1,721,122 research outputs found
A model predictive control framework for reliable microgrid energy management
No full textInternational audienc
On the microgrid energy management under a predictive control framework
No full textInternational audienceWe present an extension of a model predictive control approach for microgrid energy management. We take into account electricity costs, power consumption, generation profiles and power and energy constraints. Uncertainty due to variations in the environment (wind speed), failures and subsequent repairs of the generator, as well as battery lifespan limitations are taken into consideration. Simulation results validate the proposed approa
Optimal Control of Regulated and Liberalized Power Systems: A Passivity-based Approach
Get PDFOptimierung ist seit Beginn der Verbreitung elektrischer Energie ein zentrales Werkzeug für die Planung und den Betrieb von Energiesystemen. Der aktuell stattfindende Übergang zu erneuerbaren Energien, motiviert durch den Wunsch nach Klimaneutralität, stellt jedoch erhebliche Herausforderungen für den Betrieb von Energiesystemen dar. Die Volatilität erneuerbarer Energien führt zusammen mit den bestehenden Marktregulierungen, die auf vorhersehbare Einspeisungen ausgelegt sind, zu immer größer werdenden Stabilitätsproblemen und einer ineffizienten Betriebsweise. Diese Dissertation zielt darauf ab, optimierungsbasierte Regelungskonzepte zu entwickeln, die speziell darauf ausgelegt sind, die Herausforderungen zukünftiger Energiesysteme zu bewältigen. Die Beiträge dieser Dissertation reichen von formalen theoretischen Methoden bis hin zu deren Anwendung in elektrischen Energiesystemen. Zum einen werden grundlegende Beiträge zu Optimierungstheorie präsentiert, in denen lokale Designanforderungen für Optimalität und Konvergenz in der verteilten Optimierung entwickelt werden. Zum anderen werden zwei konkrete Regelungskonzepte für Stromnetze vorgeschlagen, die die Herausforderungen zukünftiger Energiesysteme adressieren. Diese Regelungskonzepte unterscheiden sich konzeptuell: Das erste Regelungskonzept führt zu einem vollständig regulierten Energiesystem, in dem einzelne Akteure keine eigenen Ziele verfolgen. Das zweite Regelungskonzept führt das im Rahmen dieser Dissertation entwickelte, neuartige Konzept der passivitätsbasierten ökonomischen (engl. economic) Ports ein und resultiert in einem liberalisierten Energiesystem. Diese beiden Regelungskonzepte werden verglichen und ihre Vorteile und Nachteile werden in verschiedenen Szenarien diskutiert. Alle entwickelten theoretischen Methoden und praktischen Regelungskonzepte dieser Dissertation nutzen die Passivitätstheorie. Die Kombination von Passivitätstheorie und Optimierung, die im Kern dieser Dissertation verankert ist, liefert einen Beitrag hin zu einer effizienten und stabilen Regelung zukünftiger Energiesysteme
Motion planning for multi-agent dynamical systems in a B-spline framework
No full textGénérer des trajectoires hors ligne est primordial dans les applications de planification des mouvements afin de garantir la sécurité, l'efficacité et la fiabilité des performances du système lors de l'exécution en ligne. Hors ligne, l'accent est mis sur l'optimisation de la trajectoire sans se soucier de la complexité de calcul, alors qu'en ligne, l'optimalité et l'efficacité de calcul sont aussi importantes.Dans le cas des véhicules aériens sans pilote, ces trajectoires doivent respecter la dynamique interne et s'adapter aux contraintes environnementales. En calculant à l'avance des trajectoires optimales, les drones peuvent assurer une navigation économe en énergie, éviter les collisions et maintenir la communication avec d'autres agents dans des opérations en temps réel. Cette thèse étudie les méthodes permettant de générer de telles trajectoires hors ligne, en mettant l'accent sur leur adaptabilité et leur faisabilité pour les systèmes aériens multi-agents, contribuant ainsi aux progrès de la robotique. En outre, elle aborde les architectures distribuées en ligne pour assurer le changement de configuration entre lesagents.Les problèmes de planification de mouvement explorés dans cette thèse sont traités par une intégration cohérente des courbes B-splines, de techniques d'optimisation, d'algorithmes évolutionnaires et d'architectures de contrôle distribuées. Cette combinaison fournit un cadre complet pour la génération de trajectoires hors ligne et la planification de mouvement en ligne de systèmes dynamiques multi-agents.Plus précisément, l'accent est mis sur la génération de trajectoires qui satisfont la dynamique interne du drone - contraintes sur la vitesse, la poussée, les angles, les vitesses angulaires et les couples - tout en étant adaptées à l'environnement grâce à des contraintes sur les points de passage et l'évitement d'obstacles. En outre, les relations entre les agents sont prises en compte, telles que les contraintes de communication, le maintien et le changement de formation, tout en minimisant la consommation d'énergie.Les exemples de drones traités dans cette thèse sont des systèmes différentiellement plats, qui permettent d'exprimer leur dynamique interne en fonction de la trajectoire planifiée et de ses dérivées. En combinant cette propriété avec les caractéristiques des courbes B-splines, les contraintes continues peuvent être représentées efficacement. La fixation des fonctions de base des B-splines permet de formuler l'ensemble du problème d'optimisation en fonction d'un nombre fini de points de contrôle, qui définissent la forme de la courbe. Le problème d'optimisation continue, initialement complexe, est ainsi ramené à un problème plus simple : l'optimisation des positions d'un nombre fini de points de contrôle.Les contributions théoriques incluent des approches novatrices pour traiter les problèmes d'optimisation liés à la génération de trajectoires. Pour simplifier la résolution hors ligne des problèmes d'optimisation avec contraintes, des approximations des fonctions non linéaires décrivant le coût et les contraintes sont réalisées à l'aide de l'opérateur de Schoenberg. L'expression d'une trajectoire en B-spline en fonction de plus de points de contrôle permet non seulement de resserrer l'enveloppe de la trajectoire afin d'éviter les obstacles, mais aussi d'augmenter les degrés de liberté des suiveurs pour changer de formation sans violer les contraintes dynamiques.Les architectures distribuées sont bien adaptées à la planification de trajectoires en ligne, mais elles nécessitent des contrôleurs de faible complexité. Des approches basées sur la commande prédictive et sur les jeux de population permettent de générer des trajectoires en ligne pour plusieurs drones.Les validations expérimentales en intérieur présentées dans cette thèse comblent le fossé entre les développements théoriques et les applications pratiques, démontrant la faisabilité et l'efficacité des méthodes proposées.Generating offline feasible trajectories is paramount in motion planning applications to ensure safe, efficient, and reliable system performance during online execution. At the offline stage, the focus is primarily on optimizing the trajectory without concern for computational complexity, while at the online stage, both optimality and computational efficiency are equally important.For the specific case of Unmanned Aerial Vehicles (UAVs), these trajectories must not only comply with internal dynamics but also adapt to environmental constraints. By precomputing optimal paths, UAVs can ensure energy-efficient navigation, avoid collisions, and maintain communication with other agents in real-time operations. This thesis investigates methods for generating such offline trajectories, emphasizing their adaptability and feasibility for multi-agent aerial systems. Additionally, it addresses online distributed architectures to ensure reliable transitions between different configurations of multi-agent systems.The motion planning problems explored in this thesis are addressed through a coherent integration of several techniques, including B-spline curves, optimization, evolutionary computation, and distributed control architectures. This comprehensive framework is applied both to the generation of offline trajectories and to the online motion planning of multi-agent dynamical systems.Specifically, the focus is on generating trajectories that satisfy UAV internal dynamics - constraints on velocity, thrust, angles, angular velocities, and torques - while being adapted to the environment through constraints on waypoint passing and obstacle avoidance. Additionally, relations between agents are considered, such as communication constraints, formation maintenance, and formation switching, all while minimizing energy consumption. The UAV examples addressed in this thesis exhibit the differential flatness property, which allows their internal dynamics to be expressed as a function of the planned trajectory and its derivatives. By combining this property with the mathematical and geometrical characteristics of B-spline curves, continuous constraints can be efficiently represented. Fixing the basis functions of the B-splines enables the entire optimization problem to be formulated in terms of a finite number of coefficients, known as control points, that define the curve’s shape. This reduces the initially complex, continuous optimization problem to a simpler one: optimizing the positions of a finite number of control points.Theoretical contributions include novel approaches to handling optimization problems for trajectory generation. To simplify the offline resolution of constrained optimization problems, approximations of the nonlinear functions describing the cost and constraints are made using the Schoenberg operator. These approximations lead to more accurate estimations of energy consumption compared to traditional methods in the literature. A knot refinement procedure is also introduced to tighten the bounds on trajectory shapes for obstacle avoidance and to increase the degrees of freedom for formation switching, while ensuring compliance with all other dynamic constraints.Distributed architectures are well-suited for online multi-agent motion planning, though they require low-complexity controllers. In this thesis, the optimization problem is solved online by decomposing the global problem into subproblems, each handled by individual agents. Approaches based on Model Predictive Control (MPC) and Population Games are used to generate trajectories online for multiple UAVs.The indoor experimental validations conducted with multiple nanodrones bridge the gap between theoretical developments and practical applications, demonstrating the feasibility and effectiveness of the proposed methods
Constrained control of nonlinear systems via flat mappings : theory and experiments
No full textMalgré les progrès réalisés dans les approches de commande basées sur l’optimisation, il existe encore aujourd'hui un besoin crucial de contrôleurs à faible complexité pour les systèmes non linéaires capables d'assurer la stabilité et de satisfaire des contraintes opérationnelles complexes. Ces contrôleurs offrent des solutions efficaces sur le plan informatique, essentielles pour les applications en temps réel où la précision, la sécurité et des performances garanties sont primordiales.Pour simplifier la commande, on peut réduire la non-linéarité du modèle. Dans ce but, la théorie des systèmes différentiellement plats offre deux avantages : la linéarisation par retour d'état et la paramétrisation différentielle. Ces avantages découlent d'une sortie plate spécifique et d'une transformation linéarisante des coordonnées. Malgré sa simplification de la dynamique du système, cette approche déforme fréquemment les contraintes d'état ou d'entrée dans les nouvelles coordonnées, rendant leur validation plus complexe avec les méthodes d'optimisation habituelles. Trouver la sortie plate idéale pour la conception de commande reste un défi majeur.Cette thèse aborde ces problèmes en développant des méthodes pour gérer les contraintes complexes et réduire la complexité de calcul dans les problèmes de contrôle non linéaire contraints. Elle va également au-delà des systèmes plats, en utilisant des arguments basés sur Lyapunov pour les systèmes affines de contrôle afin d'assurer la stabilité et la satisfaction des contraintes.Pour gérer les contraintes complexes du système de coordonnées transformé, celles-ci sont simplifiées en ensembles convexes, inégalités linéaires ou contraintes mixtes en nombres entiers (MI). Pour contrôler les quadricoptères, on explore différentes approximations internes des contraintes pour des stratégies de contrôle efficaces comme la MPC implicite, explicite et robuste, ainsi que des conceptions de commande saturée adaptative. Ces approches simplifient en ligne tout en maintenant la stabilité, malgré des compromis sur le conservatisme.De plus, une méthode est développée pour générer une fonction de Lyapunov contrôlée (CLF) en utilisant la programmation linéaire, appliquée ensuite pour la commande en ligne. La stabilisation du système réduit ainsi le coût de calcul, au détriment de l'optimalité des performances. Un nouveau concept de SCLF est introduit pour formaliser ce compromis. Les résultats théoriques sont confirmés par des simulations et des tests expérimentaux sur un banc d'essai de nanodrones.De plus, des réseaux neuronaux linéaires rectifiés sont utilisés pour décomposer toutes les contraintes en contraintes linéaires MI dans l'espace de sortie plat. Cela permet d'utiliser des stratégies d'optimisation telles que le MPC et le contrôle basé sur la CLF. Malgré la non-convexité, les solveurs de programmation linéaire MI et quadratique MI gèrent efficacement les contraintes.Pour choisir les sorties plates, on utilise le paramétrage B-spline pour optimiser les trajectoires d'un drone. Les diverses sorties plates donnent lieu à des coûts et contraintes variés, engendrant des trajectoires distinctes. De plus, avec un estimateur d’état étendu, les perturbations se propagent différemment selon les transformations basées sur la platitude, créant des ensembles invariants positifs robustes de tailles variables. Ce résultat ouvre la voie à de futures recherches sur le choix optimal de la sortie plate en conception de commande.En résumé, à travers des expériences approfondies, la thèse comble le fossé entre la théorie et la pratique en appliquant des concepts avancés de théorie de commande à des scénarios de planification de mouvement réels. Elle démontre comment les résultats théoriques, tels que ceux combinant la platitude, le MPC et le CLF, peuvent être efficacement mis en œuvre, soulignant leur polyvalence et leur attrait dans la résolution de problèmes complexes et pratiques dans divers domaines.In today's landscape, despite advancements in AI techniques, there remains a critical need for low-complexity controllers for nonlinear systems that can ensure stability and satisfy convoluted constraints. These controllers offer computationally efficient solutions, essential for real-time applications where accuracy, safety, and guaranteed performance are paramount.The theory of differentially flat systems has proven advantageous in various engineering fields, offering two key benefits: feedback linearization and differential parameterization, achieved through a specific choice of output called the flat output and a linearizing coordinate transformation. While this approach simplifies the system dynamics, it often distorts state or input constraints in the new coordinates, complicating their resolution with standard optimization methods. Furthermore, selecting the optimal flat output for control remains a significant challenge.This thesis addresses these issues by developing methods to handle complex constraints and reduce computational complexity in constrained nonlinear control problems. It also extends beyond flat systems, utilizing Lyapunov-based arguments for control affine systems to ensure stability and constraint satisfaction.To address complex constraints in the transformed coordinate system, the constraints are simplified into convex sets, linear inequalities, or mixed-integer (MI) constraints. For quadcopter position control, various inner approximations of these constraints are explored, enabling efficient control strategies such as implicit, explicit, and robust tube Model Predictive Control (MPC), as well as adaptive saturated control designs. These approaches reduce online complexity while maintaining stability, though they require trade-offs in terms of conservatism within the feasible domain.Additionally, since linearity implies affinity in the control input, a method is developed to artificially generate a control Lyapunov function (CLF) using linear programming, which is then applied for online control. Stabilizing the system in this way reduces computational overhead, with a trade-off of some optimality in performance. A novel concept of sub-control Lyapunov functions is introduced to formalize this compromise. Theoretical findings are validated through extensive simulations and experimental tests using a nano-drone testbed.Moreover, to generalize the handling of complex constraints in the flat output space, Rectified Linear Neural Networks are employed to decompose the constraint set into MI linear constraints. This enables the use of established optimization-based strategies like MPC and CLF-based control. While this introduces non-convexity, simulations show that the constraints can still be efficiently managed by MI linear and MI quadratic programming solvers.Regarding the selection of flat outputs, B-spline parameterization is applied to explore the optimal trajectory generation for an unmanned aerial vehicle model. Results indicate that different flat outputs result in varied cost and constraint formulations, producing trajectories with distinct characteristics. Additionally, when using extended state observers for output feedback, it is shown that disturbances propagate differently depending on the flatness-based transformations, resulting in minimal robust positive invariant sets of varying sizes. This lays the groundwork for future research into selecting the optimal flat output.Through extensive experiments, the thesis bridges the gap between theory and practice by applying advanced control theory concepts to real-world motion planning scenarios. It demonstrates how theoretical results, such as those combining flatness, MPC, and CLF, can be effectively implemented, emphasizing their versatility and appeal in solving complex, practical problems across various domains
LP-generated Control Lyapunov Functions with application to multicopter control
No full textInternational audienceIn this work, we study a technique of exploiting open-loop generated trajectories for a constrained control problem, using them to shape suitable non-quadratic Control Lyapunov Functions. These trajectories, generated off-line, allow detecting a suitable domain of attraction in which a candidate Lyapunov function has a negative derivative. Given a suitably constructed basis function, our working machinery is based on linear programming, hence, the technique can be applied to problems of non-trivial size in terms of the number of basis functions and points in the state space. For linear systems, we seek convex Lyapunov functions, which are homogeneous polynomials. Simulation and experimental results for drone control are given
A walk through constrained optimization-based control problems
No full textThis manuscript presents the professional, academic and scientific results obtained during the last eight years of my career (after obtaining the PhD title in Automation in 2012) as well as the research directions that I wish to follow in the medium term (based on open questions identified in my area of interest).In particular, and as will be discovered throughout the manuscript, I am interested in the application of optimization-based control strategies for complex systems. My research contributions offer a geometric viewpoint of various control problems which appear in motion planning for autonomous (aerial, aquatic) vehicles and interconnected systems like DC microgrids or water networks.Why optimization-based control? Today’s systems have complex architectures, are bounded by heterogeneous constraints and have to respect challenging operational costs. Thus, optimization-based approaches, which fully exploit changes in mission, condition and environment, are becoming ubiquitous within the community.Why a geometric viewpoint? Most control problems can be better understood if seen from a geometrical viewpoint. Such an interpretation may lead to new theoretical insights and streamline their representation. Furthermore, there are many tools which can be readily applied such as set-based methods and combinatorial results.The first part of the manuscript gives a brief overview of my professional and academic career up to date (post-thesis). The main stages were the follow-up postdoctoral fellowship carried within the EDF chair, École Centrale Paris and the subsequent employment at Univ. Grenoble Alpes, Grenoble INP, Esisar (École Nationale Supérieure in Advanced Systems and Networks), LCIS (Laboratory for Systems Design and Integration) laboratory where I currently hold the position of Associate Professor.Along this path, I participated in various research and teaching activities which allowed me to develop my capacity for independent work.The second part of the manuscript lists the main scientific results obtained after the end of the thesis. In particular, I consider the following to be relevant research areas:i) the application of differential flatness for the resolution of various constrained-optimization problems (with auxiliary tools such as port-Hamiltonian modeling and spline representations);ii) motion planning via model predictive control, for unmanned surface and aerial vehicles (with particular emphasis on multicopter study and experimental validation);iii) the study and application of hierarchical control strategies for DC microgrids (power balancing, profile generation and tracking, converter control, etc.).The third part of the manuscript summarizes the problems that I have identified in recent years and the approaches that I wish to apply. A brief list covers:i) application of spline approximation theory to the flat-based representations of nonlinear dynamics to reduce complexity;ii) combining a particular class of models with flat representations (in view of automated model reformulation and subsequent resolution of constrained optimization problems);iii) extensions of modeling and control for larger scale systems (accounting for the multiple time scales, profile generation, reliability and fault propagation) with learning-based methods
A walk through constrained optimization-based control problems
No full textThis manuscript presents the professional, academic and scientific results obtained during the last eight years of my career (after obtaining the PhD title in Automation in 2012) as well as the research directions that I wish to follow in the medium term (based on open questions identified in my area of interest).In particular, and as will be discovered throughout the manuscript, I am interested in the application of optimization-based control strategies for complex systems. My research contributions offer a geometric viewpoint of various control problems which appear in motion planning for autonomous (aerial, aquatic) vehicles and interconnected systems like DC microgrids or water networks.Why optimization-based control? Today’s systems have complex architectures, are bounded by heterogeneous constraints and have to respect challenging operational costs. Thus, optimization-based approaches, which fully exploit changes in mission, condition and environment, are becoming ubiquitous within the community.Why a geometric viewpoint? Most control problems can be better understood if seen from a geometrical viewpoint. Such an interpretation may lead to new theoretical insights and streamline their representation. Furthermore, there are many tools which can be readily applied such as set-based methods and combinatorial results.The first part of the manuscript gives a brief overview of my professional and academic career up to date (post-thesis). The main stages were the follow-up postdoctoral fellowship carried within the EDF chair, École Centrale Paris and the subsequent employment at Univ. Grenoble Alpes, Grenoble INP, Esisar (École Nationale Supérieure in Advanced Systems and Networks), LCIS (Laboratory for Systems Design and Integration) laboratory where I currently hold the position of Associate Professor.Along this path, I participated in various research and teaching activities which allowed me to develop my capacity for independent work.The second part of the manuscript lists the main scientific results obtained after the end of the thesis. In particular, I consider the following to be relevant research areas:i) the application of differential flatness for the resolution of various constrained-optimization problems (with auxiliary tools such as port-Hamiltonian modeling and spline representations);ii) motion planning via model predictive control, for unmanned surface and aerial vehicles (with particular emphasis on multicopter study and experimental validation);iii) the study and application of hierarchical control strategies for DC microgrids (power balancing, profile generation and tracking, converter control, etc.).The third part of the manuscript summarizes the problems that I have identified in recent years and the approaches that I wish to apply. A brief list covers:i) application of spline approximation theory to the flat-based representations of nonlinear dynamics to reduce complexity;ii) combining a particular class of models with flat representations (in view of automated model reformulation and subsequent resolution of constrained optimization problems);iii) extensions of modeling and control for larger scale systems (accounting for the multiple time scales, profile generation, reliability and fault propagation) with learning-based methods
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