolic pathways that integrate both genetic and enzymatic control. Moreover, due to these conditions, we can state that: regardless the size of a doubly controlled linear metabolic pathway, the local stability of its steady state depends only on the dynamics of its input and output flux with respect to the concentration of its end product. These results are proved theoretically using some properties of the cooperative matrices
Atteignabilité hybride des systèmes dynamiques continus par analyse par intervalles : application à l'estimation ensembliste
No full textThis thesis addresses the computation of conservative over-approximation of the solutions of uncertain ordinary di erential equations and its application to the estimation and the analysis of uncertain continuous-time dynamical systems. The main feature of the methods and algorithms presented in this thesis is the fact that they are numerically veri ed and hence can be used to obtain numerical proof of properties. This thesis is organized in two parts. The first part is devoted to the mathematical tools and the guaranteed numerical integration methods for uncertain ordinary di erential equations. These methods make it possible to characterize in a guaranteed way all the state trajectories generated by an uncertain dynamical system whose uncertainties are in a natural way described by bounded boxes. Accordingly, we have developed a hybrid integration method which gives better results than the integration methods based on interval Taylor models. The second part is dedicated to the resolution of identi cation and observation issues in a bounded error context. It also deals with continuous reachability computation for the veri cation of the properties of hybrid dynamical systems.Cette thèse porte sur le calcul d'une sur-approximation conservative pour les solutions d'équations différentielles ordinaires en présence d'incertitudes et sur son application à l'estimation et l'analyse de systèmes dynamiques à temps continu. L'avantage principal des méthodes et des algorithmes de calculs présentés dans cette thèse est qu'ils apportent une preuve numérique de résultats. Cette thèse est organisée en deux parties. La première partie est consacrée aux outils mathématiques et aux méthodes d'intégration numérique garantie des équations diff érentielles incertaines. Ces méthodes permettent de caractériser de manière garantie l'ensemble des trajectoires d'état engendrées par un système dynamique incertain dont les incertitudes sont naturellement représentées par des intervalles bornés. Dans cette optique, nous avons développé une méthode d'intégration hybride qui donne de meilleurs résultats que les méthodes d'intégration basées sur les modèles de Taylor intervalles. La seconde partie aborde les problèmes de l'identification et de l'observation dans un contexte à erreurs bornées ainsi que le problème d'atteignabilité continue pour la véri cation de propriétés des systèmes dynamiques hybrides
Hybrid reachability of continuous dynamical systems by interval analysis : application to the set-membership estimation
No full textCette thèse porte sur le calcul d'une sur-approximation conservative pour les solutions d'équations différentielles ordinaires en présence d'incertitudes et sur son application à l'estimation et l'analyse de systèmes dynamiques à temps continu. L'avantage principal des méthodes et des algorithmes de calculs présentés dans cette thèse est qu'ils apportent une preuve numérique de résultats. Cette thèse est organisée en deux parties. La première partie est consacrée aux outils mathématiques et aux méthodes d'intégration numérique garantie des équations diff érentielles incertaines. Ces méthodes permettent de caractériser de manière garantie l'ensemble des trajectoires d'état engendrées par un système dynamique incertain dont les incertitudes sont naturellement représentées par des intervalles bornés. Dans cette optique, nous avons développé une méthode d'intégration hybride qui donne de meilleurs résultats que les méthodes d'intégration basées sur les modèles de Taylor intervalles. La seconde partie aborde les problèmes de l'identification et de l'observation dans un contexte à erreurs bornées ainsi que le problème d'atteignabilité continue pour la véri cation de propriétés des systèmes dynamiques hybrides.This thesis addresses the computation of conservative over-approximation of the solutions of uncertain ordinary di erential equations and its application to the estimation and the analysis of uncertain continuous-time dynamical systems. The main feature of the methods and algorithms presented in this thesis is the fact that they are numerically veri ed and hence can be used to obtain numerical proof of properties. This thesis is organized in two parts. The first part is devoted to the mathematical tools and the guaranteed numerical integration methods for uncertain ordinary di erential equations. These methods make it possible to characterize in a guaranteed way all the state trajectories generated by an uncertain dynamical system whose uncertainties are in a natural way described by bounded boxes. Accordingly, we have developed a hybrid integration method which gives better results than the integration methods based on interval Taylor models. The second part is dedicated to the resolution of identi cation and observation issues in a bounded error context. It also deals with continuous reachability computation for the veri cation of the properties of hybrid dynamical systems
Estimation of Unknown Aerodynamic Forces of an AWE System
No full textInternational audienceAirborne Wind Energy systems (AWE) represent a promising solution to environmental challenges that has revolutionized research in the wind industry. The studied AWE system in this work is equipped with a multicopter drone in order to perform take-off and landingmaneuvers. An estimation strategy based on an Extended Kalman Filter (EKF) is proposed to obtain precise information regarding the state vector of the system, the unknown forces that acting on it and its aerodynamic coefficients
Modeling and control of new generation of tethered energy drone
No full textLes systèmes éoliens aéroportés ont attiré beaucoup d’attention ces dernières années. Le but de ce système est de proposer un design alternatif aux éoliennes conventionnelles, grâce à un profil aérodynamique attaché au sol par un câble. L’idée est d’utiliser moins de structures et de fondations que pour les éoliennes conventionnelles et d’ainsi atteindre des vents de hautes altitudes qui sont plus stables et plus forts. Plus facile à transporter et à installer, ces systèmes peuvent permettre d’exploiter des gisements éoliens inaccessibles par les technologies actuelles, et sont bien mieux adaptés pour une installation sur des plateformes flottantes. Enfin, ces systèmes peuvent également être installés sur des bateaux comme complément de propulsion éolien, ce qui peut permettre de réduire significativement le recours aux combustibles fossiles dans ce domaine.Il existe deux catégories de système éolien aéroporté : les systèmes avec production au sol et ceux avec production embarquée. Pour la production au sol,l’élément volant est relié à une génératrice au sol grâce à un câble. Pour la production embarquée, la production d’énergie se fait en vol et est récupérée au sol à l’aide d’un câble conducteur.Dans la littérature, la modélisation, le contrôle et l’optimisation de ces systèmes sont des sujets largements traités que ce soit théoriquement, en simulation ou expérimentalement. Cependant, un point important qui a été peu étudié est son décollage et son aterrissage, notamment pour la commercialisation de tels systèmes.L’objectif de la thèse est de proposer une solution de décollage et d’aterrissage pour système éolien aéroporté. Pour cela, la solution envisagée utilise un drone sur lequel seront fixés d’une part le profil aérodynamique et d’autre part le câble. Après avoir modéliser le système, un contrôleur a été développer pour permettre de faire décoller et atterir le système en sécurité, tout en gardant le câble tendu. L’objectif étant d’atteindre une position souhaité et non de suivre parfaitement une trajectoire, une certaine erreur est tolérée tant que le système reste dans une zone de sécurité, pour ainsi éviter les crashs. Ce contrôleur a ensuite été testé et valié en simulation puis sur un protoype expérimental développé pour cette thèse. Les tests ont aussi été réalisés en présence de vent pour tester la robustesse du contrôleur. Pour des faibles vitesses de vent, le contrôleur arrive à rejeter cette perturbation, mais quand celui ci augmente, ild evient nécessaire d’intégrer les forces aérodynamiques au contrôleur. C’est pour ça qu’un filtre de Kalman fut ajouter pour estimer les forces aérodynamiques et ainsi pouvoir les prendre en compte dans le contrôleur.The French energy transition law imposes a reduction of the fossil energies down to 50% within 10 years. Transition scenarios foresees renewable part of energy production to reach between 40% and 70%, with an increasing portion of wind energy. By 2027, the IEA predicts that wind will be the number-one source of the EU’s energy, but even that will not be enough to meet stringent emissions targets. Considering for example the floating offshore wind turbines, the material amount per unit of power involved in the construction of wind turbines and floating devices may render this concept unsustainable if it is scaled with current fossils energy production levels.The emerging airborne wind energy (AWE) sector offers breakthrough concepts that will allow diversifying the wind energy production offer.Recent research results are gradually assessing and eliminating feasibility risks and improving the understanding of AWE systems.A key premise for airborne wind is that it should be able to significantly reduce costs by cutting the amount of materials required for each generation unit, compared to traditional turbines. On the other hand, and unlike turbines, AWE systems have to cope with partially unpredictable wind to remain airborne and need to land when wind conditions are poor. Landings and launches are hard to automate, and each one raises the risk of catastrophic failure. Indeed, the presence of atmospheric turbulence in the lower layers of the atmospheric boundary layer as well as possibly the movement of the landing platform make the wind conditions very delicate (high turbulence and significant speed gradients). For example, in 2019, Makani's offshore 600kW energy kite prototype was lost during landing.In order to safely perform the take-off and landing phases of a drone-based AWE system, the objective is to steer it to a desired location (or position) in the air while maintaining the tether to a defined range of tension. To achieve that, a nonlinear multi-objectives controller is proposed to control simultaneously the drone and the on-ground winch. Since the main goal is to reach a target position and not to follow up closely a user-defined trajectory, a margin on the tracking error is tolerated while the system stays in a safety zone to avoid crashes. This controller is then tested and validated in simulation and experimentally on a developed prototype. Wind disturbances are also added to test the robustness of the controller. It appears that for high wind speed the aerodynamic forces have to be taken into account in the controller design. That is why an Extended Kalman Filter (EKF) has been developed to estimate these forces and include them to the controller
Tight set-valued state estimation by combining reachability analysis and set-filtering approaches
No full textInternational audienceIn this work, a new approach to design set-valued state estimator for linear discrete-time systems subject to additive and bounded process and measurement uncertainties is proposed. First, the system state equation is rewritten to obtain a stable numerical scheme on which an explicit reachability method is developed, based on zonotopic set computation and a re-initialization procedure. Then, to enhance the accuracy of the computed reachable set, a set-filtering technique is designed based on the system output equation and its intrinsic invariant relationships. The implementation of this filtering method is based on interval analysis coupled to contractor algorithms. The convergence property of the proposed set-valued state estimator is shown under the classical detectability assumption of linear systems. Some simulation results are presented to show the merit of the proposed new set-membership state estimation approach
Using hybrid automata for set-membership state estimation with uncertain nonlinear continuous-time systems
No full textInternational audienceThis paper deals with set-membership state estimation for continuous-time systems from discrete-time measurements, in the unknown but bounded error framework. The classical predictor-corrector approach to state estimation uses interval Taylor methods for solving the prediction phase, which are known to have poor performance in presence of large model or input uncertainty. In this paper, we show how to derive more efficient predictors by using a nonlinear hybridization method which builds hybrid automata to characterize the boundaries of reachable sets. The derived continuous-discrete set-membership predictor-corrector estimator is then tested with simulated data from a bioreactor. Our method is compared to classical continuous-time interval observers and is shown to have promising performance
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