30 research outputs found

    On the Reachability of a Feedback Controlled Leontief-Type Singular Model Involving Scheduled Production, Recycling and Non-Renewable Resources

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    This paper proposes and studies the reachability of a singular regular dynamic discrete Leontief-type economic model which includes production industries, recycling industries, and non-renewable products in an integrated way. The designed prefixed final state to be reached, under discussed reachability conditions, is subject to necessary additional positivity-type constraints which depend on the initial conditions and the final time for the solution to match such a final prescribed state. It is assumed that the model may be driven by both the demand and an additional correcting control in order to achieve the final targeted state in finite time. Formal sufficiency-type conditions are established for the proposed singular Leontief model to be reachable under positive feedback, correcting controls designed for appropriate demand/supply regulation. Basically, the proposed regulation scheme allows fixing a prescribed final state of economic goods stock in finite time if the model is reachable.RTI2018-094336-B-100 (MCIU/AEI/FEDER, UE) and Basque Government Grant IT1207-19

    Author index to volumes 301–400

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    Control and Estimation Oriented Model Order Reduction for Linear and Nonlinear Systems

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    Optimization based controls are advantageous in meeting stringent performance requirements and accommodating constraints. Although computers are becoming more powerful, solving optimization problems in real-time remains an obstacle because of associated computational complexity. Research efforts to address real-time optimization with limited computational power have intensified over the last decade, and one direction that has shown some success is model order reduction. This dissertation contains a collection of results relating to open- and closed-loop reduction techniques for large scale unconstrained linear descriptor systems, constrained linear systems, and nonlinear systems. For unconstrained linear descriptor systems, this dissertation develops novel gramian and Riccati solution approximation techniques. The gramian approximation is used for an open-loop reduction technique following that of balanced truncation proposed by (Moore, 1981) for ordinary linear systems and (Stykel, 2004) for linear descriptor systems. The Riccati solution is used to generalize the Linear Quadratic Gaussian balanced truncation (LQGBT) of (Verriest, 1981) and (Jonckheere and Silverman, 1983). These are applied to an electric machine model to reduce the number of states from >>100000 to 8 while improving accuracy over the state-of-the-art modal truncation of (Zhou, 2015) for the purpose of condition monitoring. Furthermore, a link between unconstrained model predictive control (MPC) with a terminal penalty and LQG of a linear system is noted, suggesting an LQGBT reduced model as a natural model for reduced MPC design. The efficacy of such a reduced controller is demonstrated by the real-time control of a diesel airpath. Model reduction generally introduces modeling errors, and controlling a constrained plant subject to modeling errors falls squarely into robust control. A standard assumption of robust control is that inputs/states/outputs are constrained by convex sets, and these sets are ``tightened'' for robust constraint satisfaction. However, robust control is often overly conservative, and resulting control strategies cannot take advantage of the true admissible sets. A new reduction problem is proposed that considers the reduced order model accuracy and constraint conservativeness. A constant tube methodology for reduced order constrained MPC is presented, and the proposed reduced order model is found to decrease the constraint conservativeness of the reduced order MPC law compared to reduced order models obtained by gramian and LQG reductions. For nonlinear systems, a reformulation of the empirical gramians of (Lall et al., 1999) and (Hahn et al., 2003) into simpler, yet more general forms is provided. The modified definitions are used in the balanced truncation of a nonlinear diesel airpath model, and the reduced order model is used to design a reduced MPC law for tracking control. Further exploiting the link between the gramian and Riccati solution for linear systems, the new empirical gramian formulation is extended to obtain empirical Riccati covariance matrices used for closed-loop model order reduction of a nonlinear system. Balanced truncation using the empirical Riccati covariance matrices is demonstrated to result in a closer-to-optimal nonlinear compensator than the previous balanced truncation techniques discussed in the dissertation.PHDNaval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/140839/1/riboch_1.pd

    Learning Neural Graph Representations in Non-Euclidean Geometries

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    The success of Deep Learning methods is heavily dependent on the choice of the data representation. For that reason, much of the actual effort goes into Representation Learning, which seeks to design preprocessing pipelines and data transformations that can support effective learning algorithms. The aim of Representation Learning is to facilitate the task of extracting useful information for classifiers and other predictor models. In this regard, graphs arise as a convenient data structure that serves as an intermediary representation in a wide range of problems. The predominant approach to work with graphs has been to embed them in an Euclidean space, due to the power and simplicity of this geometry. Nevertheless, data in many domains exhibit non-Euclidean features, making embeddings into Riemannian manifolds with a richer structure necessary. The choice of a metric space where to embed the data imposes a geometric inductive bias, with a direct impact on the performance of the models. This thesis is about learning neural graph representations in non-Euclidean geometries and showcasing their applicability in different downstream tasks. We introduce a toolkit formed by different graph metrics with the goal of characterizing the topology of the data. In that way, we can choose a suitable target embedding space aligned to the shape of the dataset. By virtue of the geometric inductive bias provided by the structure of the non-Euclidean manifolds, neural models can achieve higher performances with a reduced parameter footprint. As a first step, we study graphs with hierarchical structures. We develop different techniques to derive hierarchical graphs from large label inventories. Noticing the capacity of hyperbolic spaces to represent tree-like arrangements, we incorporate this information into an NLP model through hyperbolic graph embeddings and showcase the higher performance that they enable. Second, we tackle the question of how to learn hierarchical representations suited for different downstream tasks. We introduce a model that jointly learns task-specific graph embeddings from a label inventory and performs classification in hyperbolic space. The model achieves state-of-the-art results on very fine-grained labels, with a remarkable reduction of the parameter size. Next, we move to matrix manifolds to work on graphs with diverse structures and properties. We propose a general framework to implement the mathematical tools required to learn graph embeddings on symmetric spaces. These spaces are of particular interest given that they have a compound geometry that simultaneously contains Euclidean as well as hyperbolic subspaces, allowing them to automatically adapt to dissimilar features in the graph. We demonstrate a concrete implementation of the framework on Siegel spaces, showcasing their versatility on different tasks. Finally, we focus on multi-relational graphs. We devise the means to translate Euclidean and hyperbolic multi-relational graph embedding models into the space of symmetric positive definite (SPD) matrices. To do so we develop gyrocalculus in this geometry and integrate it with the aforementioned framework

    Approximation Methods for Non-linear Gravitational Clustering

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    We discuss various analytical approximation methods for following the evolution of cosmological density perturbations into the strong (i.e. nonlinear) clustering regime. These methods can be classified into five types: (i) simple extrapolations from linear theory, such as the high--peak model and the lognormal model; (ii) {\em dynamical} approximations, including the Zel'dovich approximation and its extensions; (iii) non--linear models based on purely geometric considerations, of which the main example is the Voronoi model; (iv) statistical solutions involving scaling arguments, such as the hierarchical closure {\em ansatz} for BBGKY, fractal models and the thermodynamic model of Saslaw; (v) numerical techniques based on particles and/or hydrodynamics. We compare the results of full dynamical evolution using particle codes and the various other approximation schemes. To put the models we discuss into perspective, we give a brief review of the observed properties of galaxy clustering and the statistical methods used to quantify it, such as correlation functions, power spectra, topology and spanning trees.Comment: 175 pages, 20 figures. To appear in Phys. Rep. 1995. Hard copies of figures/Manuscript available upon request from: [email protected]

    Model-based Fault Diagnosis and Fault Accommodation for Space Missions : Application to the Rendezvous Phase of the MSR Mission

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    The work addressed in this thesis draws expertise from actions undertaken between the EuropeanSpace Agency (ESA), the industry Thales Alenia Space (TAS) and the IMS laboratory (laboratoirede l’Intégration du Matériau au Système) which develop new generations of integrated Guidance, Navigationand Control (GNC) units with fault detection and tolerance capabilities. The reference mission isthe ESA’s Mars Sample Return (MSR) mission. The presented work focuses on the terminal rendezvoussequence of the MSR mission which corresponds to the last few hundred meters until the capture. Thechaser vehicle is the MSR Orbiter, while the passive target is a diameter spherical container. The objectiveat control level is a capture achievement with an accuracy better than a few centimeter. The research workaddressed in this thesis is concerned by the development of model-based Fault Detection and Isolation(FDI) and Fault Tolerant Control (FTC) approaches that could significantly increase the operational andfunctional autonomy of the chaser during rendezvous, and more generally, of spacecraft involved in deepspace missions. Since redundancy exist in the sensors and since the reaction wheels are not used duringthe rendezvous phase, the work presented in this thesis focuses only on the thruster-based propulsionsystem. The investigated faults have been defined in accordance with ESA and TAS requirements andfollowing their experiences. The presented FDI/FTC approaches relies on hardware redundancy in sensors,control redirection and control re-allocation methods and a hierarchical FDI including signal-basedapproaches at sensor level, model-based approaches for thruster fault detection/isolation and trajectorysafety monitoring. Carefully selected performance and reliability indices together with Monte Carlo simulationcampaigns, using a high-fidelity industrial simulator, demonstrate the viability of the proposedapproaches.Les travaux de recherche traités dans cette thèse s’appuient sur l’expertise des actionsmenées entre l’Agence spatiale européenne (ESA), l’industrie Thales Alenia Space (TAS) et le laboratoirede l’Intégration du Matériau au Système (IMS) qui développent de nouvelles générations d’unités intégréesde guidage, navigation et pilotage (GNC) avec une fonction de détection des défauts et de tolérance desdéfauts. La mission de référence retenue dans cette thèse est la mission de retour d’échantillons martiens(Mars Sample Return, MSR) de l’ESA. Ce travail se concentre sur la séquence terminale du rendez-vous dela mission MSR qui correspond aux dernières centaines de mètres jusqu’à la capture. Le véhicule chasseurest l’orbiteur MSR (chasseur), alors que la cible passive est un conteneur sphérique. L’objectif au niveaude contrôle est de réaliser la capture avec une précision inférieure à quelques centimètres. Les travaux derecherche traités dans cette thèse s’intéressent au développement des approches sur base de modèle de détectionet d’isolation des défauts (FDI) et de commande tolérante aux défaillances (FTC), qui pourraientaugmenter d’une manière significative l’autonomie opérationnelle et fonctionnelle du chasseur pendant lerendez-vous et, d’une manière plus générale, d’un vaisseau spatial impliqué dans des missions située dansl’espace lointain. Dès lors que la redondance existe dans les capteurs et que les roues de réaction ne sontpas utilisées durant la phase de rendez-vous, le travail présenté dans cette thèse est orienté seulementvers les systèmes de propulsion par tuyères. Les défaillances examinées ont été définies conformément auxexigences de l’ESA et de TAS et suivant leurs expériences. Les approches FDI/FTC présentées s’appuientsur la redondance de capteurs, la redirection de contrôle et sur les méthodes de réallocation de contrôle,ainsi que le FDI hiérarchique, y compris les approches à base de signaux au niveau de capteurs, les approchesà base de modèle de détection/localisation de défauts de propulseur et la surveillance de sécuritéde trajectoire. Utilisant un simulateur industriel de haute-fidélité, les indices de performance et de fiabilitéFDI, qui ont été soigneusement choisis accompagnés des campagnes de simulation de robustesse/sensibilitéMonte Carlo, démontrent la viabilité des approches proposées
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