Cette thèse traite des méthodes de descente d’ordre un pour les problèmes de minimisation. Elle comprend trois parties. Dans la première partie, nous apportons une vue d’ensemble des bornes d’erreur et les premières briques d’unification d’un concept. Nous montrons en effet la place centrale de l’inégalité du gradient de Lojasiewicz, en mettant en relation cette inégalité avec les bornes d’erreur. Dans la seconde partie, en usant de l’inégalité de Kurdyka-Lojasiewicz (KL), nous apportons un nouvel outil pour calculer la complexité des m´méthodes de descente d’ordre un pour la minimisation convexe. Notre approche est totalement originale et utilise une suite proximale “worst-case” unidimensionnelle. Ces résultats introduisent une méthodologie simple : trouver une borne d’erreur, calculer la fonction KL désingularisante quand c’est possible, identifier les constantes pertinentes dans la méthode de descente, et puis calculer la complexité en usant de la suite proximale “worst-case” unidimensionnelle. Enfin, nous étendons la méthode extragradient pour minimiser la somme de deux fonctions, la première étant lisse et la seconde convexe. Sous l’hypothèse de l’inégalité KL, nous montrons que la suite produite par la méthode extragradient converge vers un point critique de ce problème et qu’elle est de longueur finie. Quand les deux fonctions sont convexes, nous donnons la vitesse de convergence O(1/k) qui est classique pour la méthode de gradient. De plus, nous montrons que notre complexité de la seconde partie peut être appliquée à cette méthode. Considérer la méthode extragradient est l’occasion de d´écrire la recherche linéaire exacte pour les méthodes de décomposition proximales. Nous donnons des détails pour l’implémentation de ce programme pour le problème des moindres carrés avec régularisation ℓ1 et nous donnons des résultats numériques qui suggèrent que combiner des méthodes non-accélérées avec la recherche linéaire exacte peut être un choix performant. / This thesis focuses on first order descent methods in the minimization problems. There are three parts. Firstly, we give an overview on local and global error bounds. We try to provide the first bricks of a unified theory by showing the centrality of the Lojasiewicz gradient inequality. In the second part, by using Kurdyka- Lojasiewicz (KL) inequality, we provide new tools to compute the complexity of first-order descent methods in convex minimization. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence. This result inaugurates a simple methodology: derive an error bound, compute the KL esingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Lastly, we extend the extragradient method to minimize the sum of two functions, the first one being smooth and the second being convex. Under Kurdyka-Lojasiewicz assumption, we prove that the sequence produced by the extragradient method converges to a critical point of this problem and has finite length. When both functions are convex, we provide a O(1/k) convergence rate. Furthermore, we show that our complexity result in the second part can be applied to this method. Considering the extragradient method is the occasion to describe exact line search for proximal decomposition methods. We provide details for the implementation of this scheme for the ℓ1 regularized least squares problem and give numerical results which suggest that combining nonaccelerated methods with exact line search can be a competitive choice.

<p>The overall objective of the Wallenberg Laboratory for Information Technology and Autonomous Systems (WITAS) at Linköping University is the development of an intelligent command and control system, containing vision sensors, which supports the operation of a unmanned air vehicle (UAV) in both semi- and full-autonomy modes. One of the UAV platforms of choice is the APID-MK3 unmanned helicopter, by Scandicraft Systems AB. The intended operational environment is over widely varying geographical terrain with traffic networks and vehicle interaction of variable complexity, speed, and density.</p><p>The present version of APID-MK3 is capable of autonomous take-off, landing, and hovering as well as of autonomously executing pre-defined, point-to-point flight where the latter is executed at low-speed. This is enough for performing missions like site mapping and surveillance, and communications, but for the above mentioned operational environment higher speeds are desired. In this context, the goal of this thesis is to explore the possibilities for achieving stable ‘‘aggressive’’ manoeuvrability at high-speeds, and test a variety of control solutions in the APID-MK3 simulation environment.</p><p>The objective of achieving ‘‘aggressive’’ manoeuvrability concerns the design of attitude/velocity/position controllers which act on much larger ranges of the body attitude angles, by utilizing the full range of the rotor attitude angles. In this context, a flight controller should achieve tracking of curvilinear trajectories at relatively high speeds in a robust, w.r.t. external disturbances, manner. Take-off and landing are not considered here since APIDMK3 has already have dedicated control modules that realize these flight modes.</p><p>With this goal in mind, we present the design of two different types of flight controllers: a fuzzy controller and a gradient descent method based controller. Common to both are model based design, the use of nonlinear control approaches, and an inner- and outer-loop control scheme. The performance of these controllers is tested in simulation using the nonlinear model of APID-MK3.</p> / Report code: LiU-Tek-Lic-2002:11. The format of the electronic version of this thesis differs slightly from the printed one: this is due mainly to font compatibility. The figures and body of the thesis are remaining unchanged.

No description available.

The selection and learning of kernel functions is a very important but rarely studied problem in the field of support vector learning. However, the kernel function of a support vector regression has great influence on its performance. The kernel function projects the dataset from the original data space into the feature space, and therefore the problems which can not be done in low dimensions could be done in a higher dimension through the transform of the kernel function. In this paper, there are two main contributions. Firstly, we introduce the gradient descent method to the learning of kernel functions. Using the gradient descent method, we can conduct learning rules of the parameters which indicate the shape and distribution of the kernel functions. Therefore, we can obtain better kernel functions by training their parameters with respect to the risk minimization principle. Secondly, In order to reduce the number of support vectors, we use the orthogonal least squares method. By choosing the representative support vectors, we may remove the less important support vectors in the support vector regression model. The experimental results have shown that our approach can derive better kernel functions than others and has better generalization ability. Also, the number of support vectors can be effectively reduced.

This paper proposes new iterative methods for the efficient computation of the smallest eigenvalue of the symmetric nonlinear matrix eigenvalue problems of large order with a monotone dependence on the spectral parameter. Monotone nonlinear eigenvalue problems for differential equations have important applications in mechanics and physics. The discretization of these eigenvalue problems leads to ill-conditioned nonlinear eigenvalue problems with very large sparse matrices monotone depending on the spectral parameter. To compute the smallest eigenvalue of large matrix nonlinear eigenvalue problem, we suggest preconditioned iterative methods: preconditioned simple iteration method, preconditioned steepest descent method, and preconditioned conjugate gradient method. These methods use only matrix-vector multiplications, preconditioner-vector multiplications, linear operations with vectors and inner products of vectors. We investigate the convergence and derive grid-independent error estimates of these methods for computing eigenvalues. Numerical experiments demonstrate practical effectiveness of the proposed methods for a class of mechanical problems.

The overall objective of the Wallenberg Laboratory for Information Technology and Autonomous Systems (WITAS) at Linköping University is the development of an intelligent command and control system, containing vision sensors, which supports the operation of a unmanned air vehicle (UAV) in both semi- and full-autonomy modes. One of the UAV platforms of choice is the APID-MK3 unmanned helicopter, by Scandicraft Systems AB. The intended operational environment is over widely varying geographical terrain with traffic networks and vehicle interaction of variable complexity, speed, and density. The present version of APID-MK3 is capable of autonomous take-off, landing, and hovering as well as of autonomously executing pre-defined, point-to-point flight where the latter is executed at low-speed. This is enough for performing missions like site mapping and surveillance, and communications, but for the above mentioned operational environment higher speeds are desired. In this context, the goal of this thesis is to explore the possibilities for achieving stable ‘‘aggressive’’ manoeuvrability at high-speeds, and test a variety of control solutions in the APID-MK3 simulation environment. The objective of achieving ‘‘aggressive’’ manoeuvrability concerns the design of attitude/velocity/position controllers which act on much larger ranges of the body attitude angles, by utilizing the full range of the rotor attitude angles. In this context, a flight controller should achieve tracking of curvilinear trajectories at relatively high speeds in a robust, w.r.t. external disturbances, manner. Take-off and landing are not considered here since APIDMK3 has already have dedicated control modules that realize these flight modes. With this goal in mind, we present the design of two different types of flight controllers: a fuzzy controller and a gradient descent method based controller. Common to both are model based design, the use of nonlinear control approaches, and an inner- and outer-loop control scheme. The performance of these controllers is tested in simulation using the nonlinear model of APID-MK3. / <p>Report code: LiU-Tek-Lic-2002:11. The format of the electronic version of this thesis differs slightly from the printed one: this is due mainly to font compatibility. The figures and body of the thesis are remaining unchanged.</p>

This paper proposes new iterative methods for the efficient computation of the smallest eigenvalue of the symmetric nonlinear matrix eigenvalue problems of large order with a monotone dependence on the spectral parameter. Monotone nonlinear eigenvalue problems for differential equations have important applications in mechanics and physics. The discretization of these eigenvalue problems leads to ill-conditioned nonlinear eigenvalue problems with very large sparse matrices monotone depending on the spectral parameter. To compute the smallest eigenvalue of large matrix nonlinear eigenvalue problem, we suggest preconditioned iterative methods: preconditioned simple iteration method, preconditioned steepest descent method, and preconditioned conjugate gradient method. These methods use only matrix-vector multiplications, preconditioner-vector multiplications, linear operations with vectors and inner products of vectors. We investigate the convergence and derive grid-independent error estimates of these methods for computing eigenvalues. Numerical experiments demonstrate practical effectiveness of the proposed methods for a class of mechanical problems.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19122号 / 情博第568号 / 新制||情||100(附属図書館) / 32073 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 山下 信雄, 教授 太田 快人, 教授 永持 仁 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Este trabalho apresenta o desenvolvimento de algoritmos de adaptação do padrão de marcha com a utilização de redes neurais artificiais para uma órtese ativa para membros inferiores. Trajetórias estáveis são geradas durante o processo de otimização, considerando um gerador de trajetórias baseado no critério do ZMP (Zero Moment Point) e no modelo dinâmico do equipamento. Três redes neurais são usadas para diminuir o tempo de cálculo do modelo e da otimização do ZMP, e reproduzir o gerador de trajetórias analítico. A primeira rede aproxima a dinâmica do modelo fornecendo a variação de torque necessária para a realização do processo de otimização dos parâmetros de adaptação da marcha; a segunda rede trabalha no processo de otimização, fornecendo o parâmetro otimizado de acordo com a interação paciente-órtese; a terceira rede reproduz o gerador de trajetórias para um determinado intervalo de tempo do passo que pode ser repetido para qualquer quantidade de passos. Além disso, um controle do tipo torque calculado acrescido de um controle PD é usado para garantir que as trajetórias atuais estejam seguindo as trajetórias desejadas da órtese. O modelo dinâmico da órtese na sua configuração atual, com forças de interação incluídas, é usado para gerar resultados simulados. / This work deals with neural network-based gait-pattern adaptation algorithms for an active lower limbs orthosis. Stable trajectories are generated during the optimization process, considering a trajectory generator based on the Zero Moment Point criterion and on the dynamic model. Additionally, three neural network are used to decrease the time-consuming computation of the model and ZMP optimization and to reproduce the analitical trajectory generator. The first neural network approximates the dynamic model providing the necessary torque variation to gait adaptation parameters process; the second network works in the optimization procedure, giving the adapting parameter according to orthosis-patient interaction; and the third network replaces the trajectory generation for a stablished step time interval which can be reproduced any time during the walking. Also, a computed torque controller plus the PD controller is designed to guarantee the actual trajectories are following the orthosis desired trajectories. The dynamic model of the actual active orthosis, with interaction forces included, is used to generate simulation results.

Este trabalho apresenta o desenvolvimento de algoritmos de adaptação do padrão de marcha com a utilização de redes neurais artificiais para uma órtese ativa para membros inferiores. Trajetórias estáveis são geradas durante o processo de otimização, considerando um gerador de trajetórias baseado no critério do ZMP (Zero Moment Point) e no modelo dinâmico do equipamento. Três redes neurais são usadas para diminuir o tempo de cálculo do modelo e da otimização do ZMP, e reproduzir o gerador de trajetórias analítico. A primeira rede aproxima a dinâmica do modelo fornecendo a variação de torque necessária para a realização do processo de otimização dos parâmetros de adaptação da marcha; a segunda rede trabalha no processo de otimização, fornecendo o parâmetro otimizado de acordo com a interação paciente-órtese; a terceira rede reproduz o gerador de trajetórias para um determinado intervalo de tempo do passo que pode ser repetido para qualquer quantidade de passos. Além disso, um controle do tipo torque calculado acrescido de um controle PD é usado para garantir que as trajetórias atuais estejam seguindo as trajetórias desejadas da órtese. O modelo dinâmico da órtese na sua configuração atual, com forças de interação incluídas, é usado para gerar resultados simulados. / This work deals with neural network-based gait-pattern adaptation algorithms for an active lower limbs orthosis. Stable trajectories are generated during the optimization process, considering a trajectory generator based on the Zero Moment Point criterion and on the dynamic model. Additionally, three neural network are used to decrease the time-consuming computation of the model and ZMP optimization and to reproduce the analitical trajectory generator. The first neural network approximates the dynamic model providing the necessary torque variation to gait adaptation parameters process; the second network works in the optimization procedure, giving the adapting parameter according to orthosis-patient interaction; and the third network replaces the trajectory generation for a stablished step time interval which can be reproduced any time during the walking. Also, a computed torque controller plus the PD controller is designed to guarantee the actual trajectories are following the orthosis desired trajectories. The dynamic model of the actual active orthosis, with interaction forces included, is used to generate simulation results.