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Controle inteligente LQR neuro-genético para alocação de autoestrutura em sistemas dinâmicos multivariáveisABREU, Ivanildo Silva 30 August 2008 (has links)
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Previous issue date: 2008-08-30 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta tese é apresentado um modelo neuro-genético, orientado a síntese de controladores
no espaço de estado baseado no projeto do Regulador Linear Quadrático,
para alocação de autoestrutura em sistemas dinâmicos multivariáveis. O modelo
neuro-genético representa uma fusão de um algoritmo genético e uma rede neural
recorrente para realizar a seleção das matrizes de ponderação e resolver a equação
algébrica de Riccati, respectivamente. Um modelo de 6a ordem de uma aeronave,
um modelo de 6a ordem de um gerador de indução duplamente alimentado de uma
planta eólica e um modelo de 4a ordem de um circuito elétrico, são usados para
avaliar a fusão dos paradigmas de inteligência computacional e o desempenho da
metodologia do projeto de controle. O desempenho dos modelos neuro-genéticos
são avaliados por momentos estatísticos de primeira e segunda ordem para o algoritmo
genético, enquanto que a rede neural é avaliada por superfícies da função
energia e da norma do infinito da equação algébrica de Riccati. São feitas comparações
com o método de Schur. / In this thesis is presented a neural-genetic model, oriented to state space controllers
synthesis, based on the Linear Quadratic Regulator design, for eigenstructure
assignment of multivariable dynamic systems. The neural-genetic model represents
a fusion of a genetic algorithm and a recurrent neural network to perform
the weighting matrices selection and the algebraic Riccati equation solution, respectively.
In order to a assess the LQR design, the procedure was applied in
a 6th order aircraft model, 6th order doubly fed induction generator model of a
wind plant and a 4th order electric circuit model which were used to evaluate the
fusion of the computational intelligence paradigms and the control design method
performance.The performance of the neural-genetic models are evaluated by the
first and second statistics moments for the genetic algorithm, whereas the neural
network is evaluated by surfaces of the energy function and of the norm of the
infinity of the algebraic equation of Riccati and the results compared to the results
obtained by using Schur’s Method.
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Estimation over heterogeneous sensor networksSandberg, Henrik, Rabi, Maben, Skoglund, Mikael, Johansson, Karl Henrik January 2008 (has links)
Design trade-offs between estimation performance, processing delay and communication cost for a sensor scheduling problem is discussed. We consider a heterogeneous sensor network with two types of sensors: the first type has low-quality measurements, small processing delay and a light communication cost, while the second type is of high quality, but imposes a large processing delay and a high communication cost. Such a heterogeneous sensor network is common in applications, where for instance in a localization system the poor sensor can be an ultrasound sensor while the more powerful sensor can be a camera. Using a time-periodic Kalman filter, we show how one can find an optimal schedule of the sensor communication. One can significantly improve estimation quality by only using the expensive sensor rarely. We also demonstrate how simple sensor switching rules based on the Riccati equation drives the filter into a stable time-periodic Kalman filter. ᅵ 2008 IEEE. / <p>QC 20110224</p>
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Commande h∞ à base de modèles non entiers / H∞ control of fractional order modelsFadiga, Lamine 12 June 2014 (has links)
Les études menées permettent d’étendre la méthodologie de commande H∞ aux modèles décrits par des équations différentielles faisant intervenir des ordres de dérivation non entiers. Deux approches sont proposées. La première consiste à réécrire le modèle non entier comme un modèle entier incertain afin de pouvoir utiliser les méthodes de commande H∞ développées pour les modèles entiers. La seconde approche consiste à développer des conditions LMI spécifiques aux modèles non entiers à partir de leur pseudo représentation d’état. Ces deux approches sont appliquées à l’isolation vibratoire d’un pont. / The general theme of the work enables to extend H∞ control methodology to fractional order models. Two approaches are proposed. The first one consists in rewriting the fractional order model as an uncertain integer order model in order to use existing H∞ control methods for integer order models. The second approach consists in developing specific LMI conditions for fractional order models based on their pseudo state space representation. These two approaches are applied to the vibratory isolation of a bridge.
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Steepest descent as Linear Quadratic RegulationDufort-Labbé, Simon 08 1900 (has links)
Concorder un modèle à certaines observations, voilà qui résume assez bien ce que l’apprentissage machine cherche à accomplir. Ce concept est maintenant omniprésent dans nos vies, entre autre grâce aux percées récentes en apprentissage profond. La stratégie d’optimisation prédominante pour ces deux domaines est la minimisation d’un objectif donné. Et pour cela, la méthode du gradient, méthode de premier-ordre qui modifie les paramètres du modèle à chaque itération, est l’approche dominante. À l’opposé, les méthodes dites de second ordre n’ont jamais réussi à s’imposer en apprentissage profond. Pourtant, elles offrent des avantages reconnus qui soulèvent encore un grand intérêt. D’où l’importance de la méthode du col, qui unifie les méthodes de premier et second ordre sous un même paradigme.
Dans ce mémoire, nous établissons un parralèle direct entre la méthode du col et le domaine du contrôle optimal ; domaine qui cherche à optimiser mathématiquement une séquence de décisions. Et certains des problèmes les mieux compris et étudiés en contrôle optimal sont les commandes linéaires quadratiques. Problèmes pour lesquels on connaît très bien la solution optimale. Plus spécifiquement, nous démontrerons l’équivalence entre une itération de la méthode du col et la résolution d’une Commande Linéaire Quadratique (CLQ).
Cet éclairage nouveau implique une approche unifiée quand vient le temps de déployer nombre d’algorithmes issus de la méthode du col, tel que la méthode du gradient et celle des gradients naturels, sans être limitée à ceux-ci. Approche que nous étendons ensuite aux problèmes à horizon infini, tel que les modèles à équilibre profond. Ce faisant, nous démontrons pour ces problèmes que calculer les gradients via la différentiation implicite revient à employer l’équation de Riccati pour solutionner la CLQ associée à la méthode du gradient. Finalement, notons que l’incorporation d’information sur la courbure du problème revient généralement à rencontrer une inversion matricielle dans la méthode du col. Nous montrons que l’équivalence avec les CLQ permet de contourner cette inversion en utilisant une approximation issue des séries de Neumann. Surprenamment, certaines observations empiriques suggèrent que cette approximation aide aussi à stabiliser le processus d’optimisation quand des méthodes de second-ordre sont impliquées ; en agissant comme un régularisateur adaptif implicite. / Machine learning entails training a model to fit some given observations, and recent advances in the field, particularly in deep learning, have made it omnipresent in our lives. Fitting a model usually requires the minimization of a given objective. When it comes to deep learning, first-order methods like gradient descent have become a default tool for optimization in deep learning. On the other hand, second-order methods did not see widespread use in deep learning. Yet, they hold many promises and are still a very active field of research. An important perspective into both methods is steepest descent, which allows you to encompass first and second-order approaches into the same framework.
In this thesis, we establish an explicit connection between steepest descent and optimal control, a field that tries to optimize sequential decision-making processes. Core to it is the family of problems known as Linear Quadratic Regulation; problems that have been well studied and for which we know optimal solutions. More specifically, we show that performing one iteration of steepest descent is equivalent to solving a Linear Quadratic Regulator (LQR). This perspective gives us a convenient and unified framework for deploying a wide range of steepest descent algorithms, such as gradient descent and natural gradient descent, but certainly not limited to. This framework can also be extended to problems with an infinite horizon, such as deep equilibrium models. Doing so reveals that retrieving the gradient via implicit differentiation is equivalent to recovering it via Riccati’s solution to the LQR associated with gradient descent. Finally, incorporating curvature information into steepest descent usually takes the form of a matrix inversion. However, casting a steepest descent
step as a LQR also hints toward a trick that allows to sidestep this inversion, by leveraging Neumann’s series approximation. Empirical observations provide evidence that this approximation actually helps to stabilize the training process, by acting as an adaptive damping parameter.
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Théorie non linéaire du potentiel et équations quasilinéaires avec données mesures / Nonlinear potential theory and quasilinear equations with measure dataNguyen, Quoc-Hung 25 September 2014 (has links)
Cette thèse concerne l’existence et la régularité de solutions d’équations non-linéaires elliptiques, d’équations paraboliques et d’équations de Hesse avec mesures, et les critères de l’existence de solutions grandes d’équations elliptiques et paraboliques non-linéaires. / This thesis is concerned to the existence and regularity of solutions to nonlinear elliptic, parabolic and Hessian equations with measure, and criteria for the existence of large solutions to some nonlinear elliptic and parabolic equations.
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THÉORIE NON LINÉAIRE DU POTENTIEL ET ÉQUATIONS QUASILINÉAIRES AVEC DONNÉES MESURESNguyen, Quoc-Hung 25 September 2014 (has links) (PDF)
Cette thése concerne l'existence et la régularité de solutions d'équations non-linéaires elliptiques, d'équations paraboliques et d'équations de Hesse avec mesures, et les critéres de l'existence de solutions grandes d'équations elliptiques et paraboliques non-linéaires. \textbf{Liste de publications} \begin{description} \item[1.] Avec M. F. Bidaut-Véron, L. Véron; {\em Quasilinear Lane-Emden equations with absorption and measure data,} Journal des Mathématiques Pures et Appliquées,~{\bf 102}, 315-337 (2014). \item[2] Avec L. Véron; {\em Quasilinear and Hessian type equations with exponential reaction and measure data,} Archive for Rational Mechanics and Analysis, {\bf 214}, 235-267 (2014). \item[3] Avec L. Véron; {\em Wiener criteria for existence of large solutions of quasilinear elliptic equations with absorption,} 17 pages, soumis, arXiv:1308.2956. \item[4] Avec M. F. Bidaut-Véron; {\em Stability properties for quasilinear parabolic equations with measure data,} 29 pages, á apparaître dans Journal of European Mathematical Society, arXiv:1409.1518. \item[5] Avec M. F. Bidaut-Véron; {\em Evolution equations of $p$-Laplace type with absorption or source terms and measure data}, 21 pages, á apparaître dans Communications in Contemporary Mathematics, arXiv:1409.1520. \item[6] {\em Potential estimates and quasilinear parabolic equations with measure data,} 118 pages, arXiv:1405.2587v1. \item[7] Avec L. Véron; {\em Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain,} 29 pages, soumis,\\ arXiv:1406.3850. \item[8] Avec M. F. Bidaut-Véron; {Pointwise estimates and existence of solutions of porous medium and $p$-Laplace evolution equations with absorption and measure data,\em } 27 pages, soumis, arXiv:1407.2218. \end{description}\begin{description} \item[1.] Avec M. F. Bidaut-Véron, L. Véron; {\em Quasilinear Lane-Emden equations with absorption and measure data,} Journal des Mathématiques Pures et Appliquées,~{\bf 102}, 315-337 (2014). \item[2] Avec L. Véron; {\em Quasilinear and Hessian type equations with exponential reaction and measure data,} Archive for Rational Mechanics and Analysis, {\bf 214}, 235-267 (2014). \item[3] Avec L. Véron; {\em Wiener criteria for existence of large solutions of quasilinear elliptic equations with absorption,} 17 pages, soumis, arXiv:1308.2956. \item[4] Avec M. F. Bidaut-Véron; {\em Stability properties for quasilinear parabolic equations with measure data,} 29 pages, á apparaître dans Journal of European Mathematical Society, arXiv:1409.1518. \item[5] Avec M. F. Bidaut-Véron; {\em Evolution equations of $p$-Laplace type with absorption or source terms and measure data}, 21 pages, á apparaître dans Communications in Contemporary Mathematics, arXiv:1409.1520. \item[6] {\em Potential estimates and quasilinear parabolic equations with measure data,} 118 pages, arXiv:1405.2587v1. \item[7] Avec L. Véron; {\em Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain,} 29 pages, soumis,\\ arXiv:1406.3850. \item[8] Avec M. F. Bidaut-Véron; {Pointwise estimates and existence of solutions of porous medium and $p$-Laplace evolution equations with absorption and measure data,\em } 27 pages, soumis, arXiv:1407.2218. \end{description}
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