La norme 3G/UMTS a permis de développer les premières applications multimédia pour téléphones et tablettes mobiles. Le nouveau standard 4G/LTE (Long Term Evolution) a pour objectif le très haut débit mobile. Dans ce standard, beaucoup d’efforts ont portés sur la reconfiguration automatique des réseaux en fonction de la demande des clients dans un processus appelé Self-Organizing Network (SON). Le travail de cette thèse s’inscrit dans cette direction. La reconfiguration de réseaux est comprise principalement dans le sens des modèles, des méthodes et des outils pour analyser les indicateurs remontés du réseau et configurer automatiquement les paramètres. Nous avons essentiellement travaillé sur les paramètres des aériens, l’allocation des fréquences, des puissances d’émission et des inclinaisons verticales.Dans cette optique, étant donné la forte variabilité des données d’entrée de l’optimisation issues des remontées de réseau, cette thèse porte sur les modèles et algorithmes d’optimisation robuste dans le contexte de l’optimisation sous contraintes. L’optimisation robuste fait référence à un ensemble de procédés pour proposer des solutions à des problèmes combinatoires dans un contexte de données incertaines et de scénarios variables dans le temps. Une première partie est dédiée à l’état de l’art et présente les principes des Self-Organizing Network (SON). La deuxième partie est consacrée à l’état de l’art des méthodes en optimisation robuste. En troisième partie nous présentons la modélisation mathématique du problème d’optimisation pour lequel les données de trafic (répartitions des clients sur la zone de service et leurs demandes respectives) prennent des valeurs variables dans le temps. Une phase de diagnostic sur le fonctionnement du réseau à partir des données, et une étude de sensibilité des solutions vis-à-vis des variations dans la réalisation des données ont été faites en quatrième partie avec des algorithmes de recherche locale. La cinquième partie présente le travail de conception, développement et test sur scénarios, d’une Recherche Tabou ainsi qu’une analyse approfondie sur les méthodes de pilotage envisagées pour les SON en 4G. / The standard 3G/UMTS has launched the first multimedia applications for mobile phones and tablets. The new standard 4G/LTE (Long Term Evolution) has mobile broadband objective. In this standard a huge effort has been done on automatic network reconfiguration based on customer demand variation in a process called Self-Organizing Network (SON). The work of this thesis lies in this direction. Reconfiguration of networks lies mainly in the direction of models, methods and tools to analyze network Key Performance Indicators and automatically configure its settings. We mainly worked on the air interface parameters such that frequency assignment, emitted power and pattern vertical inclination.In this context, given the high variability of optimization input data issued from the network, this thesis focuses on robust optimization under constraints. The robust optimization refers to a set of processes to provide solutions to combinatorial problems with uncertain and variable scenarios of data over time. The first Section presents the principles of Self-Organizing Network (SON). The second Section concerns the state of the art on robust optimization. The third Section defines the mathematical model to optimize for which traffic data (distribution of customers and throughput requirements on the service area) take variable values over time. A data diagnostic phase on the network operation and a sensitivity analysis of the solutions were made in the fourth Section with several local search algorithms. The fifth Section presents the work of design, development and test of a Tabu Search method and a thorough analysis of SON control methodology proposed for 4G.

The reliability issue of the infrastructure systems has become one of the major concerns of the system operators. This dissertation is a collection of four published and working papers that address the specific reliable design and operations problems from three different application settings: transportation/telecommunications network, distribution network, and power plant. In these four projects, key random factors like site disruption and uncertain demand are explicitly considered and proper research tools including stochastic programming, robust optimization, and variants of robust optimization are applied to formulate the problems based on which the important and challenging modelling elements (nonlinear congestion, disruption caused demand variation, etc.) can be introduced and studied. Besides, for each of the optimization models, we also develop advanced solution algorithms that can solve large-scale instances within a short amount of time and devise comprehensive numerical experiments to derive insights. The modelling techniques and solution methods can be easily extended to study reliability issues in other applications.

In this thesis, we consider a robust state estimation problem for discrete-time, homogeneous, first-order, finite-state finite-alphabet hidden Markov models (HMMs). Based on Kolmogorov's Theorem on the existence of a process, we first present the Kolmogorov model for the HMMs under consideration. A new change of measure is introduced. The statistical properties of the Kolmogorov representation of an HMM are discussed on the canonical probability space. A special Kolmogorov measure is constructed. Meanwhile, the ergodicity of two expanded Markov chains is investigated. In order to describe the uncertainty of HMMs, we study probability distance problems based on the Kolmogorov model of HMMs. Using a change of measure technique, the relative entropy and the relative entropy rate as probability distances between HMMs, are given in terms of the HMM parameters. Also, we obtain a new expression for a probability distance considered in the existing literature such that we can use an information state method to calculate it. Furthermore, we introduce regular conditional relative entropy as an a posteriori probability distance to measure the discrepancy between HMMs when a realized observation sequence is given. A representation of the regular conditional relative entropy is derived based on the Radon-Nikodym derivative. Then a recursion for the regular conditional relative entropy is obtained using an information state method. Meanwhile, the well-known duality relationship between free energy and relative entropy is extended to the case of regular conditional relative entropy given a sub-[special character]-algebra. Finally, regular conditional relative entropy constraints are defined based on the study of the probability distance problem. Using a Lagrange multiplier technique and the duality relationship for regular conditional relative entropy, a finite horizon robust state estimator for HMMs with regular conditional relative entropy constraints is derived. A complete characterization of the solution to the robust state estimation problem is also presented.

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In airline scheduling a variety of planning and operational decision problems have to be solved. In this thesis we consider the problems aircraft routing and crew pairing: aircraft and crew must be allocated to flights of a schedule in a minimal cost way. Although these problems are not independent, they are usually formulated as independent mathematical optimisation models and solved sequentially. This approach might lead to a suboptimal allocation of aircraft and crew, since a solution of one of the problems may restrict the set of feasible solutions of the problem solved subsequently. Also, in minimal cost solutions, aircraft and crew are highly utilised and short turn around times are usually used for aircraft and crew. If such a solution is used in operations, a short delay of one flight can cause very severe disruptions of the schedule later in the day due to the lack of buffer times. We formulate an integrated aircraft routing and crew pairing model that can generate solutions that incur small costs and are also robust to typical stochastic variability in airline operations. We propose two new solution methods to solve the integrated model. The first approach is an optimisation based heuristic approach that is capable of generating good quality solutions quickly, the second approach can solve the integrated model to optimality. In an extension of the integrated model we allow the departure times of some flights in the schedule to vary in some time window. This creates additional flexibility that leads to aircraft routing and crew pairing solutions with improved cost and robustness compared to the integrated model without time windows. Using data from domestic Air New Zealand schedules, we evaluate the benefits of the approaches on real world problem instances. Our solutions satisfy all rules imposed for these problems and are ready to be implemented in practice. We generate solutions that dramatically improve the cost and robustness of solutions obtained by existing methods.

<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.

<p>Scania has a policy to attain a high crashworthiness standard and their trucks have to conform to Swedish cab safety standards. The main objective of this thesis is to clarify which parameter variations, present during the second part of the Swedish cab crashworthiness test on a Scania R-series cab, that have significance on the intrusion response. An LS-DYNA FE-model of the test case is analysed where parameter variations are introduced through the use of the probabilistic analysis tool LS-OPT.</p><p>Example of analysed variations are the sheet thickness variation as well as the material variations such as stress-strain curve of the structural components, but also variations in the test setup such as the pendulum velocity and angle of approach on impact are taken into account. The effect of including the component forming in the analysis is investigated, where the variations on the material parameters are implemented prior to the forming. An additional objective is to analyse the influence of simulation and model dependent variations and weigh their respective effect on intrusion with the above stated physical variations.</p><p>A submodel is created due to the necessity to speed up the simulations since the numerous parameter variations yield a large number of different designs, resulting in multiple analyses.</p><p>Important structural component sensitivities are taken from the results and should be used as a pointer where to focus the attention when trying to increase the robustness of the cab. Also, the results show that the placement of the pendulum in the y direction (sideways seen from the driver perspective) is the most significant physical parameter variation during the Swedish pendulum test. It is concluded that to be able to achieve a fair comparison of the structural performance from repeated crash testing, this pendulum variation must be kept to a minimum. </p><p>Simulation and model dependent parameters in general showed to have large effects on the intrusion. It is concluded that further investigations on individual simulation or model dependent parameters should be performed to establish which description to use. </p><p>Mapping material effects from the forming simulation into the crash model gave a slight stiffer response compared to the mean pre-stretch approximations currently used by Scania. This is still however a significant result considering that Scanias approximations also included bake hardening effects from the painting process. </p>

<p>This thesis contains new results on the problem of coordinating a group of vehicles. The main motivation driving this work is the development of control laws that steer individual members of a formation, such that desired group behavior emerges. Special attention is paid to analysis of coordination issues, in particular formation control of marine craft where robustness to unknown environmental forces is important. Coordinated control applications for marine craft include: underway replenishment, maintaining a formation for increased safety during travel and instrument resolution, and cooperative transportation. A review of formation control structures is given, together with a discussion of special issues that arise in coordination of independent vehicles.</p><p>The main contributions of this thesis may be grouped into two categories:</p><p>• Path-following designs for controlling a group of vehicles</p><p>• Multi-body motivated formation modeling and control</p><p>A previously developed path following design is used to control a group of vehicles by synchronizing the individual path parameters. The path following design is advantageous since the path parameter, i.e., that parameter which determines position along a path, is scalar; hence coordination is achieved with a little amount of real-time communication. The path following design is also extended to the output-feedback case for systems where only parts of the state vector are known. The path following scheme is exploited further in a passivity-based design for coordination where the structural properties render an extended selection of functions for synchronization available. Performance and robustness properties in different operational conditions can be enhanced with a careful selection of these functions. Two designs are presented; a cascaded interconnection where a consensus system provides synchronized path parameters as input to the individual path following systems renders time-varying formations possible and increases robustness to communication problems; a feedback interconnection which is more robust to vehicle failures. Both designs are extended to sampled-data designs where plant and controller dynamics are updated in continuous-time and path parameters are exchanged over a communication network where transmission occurs at discrete intervals. Bias estimation is included to provide integral action against slowlyvarying environmental forces and model uncertainties.</p><p>A scheme for formation modeling and control, inspired by analytical mechanics of multi-body systems and Lagrangian multipliers, is proposed. In this approach to formation control, various formation behaviors are determined by imposing constraint functions on group members. Several examples illustrate these formation behaviors. The stabilization scheme presented is made more robust with respect to unknown time-varying disturbances. In addition, the scheme is extended towards adaptive estimation of unknown plant and parameters. Furthermore, it can be applied with no major modifications to the case of position control for a single vehicle.</p><p>The formation control scheme is such that it may be used in combination with a set of position control laws for a single vessel, thus enabling the designer to choose from a large class of control laws available in the literature. The input-to-state stability (ISS) framework is utilised to investigate robustness to environmental and communication disturbances. A loop-transform, together with the ISS framework, yields an upper bound on the inter-vessel time delay below which formation stability is maintained.</p>

We propose an approach to address data uncertainty for discrete optimization problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. When both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty, we propose a robust integer programming problem of moderately larger size that allows to control the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation. When only the cost coefficients are subject to uncertainty and the problem is a 0 - 1 discrete optimization problem on n variables, then we solve the robust counterpart by solving n + 1 instances of the original problem. Thus, the robust counterpart of a polynomially solvable 0 -1 discrete optimization problem remains polynomially solvable. Moreover, we show that the robust counterpart of an NP-hard α-approximable 0 - 1 discrete optimization problem remains α-approximal. / Singapore-MIT Alliance (SMA)

In this dissertation, we extend several relatively new developments in statistical model selection and data mining in order to improve one of the workhorse statistical tools - mixture modeling (Pearson, 1894). The traditional mixture model assumes data comes from several populations of Gaussian distributions. Thus, what remains is to determine how many distributions, their population parameters, and the mixing proportions. However, real data often do not fit the restrictions of normality very well. It is likely that data from a single population exhibiting either asymmetrical or nonnormal tail behavior could be erroneously modeled as two populations, resulting in suboptimal decisions. To avoid these pitfalls, we develop the mixture model under a broader distributional assumption by fitting a group of multivariate elliptically-contoured distributions (Anderson and Fang, 1990; Fang et al., 1990). Special cases include the multivariate Gaussian and power exponential distributions, as well as the multivariate generalization of the Student’s T. This gives us the flexibility to model nonnormal tail and peak behavior, though the symmetry restriction still exists. The literature has many examples of research generalizing the Gaussian mixture model to other distributions (Farrell and Mersereau, 2004; Hasselblad, 1966; John, 1970a), but our effort is more general. Further, we generalize the mixture model to be non-parametric, by developing two types of kernel mixture model. First, we generalize the mixture model to use the truly multivariate kernel density estimators (Wand and Jones, 1995). Additionally, we develop the power exponential product kernel mixture model, which allows the density to adjust to the shape of each dimension independently. Because kernel density estimators enforce no functional form, both of these methods can adapt to nonnormal asymmetric, kurtotic, and tail characteristics. Over the past two decades or so, evolutionary algorithms have grown in popularity, as they have provided encouraging results in a variety of optimization problems. Several authors have applied the genetic algorithm - a subset of evolutionary algorithms - to mixture modeling, including Bhuyan et al. (1991), Krishna and Murty (1999), and Wicker (2006). These procedures have the benefit that they bypass computational issues that plague the traditional methods. We extend these initialization and optimization methods by combining them with our updated mixture models. Additionally, we “borrow” results from robust estimation theory (Ledoit and Wolf, 2003; Shurygin, 1983; Thomaz, 2004) in order to data-adaptively regularize population covariance matrices. Numerical instability of the covariance matrix can be a significant problem for mixture modeling, since estimation is typically done on a relatively small subset of the observations. We likewise extend various information criteria (Akaike, 1973; Bozdogan, 1994b; Schwarz, 1978) to the elliptically-contoured and kernel mixture models. Information criteria guide model selection and estimation based on various approximations to the Kullback-Liebler divergence. Following Bozdogan (1994a), we use these tools to sequentially select the best mixture model, select the best subset of variables, and detect influential observations - all without making any subjective decisions. Over the course of this research, we developed a full-featured Matlab toolbox (M3) which implements all the new developments in mixture modeling presented in this dissertation. We show results on both simulated and real world datasets. Keywords: mixture modeling, nonparametric estimation, subset selection, influence detection, evidence-based medical diagnostics, unsupervised classification, robust estimation.