The primary objective of this thesis is to leverage on the framework of H∞ loop-shaping control to formulate efficient and powerful optimization algorithms in LMI framework for the synthesis of performance loop-shaping weights. The H∞ loop-shaping design procedure is an efficient controller synthesis technique that combines classical loop-shaping concepts with H∞ synthesis. This procedure establishes a good tradeoff between robust stability and robust performance of a closed-loop system in a systematic manner. However, the selection of pre- and/or post-compensators, a crucial step in the design procedure, is nontrivial as factors such as the right half plane poles/zeros of the nominal plant, roll-off rate around the crossover frequency, strength of cross-coupling in multi-input multi-output systems, expected bandwidth, etc. must be adequately considered.Firstly, a frequency-dependent weight optimization framework is formulated in state-space form in order to remove the dependency on frequency while retaining the objective of maximizing the robust stability margin of a closed-loop system. This formulation facilitates the synthesis of low-order controllers, which is desirable from an implementation perspective.A weight optimization framework that incorporates smoothness constraints in order to prevent the cancellation of important modes of the system, for example, lightly damped poles/zeros of flexible structures, is subsequently formulated. The proposed formulation is intuitive from a design perspective as the smoothness constraints are expressed as gradient constraints on a log-log scale in dB/decade, consistent with the notation used in Bode plot for single-input single-output systems and singular value plots for multi-input multi-output systems.Thereafter, an optimization framework that maximizes the robust performance of a closed-loop system is presented. The philosophy in this framework is in line with practical design objectives that give the best achievable robust performance on a particular problem once a level of robust stability margin is demanded.Lastly, a novel unmanned vehicle is proposed. The vehicle uses a full six-degree-of-freedom tri-rotor actuation, capable of fully decoupled thrust and torque vectoring in all the 3D space. This vehicle can act as an unmanned ground vehicle or unmanned aerial vehicle, but the objective herein is restricted to the upright stability of the vehicle while operating on the ground as this is a precursor to rolling motion. The full nonlinear model of the vehicle is derived and linearized for subsequent controller synthesis, and this is thereafter validated by means of numerical simulations.

Nous proposons d’étudier la méthodologie de la segmentation de processus avec un bruit autorégressif sous ses aspects théoriques et pratiques. Par « segmentation » on entend ici l’inférence de points de rupture multiples correspondant à des changements abrupts dans la moyenne de la série temporelle. Le point de vue adopté est de considérer les paramètres de l’autorégression comme des paramètres de nuisance, à prendre en compte dans l’inférence dans la mesure où cela améliore la segmentation.D’un point de vue théorique, le but est de conserver un certain nombre de propriétés asymptotiques de l’estimation des points de rupture et des paramètres propres à chaque segment. D’un point de vue pratique, on se doit de prendre en compte les limitations algorithmiques liées à la détermination de la segmentation optimale. La méthode proposée, doublement contrainte, est basée sur l’utilisation de techniques d’estimation robuste permettant l’estimation préalable des paramètres de l’autorégression, puis la décorrélation du processus, permettant ainsi de s’approcher du problème de la segmentation dans le cas d’observations indépendantes. Cette méthode permet l’utilisation d’algorithmes efficaces. Elle est assise sur des résultats asymptotiques que nous avons démontrés. Elle permet de proposer des critères de sélection du nombre de ruptures adaptés et fondés. Une étude de simulations vient l’illustrer. / We propose to study the methodology of autoregressive processes segmentation under both its theoretical and practical aspects. “Segmentation” means here inferring multiple change-points corresponding to mean shifts. We consider autoregression parameters as nuisance parameters, whose estimation is considered only for improving the segmentation.From a theoretical point of view, we aim to keep some asymptotic properties of change-points and other parameters estimators. From a practical point of view, we have to take into account the algorithmic constraints to get the optimal segmentation. To meet these requirements, we propose a method based on robust estimation techniques, which allows a preliminary estimation of the autoregression parameters and then the decorrelation of the process. The aim is to get our problem closer to the segmentation in the case of independent observations. This method allows us to use efficient algorithms. It is based on asymptotic results that we proved. It allows us to propose adapted and well-founded number of changes selection criteria. A simulation study illustrates the method.

This thesis is a pilot study on the subsampling methods for robust estimation in regression models when there are possible outliers in the data. Two basic proposals of the subsampling method are investigated. The main idea is to identify good data points through fitting the model to randomly chosen subsamples. Subsamples containing no outliers are identified by good fit and they are combined to form a subset of good data points. Once the combined sets containing only good data points are identified, classical estimation methods such as the least-squares method and the maximum likelihood method can be applied to do regression analysis using the combined set. Numerical evidence suggest that the subsampling method is robust against outliers with high breakdown point, and it is competitive to other robust methods in terms of both robustness and efficiency. It has wide application to a variety of regression models including the linear regression models, the non-linear regression models and the generalized linear regression models. Research is ongoing with the aim of making this method an effective and practical method for robust inference on regression models.

This master thesis is focused on methods of outlier detection. The aim of this work is to assess the suitability of using robust methods on real data of EKO-KOM, a.s. The first part of the thesis provides an overview and a theoretical treatise on classic and robust methods of outlier detection. These methods are subsequently applied to the obtained data file of EKO-KOM, a.s. in the practical part of the thesis. At the conclusion of the thesis, there are recommendations about suitability of methods, which are based on comparison of classical and robust methods.

Le problème de filtrage consiste à estimer l'état d'un système dynamique, appelé signal qui est souvent un processus markovien, à partir d'observation bruitées des états passés du système. Dans ce mémoire, nous considérons un modèle de filtrage en temps continu pour le processus de diffusion. Le but est d'étudier la stabilité du filtre optimal par rapport à sa condition initiale au-delà de l'hypothèse de mélange (fort) pour le noyau de transition en ignorant l'ergodicité du signal / The filtering problem consists of estimating the state of a dynamic, called signal which is often a Markov process, from the noisy observation of the past states. In this thesis, we consider a filtering model in continuous time for the diffusion process. The aim is to study the stability of the optimal filter with respect to its initial condition beyond the mixing (or quasi – mixing) hypothesis for the transition kernel

Cette thèse concerne le développement d’outils de conception nécessaires à la réalisation de matériaux composites hybrides intégrant des patchs piézoélectriques shuntés électriquement par des circuits à capacité négative. L’impact des incertitudes sur les performances de ces systèmes hybrides innovants est à ce jour inconnu ou mal maîtrisé, ce qui peut compromettre leur fiabilité et nuire à leur applicabilité industrielle. La première contribution du travail de thèse a ainsi porté sur le développement et la caractérisation d’un circuit de shunt numérique adapté à un contrôle adaptatif pour une structure équipée d’un grand nombre de patchs. Les étapes de dimensionnement et de conception électronique du dispositif sont présentées et ont conduit à un prototype qui a montré expérimentalement sa capacité à générer un shunt de type capacité négative. La deuxième contribution du travail de thèse porte sur l’analyse de la robustesse de ces dispositifs en considérant le système dans sa globalité, depuis les paramètres géométriques (dimensions) ou matériaux jusqu’aux paramètres électriques. Une analyse des paramètres les plus influents est proposée et conduit à une mise en évidence des plages d’incertitudes tolérables pour une efficacité donnée. Enfin l’association des dispositifs considérés en un réseau distribué permet d’envisager une meilleure réduction des vibrations ou ondes acoustiques par un accroissement notamment de la largeur de bande fréquentielle dans laquelle le système est efficace. Le circuit numérique développé dans la thèse permet d’envisager cette extension au caractère distribué par sa miniaturisation, son adaptabilité et son intégrabilité. La dernière contribution du travail de thèse porte donc sur des perspectives d’extension du travail développé à un système distribué pour la génération d’une inter face active intégrée à la structure. / This thesis deals with the development of design tools needed for the realization of hybridcomposite materials incorporating piezoelectric patches electrically shunted by negativecapacitance circuits. The impact of uncertainty on the performance of these innovative hybridsystems is yet unknown or poorly controlled, which can compromise their reliability and harmtheir industrial applicability. The first thesis contribution has focused on the development andcharacterization of a digital shunt circuit adapted to an adaptive control for a structureequipped with a large number of patches. The design steps and electronic device design arepresented and led to a prototype that has shown experimentally its ability to implement anegative capacitance shunt. The second contribution of the thesis is the analysis of therobustness of these devices by considering the whole system, from geometric to materialsparameters, including the electrical parameters. An analysis of the most significantparameters is proposed and has highlighted the tolerable uncertainty ranges for a givenefficiency. Finally, the combination of the developed digital devices inside a distributednetwork provides a better reduction of acoustic waves or vibrations by increasing theefficiency bandwidth. The use of the developed digital circuit in such distributed systems hasbeen made possible by its miniaturization, adaptability and integrability. The last contributionof the thesis therefore focuses on prospects in fully integrated active interfaces.

Transportation system is one of the key functioning components of the modern society and plays an important role in the circulation of commodity and growth of economy. Transportation system is not only the major influencing factor of the efficiency of large-scale complex industrial logistics, but also closely related to everyone’s daily life. The goals of an ideal transportation system are focused on improving mobility, accessibility, safety, enhancing the coordination of different transportation modals and reducing the impact on the environment, all these activities require sophisticated design and plan that consider different factors, balance tradeoffs and maintaining efficiency. Hence, the design and planning of transportation system are strongly considered to be the most critical problems in transportation research. Transportation system planning and design is a sequential procedure which generally contains two levels: strategic and operational. This dissertation conducts extensive research covering both levels, on the strategic planning level, two network design problems are studied and on the operational level, routing and scheduling problems are analyzed. The main objective of this study is utilizing operations research techniques to generate and provide managerial decision supports in designing reliable and efficient transportation system. Specifically, three practical problems in transportation system design and operations are explored. First, we collaborate with a public transit company to study the bus scheduling problem for a bus fleet with multiples types of vehicles. By considering different cost characteristics, we develop integer program and exact algorithm to efficiently solve the problem. Next, we examine the network design problem in emergency medical service and develop a novel two stage robust optimization framework to deal with uncertainty, then propose an approximate algorithm which is fast and efficient in solving practical instance. Finally, we investigate the major drawback of vehicle sharing program network design problem in previous research and provide a counterintuitive finding that could result in unrealistic solution. A new pessimistic model as well as a customized computational scheme are then introduced. We benchmark the performance of new model with existing model on several prototypical network structures. The results show that our proposed models and solution methods offer powerful decision support tools for decision makers to design, build and maintain efficient and reliable transportation systems.

This thesis presents a robust nonlinear model predictive controller (RNMPC), nominal nonlinear model predictive controller (NMPC) and single-loop proportional-integral-derivative (PID) controllers that are applied to a nonlinear model of a run-of-mine (ROM) ore milling circuit. The model consists of nonlinear modules for the individual process units of the milling circuit (such as the mill, sump and cyclone), which allow arbitrary milling circuit configurations to be modelled easily. This study aims to cast a complex problem of a ROM ore milling circuit into an RNMPC framework without losing the flexibility of the modularised nonlinear model and implement the RNMPC using open-source software modules. The three controllers are compared in a simulations study to determine the performance of the controllers subject to severe disturbances and model parameter variations. The disturbances include changes to the feed ore hardness, changes in the feed ore size distributions and spillage water being added to the sump. The simulations show that the RNMPC and NMPC perform better than the PID controllers with regard to the economic objectives, assuming full-state feedback is available, especially when actuator constraints become active. The execution time of the RNMPC, however, is much too long for real-time implementation and would require further research to improve the efficiency of the implementation. / Thesis (PhD)--University of Pretoria, 2009. / Electrical, Electronic and Computer Engineering / unrestricted

In this research, a novel machine learning method is designed and applied to Mine Countermeasure Missions. Similarly to some kernel methods, the proposed approach seeks to compute a linear model from another higher dimensional feature space. However, no kernel is used and the feature mapping is explicit. Computation can be done directly in the accessible feature space. In the proposed approach, the feature projection is implemented by constructing a large hidden layer, which differs from traditional belief that Multi-Layer Perceptron is usually funnel-shaped and the hidden layer is used as feature extractor. The proposed approach is a general method that can be applied to various problems. It is able to improve the performance of the neural network based methods and the learning speed of support vector machine. The classification speed of the proposed approach is also faster than that of kernel machines on the mine countermeasure mission task.

The recent advances in the field of computer vision have brought many of the laboratory algorithms into the realm of industry. However, one problem that still remains open in the field of 3D vision is the problem of noise. The challenging problem of 3D structure recovery from images is highly sensitive to the presence of input data that are contaminated by errors that do not conform to ideal assumptions. Tackling the problem of extreme data, or outliers has led to many robust methods in the field that are able to handle moderate levels of outliers and still provide accurate outputs. However, this problem remains open, especially for higher noise levels and so it has been the goal of this thesis to address the issue of robustness with respect to two central problems in 3D computer vision. The two problems are highly related and they have been presented together within a Structure from Motion (SfM) context. The first, is the problem of robustly estimating the fundamental matrix from images whose correspondences contain high outlier levels. Even though this area has been extensively studied, two algorithms have been proposed that significantly speed up the computation of the fundamental matrix and achieve accurate results in scenarios containing more than 50% outliers. The presented algorithms rely on ideas from the field of robust statistics in order to develop guided sampling techniques that rely on information inferred from residual analysis. The second, problem addressed in this thesis is the robust estimation of camera intrinsic parameters from fundamental matrices, or self-calibration. Self-calibration algorithms are notoriously unreliable for general cases and it is shown that the existing methods are highly sensitive to noise. In spite of this, robustness in self-calibration has received little attention in the literature. Through experimental results, it is shown that it is essential for a real-world self-calibration algorithm to be robust. In order to introduce robustness to the existing methods, three robust algorithms have been proposed that utilize existing constraints for self-calibration from the fundamental matrix. However, the resulting algorithms are less affected by noise than existing algorithms based on these constraints. This is an important milestone since self-calibration offers many possibilities by providing estimates of camera parameters without requiring access to the image acquisition device. The proposed algorithms rely on perturbation theory, guided sampling methods and a robust root finding method for systems of higher order polynomials. By adding robustness to self-calibration it is hoped that this idea is one step closer to being a practical method of camera calibration rather than merely a theoretical possibility.