Integrated control-structure design

A new approach for the design and control of flexible space structures is described. The approach integrates the structure and controller design processes thereby providing extra opportunities for avoiding some of the disastrous effects of control-structures interaction and for discovering new, unexpected avenues of future structural design. A control formulation based on Boyd's implementation of Youla parameterization is employed. Control design parameters are coupled with structural design variables to produce a set of integrated-design variables which are selected through optimization-based methodology. A performance index reflecting spacecraft mission goals and constraints is formulated and optimized with respect to the integrated design variables. Initial studies have been concerned with achieving mission requirements with a lighter, more flexible space structure. Details of the formulation of the integrated-design approach are presented and results are given from a study involving the integrated redesign of a flexible geostationary platform

YAM2: Yet another library for the M2M_2 variables using sequential quadratic programming

The $M_2$ variables are devised to extend $M_{T2}$ by promoting transverse masses to Lorentz-invariant ones and making explicit use of on-shell mass relations. Unlike simple kinematic variables such as the invariant mass of visible particles, where the variable definitions directly provide how to calculate them, the calculation of the $M_2$ variables is undertaken by employing numerical algorithms. Essentially, the calculation of $M_2$ corresponds to solving a constrained minimization problem in mathematical optimization, and various numerical methods exist for the task. We find that the sequential quadratic programming method performs very well for the calculation of $M_2$, and its numerical performance is even better than the method implemented in the existing software package for $M_2$. As a consequence of our study, we have developed and released yet another software library, YAM2, for calculating the $M_2$ variables using several numerical algorithms.Comment: 1+22 pages, 5 figures; matches published version; fixed title page for inspire record; The library is distributed via https://github.com/cbpark/YAM

Elemental Abundances in M31: Alpha and Iron Element Abundances from Low-Resolution Resolved Stellar Spectroscopy in the Stellar Halo

Measurements of [Fe/H] and [$\alpha$/Fe] can probe the minor merging history of a galaxy, providing a direct way to test the hierarchical assembly paradigm. While measurements of [$\alpha$/Fe] have been made in the stellar halo of the Milky Way, little is known about detailed chemical abundances in the stellar halo of M31. To make progress with existing telescopes, we apply spectral synthesis to low-resolution DEIMOS spectroscopy (R $\sim$ 2500 at 7000 Angstroms) across a wide spectral range (4500 Angstroms $<$ $\lambda$ $<$ 9100 Angstroms). By applying our technique to low-resolution spectra of 170 giant stars in 5 MW globular clusters, we demonstrate that our technique reproduces previous measurements from higher resolution spectroscopy. Based on the intrinsic dispersion in [Fe/H] and [$\alpha$/Fe] of individual stars in our combined cluster sample, we estimate systematic uncertainties of $\sim$0.11 dex and $\sim$0.09 dex in [Fe/H] and [$\alpha$/Fe], respectively. We apply our method to deep, low-resolution spectra of 11 red giant branch stars in the smooth halo of M31, resulting in higher signal-to-noise per spectral resolution element compared to DEIMOS medium-resolution spectroscopy, given the same exposure time and conditions. We find $\langle$[$\alpha$/Fe]$\rangle$ = 0.49 $\pm$ 0.29 dex and $\langle$[Fe/H]$\rangle$ = 1.59 $\pm$ 0.56 dex for our sample. This implies that---much like the Milky Way---the smooth halo of M31 is likely composed of disrupted dwarf galaxies with truncated star formation histories that were accreted early in the halo's formation.Comment: 21 pages, 14 figures, accepted to Ap

The impact of pay dispersion on organizational performance

Although there are many theories and several studies aiming to explain the impact of pay dispersion on firm performance, the existence and direction of this relationship, as well as what factors moderate it, remains unclear. Using the PRISMA methodology, the present study performed a systematic literature review and gathered a sample of 26 papers on the topic to understand how pay dispersion is defined and conceptualized, if a relationship between pay dispersion and firm performance exists and if the impact of the first on the latter is positive or negative, to gather and study the existing theories that connect pay dispersion and organizational performance and understand which ones explain the found impacts, to verify if there are any variables that moderate this relationship and, if so, which ones. The present study has found that although studies on vertical pay dispersion mainly find a positive impact, confirming tournament arguments, and studies on horizontal dispersion find a negative one, confirming equity/fairness arguments, the existence of a relationship, its direction and intensity seems to depend on several contextual factors, pointing towards a contingency perspective.Embora existam muitas teorias e vários estudos com o objetivo de explicar o impacto da dispersão salarial no desempenho organizacional, a existência e a direção dessa relação, bem como que fatores o moderam, permanecem incertas. Utilizando a metodologia PRISMA, o presente estudo executou uma revisão sistemática de literatura e reuniu uma amostra de 26 artigos sobre o tema de forma a compreender de que forma a dispersão salarial é definida e concetualizada, se existe uma relação entre a dispersão salarial e o desempenho da empresa e se o impacto da primeira no último é positivo ou negativo, reunir e estudar as teorias existentes que conectam a dispersão salarial e o desempenho organizacional e entender quais explicam os impactos encontrados, verificar se existem variáveis que moderem esse relacionamento e, em caso afirmativo, quais. Este estudo constatou que, embora os estudos sobre dispersão vertical de salários encontrem principalmente um impacto positivo, confirmando os argumentos da teoria dos torneios, e os estudos sobre dispersão horizontal encontrem um impacto negativo, confirmando argumentos de equidade/justiça, a existência de um relacionamento, a sua direção, e intensidade parecem depender de vários fatores contextuais, apontando para uma perspetiva de contingência

L2-norm multiple kernel learning and its application to biomedical data fusion

<p>Abstract</p> <p>Background</p> <p>This paper introduces the notion of optimizing different norms in the dual problem of support vector machines with multiple kernels. The selection of norms yields different extensions of multiple kernel learning (MKL) such as <it>L</it>_∞, <it>L</it>₁, and <it>L</it>₂MKL. In particular, <it>L</it>₂MKL is a novel method that leads to non-sparse optimal kernel coefficients, which is different from the sparse kernel coefficients optimized by the existing <it>L</it>_∞MKL method. In real biomedical applications, <it>L</it>₂MKL may have more advantages over sparse integration method for thoroughly combining complementary information in heterogeneous data sources.</p> <p>Results</p> <p>We provide a theoretical analysis of the relationship between the <it>L</it>₂optimization of kernels in the dual problem with the <it>L</it>₂coefficient regularization in the primal problem. Understanding the dual <it>L</it>₂problem grants a unified view on MKL and enables us to extend the <it>L</it>₂method to a wide range of machine learning problems. We implement <it>L</it>₂MKL for ranking and classification problems and compare its performance with the sparse <it>L</it>_∞and the averaging <it>L</it>₁MKL methods. The experiments are carried out on six real biomedical data sets and two large scale UCI data sets. <it>L</it>₂MKL yields better performance on most of the benchmark data sets. In particular, we propose a novel <it>L</it>₂MKL least squares support vector machine (LSSVM) algorithm, which is shown to be an efficient and promising classifier for large scale data sets processing.</p> <p>Conclusions</p> <p>This paper extends the statistical framework of genomic data fusion based on MKL. Allowing non-sparse weights on the data sources is an attractive option in settings where we believe most data sources to be relevant to the problem at hand and want to avoid a "winner-takes-all" effect seen in <it>L</it>_∞MKL, which can be detrimental to the performance in prospective studies. The notion of optimizing <it>L</it>₂kernels can be straightforwardly extended to ranking, classification, regression, and clustering algorithms. To tackle the computational burden of MKL, this paper proposes several novel LSSVM based MKL algorithms. Systematic comparison on real data sets shows that LSSVM MKL has comparable performance as the conventional SVM MKL algorithms. Moreover, large scale numerical experiments indicate that when cast as semi-infinite programming, LSSVM MKL can be solved more efficiently than SVM MKL.</p> <p>Availability</p> <p>The MATLAB code of algorithms implemented in this paper is downloadable from <url>http://homes.esat.kuleuven.be/~sistawww/bioi/syu/l2lssvm.html</url>.</p

Robust aircraft trajectory optimization under meteorological uncertainty

Mención Internacional en el título de doctorThe Air Traffic Management (ATM) system in the busiest airspaces in the world is currently being overhauled to deal with multiple capacity, socioeconomic, and environmental challenges. One major pillar of this process is the shift towards a concept of operations centered on aircraft trajectories (called Trajectory-Based Operations or TBO in Europe) instead of rigid airspace structures. However, its successful implementation (and, thus, the realization of the associated improvements in ATM performance) rests on appropriate understanding and management of uncertainty. Due to its complex socio-technical structure, the design and operations of the ATM system are heavily impacted by uncertainty, proceeding from multiple sources and propagating through the interconnections between its subsystems. One major source of ATM uncertainty is weather. Due to its nonlinear and chaotic nature, a number of meteorological phenomena of interest cannot be forecasted with complete accuracy at arbitrary lead times, which leads to uncertainty or disruption in individual air and ground operations that propagates to all ATM processes. Therefore, in order to achieve the goals of SESAR and similar programs, it is necessary to deal with meteorological uncertainty at multiple scales, from the trajectory prediction and planning processes to flow and traffic management operations. This thesis addresses the problem of single-aircraft flight planning considering two important sources of meteorological uncertainty: wind prediction error and convective activity. As the actual wind field deviates from its forecast, the actual trajectory will diverge in time from the planned trajectory, generating uncertainty in arrival times, sector entry and exit times, and fuel burn. Convective activity also impacts trajectory predictability, as it leads pilots to deviate from their planned route, creating challenging situations for controllers. In this work, we aim to develop algorithms and methods for aircraft trajectory optimization that are able to integrate information about the uncertainty in these meteorological phenomena into the flight planning process at both pre-tactical (before departure) and tactical horizons (while the aircraft is airborne), in order to generate more efficient and predictable trajectories. To that end, we frame flight planning as an optimal control problem, modeling the motion of the aircraft with a point-mass model and the BADA performance model. Optimal control methods represent a flexible and general approach that has a long history of success in the aerospace field. As a numerical scheme, we use direct methods, which can deal with nonlinear systems of moderate and high-dimensional state spaces in a computationally manageable way. Nevertheless, while this framework is well-developed in the context of deterministic problems, the techniques for the solution of practical optimal control problems under uncertainty are not as mature, and the methods proposed in the literature are not applicable to the flight planning problem as it is now understood. The first contribution of this thesis addresses this challenge by introducing a framework for the solution of general nonlinear optimal control problems under parametric uncertainty. It is based on an ensemble trajectory scheme, where the trajectories of the system under multiple scenarios are considered simultaneously within the same dynamical system and the uncertain optimal control problem is turned into a large conventional optimal control problem that can be then solved by standard, well-studied direct methods in optimal control. We then employ this approach to solve the robust flight plan optimization problem at the planning horizon. In order to model uncertainty in the wind and estimating the probability of convective conditions, we employ Ensemble Prediction System (EPS) forecasts, which are composed by multiple predictions instead of a single deterministic one. The resulting method can be used to optimize flight plans for maximum expected efficiency according to the cost structure of the airline; additionally, predictability and exposure to convection can be incorporated as additional objectives. The inherent tradeoffs between these objectives can be assessed with this methodology. The second part of this thesis presents a solution for the rerouting of aircraft in uncertain convective weather scenarios at the tactical horizon. The uncertain motion of convective weather cells is represented with a stochastic model that has been developed from the output of a deterministic satellite-based nowcast product, Rapidly Developing Thunderstorms (RDT). A numerical optimal control framework, based on the pointmass model with the addition of turn dynamics, is employed for optimizing efficiency and predictability of the proposed trajectories in the presence of uncertainty about the future evolution of the storm. Finally, the optimization process is initialized by a randomized heuristic procedure that generates multiple starting points. The combined framework is able to explore and as exploit the space of solution trajectories in order to provide the pilot or the air traffic controller with a set of different suggested avoidance trajectories, as well as information about their expected cost and risk. The proposed methods are tested on example scenarios based on real data, showing how different user priorities lead to different flight plans and what tradeoffs are then present. These examples demonstrate that the solutions described in this thesis are adequate for the problems that have been formulated. In this way, the flight planning process can be enhanced to increase the efficiency and predictability of individual aircraft trajectories, which would lead to higher predictability levels of the ATM system and thus improvements in multiple performance indicators.El sistema de gestión del tráfico aéreo (Air Traffic Management, ATM) en los espacios aéreos más congestionados del mundo está siendo reformado para lidiar con múltiples desafíos socioeconómicos, medioambientales y de capacidad. Un pilar de este proceso es el gradual reemplazo de las estructuras rígidas de navegación, basadas en aerovías y waypoints, hacia las operaciones basadas en trayectorias. No obstante, la implementación exitosa de este concepto y la realización de las ganancias esperadas en rendimiento ATM requiere entender y gestionar apropiadamente la incertidumbre. Debido a su compleja estructura socio-técnica, el diseño y operaciones del sistema ATM se encuentran marcadamente influidos por la incertidumbre, que procede de múltiples fuentes y se propaga por las interacciones entre subsistemas y operadores humanos. Uno de los principales focos de incertidumbre en ATM es la meteorología. Debido a su naturaleza no-linear y caótica, muchos fenómenos de interés no pueden ser pronosticados con completa precisión en cualquier horizonte temporal, lo que crea disrupción en las operaciones en aire y tierra que se propaga a otros procesos de ATM. Por lo tanto, para lograr los objetivos de SESAR e iniciativas análogas, es imprescindible tener en cuenta la incertidumbre en múltiples escalas espaciotemporales, desde la predicción de trayectorias hasta la planificación de flujos y tráfico. Esta tesis aborda el problema de la planificación de vuelo de aeronaves individuales considerando dos fuentes importantes de incertidumbre meteorológica: el error en la predicción del viento y la actividad convectiva. Conforme la realización del viento se desvía de su previsión, la trayectoria real se desviará temporalmente de la planificada, lo que implica incertidumbre en tiempos de llegada a sectores y aeropuertos y en consumo de combustible. La actividad convectiva también tiene un impacto en la predictibilidad de las trayectorias, puesto que obliga a los pilotos a desviarse de sus planes de vuelo para evitarla, cambiado así la situación de tráfico. En este trabajo, buscamos desarrollar métodos y algoritmos para la optimización de trayectorias que puedan integrar información sobre la incertidumbre en estos fenómenos meteorológicos en el proceso de diseño de planes de vuelo en horizontes de planificación (antes del despegue) y tácticos (durante el vuelo), con el objetivo de generar trayectorias más eficientes y predecibles. Con este fin, formulamos la planificación de vuelo como un problema de control óptimo, modelando la dinámica del avión con un modelo de masa puntual y el modelo de rendimiento BADA. El control óptimo es un marco flexible y general con un largo historial de éxito en el campo de la ingeniería aeroespacial. Como método numérico, empleamos métodos directos, que son capaces de manejar sistemas dinámicos de alta dimensión con costes computacionales moderados. No obstante, si bien esta metodología es madura en contextos deterministas, la solución de problemas prácticas de control óptimo bajo incertidumbre en la literatura no está tan desarrollada, y los métodos propuestos en la literatura no son aplicables al problema de interés. La primera contribución de esta tesis hace frente a este reto mediante la introducción de un marco numérico para la resolución de problemas generales de control óptimo no-lineal bajo incertidumbre paramétrica. El núcleo de este método es un esquema de conjunto de trayectorias, en el que las trayectorias del sistema dinámico bajo múltiples escenarios son consideradas de forma simultánea, y el problema de control óptimo bajo incertidumbre es así transformado en un problema convencional que puede ser tratado mediante métodos existentes en control óptimo. A continuación, empleamos este método para resolver el problema de la planificación de vuelo robusta. La incertidumbre en el viento y la probabilidad de ocurrencia de condiciones convectivas son modeladas mediante el uso de previsiones de conjunto o ensemble, compuestas por múltiples predicciones en lugar de una única previsión determinista. Este método puede ser empleado para maximizar la eficiencia esperada de los planes de vuelo de acuerdo a la estructura de costes de la aerolínea; además, la predictibilidad de la trayectoria y la exposición a la convección pueden ser incorporadas como objetivos adicionales. El trade-off entre estos objetivos puede ser evaluado mediante la metodología propuesta. La segunda parte de la tesis presenta una solución para reconducir aviones en escenarios tormentosos en un horizonte táctico. La evolución de las células convectivas es representada con un modelo estocástico basado en las proyecciones de Rapidly Developing Thunderstorms (RDT), un sistema determinista basado en imágenes de satélite. Este modelo es empleado por un método de control óptimo numérico, basado en un modelo de masa puntual en el que se modela la dinámica de viraje, con el objetivo de maximizar la eficiencia y predictibilidad de la trayectoria en presencia de incertidumbre sobre la evolución futura de las tormentas. Finalmente, el proceso de optimizatión es inicializado por un método heurístico aleatorizado que genera múltiples puntos de inicio para las iteraciones del optimizador. Esta combinación permite explorar y explotar el espacio de trayectorias solución para proporcionar al piloto o al controlador un conjunto de trayectorias propuestas, así como información útil sobre su coste y el riesgo asociado. Los métodos propuestos son probados en escenarios de ejemplo basados en datos reales, ilustrando las diferentes opciones disponibles de acuerdo a las prioridades del planificador y demostrando que las soluciones descritas en esta tesis son adecuadas para los problemas que se han formulado. De este modo, es posible enriquecer el proceso de planificación de vuelo para incrementar la eficiencia y predictibilidad de las trayectorias individuales, lo que contribuiría a mejoras en el rendimiento del sistema ATM.These works have been financially supported by Universidad Carlos III de Madrid through a PIF scholarship; by Eurocontrol, through the HALA! Research Network grant 10-220210-C2; by the Spanish Ministry of Economy and Competitiveness (MINECO)'s R&D program, through the OptMet project (TRA2014-58413-C2-2-R); and by the European Commission's SESAR Horizon 2020 program, through the TBO-Met project (grant number 699294).Programa de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid; la Universidad de Jaén; la Universidad de Zaragoza; la Universidad Nacional de Educación a Distancia; la Universidad Politécnica de Madrid y la Universidad Rovira iPresidente: Damián Rivas Rivas.- Secretario: Xavier Prats Menéndez.- Vocal: Benavar Sridha

Computational optimal control of the terminal bunt manoeuvre

This work focuses on a study of missile guidance in the form of trajectory shaping of a generic cruise missile attacking a fixed target which must be struck from above. The problem is reinterpreted using optimal control theory resulting in two formulations: I) minimum time-integrated altitude and 2) minimum flight time. Each formulation entails nonlinear, two-dimensional missile flight dynamics, boundary conditions and path constraints. Since the thus obtained optimal control problems do not admit analytical solutions, a recourse to computational optimal control is made. The focus here is on informed use of the tools of computational optimal control, rather than their development. Each of the formulations is solved using a three-stage approach. In stage I, the problem is discretised, effectively transforming it into a nonlinear programming problem, and hence suitable for approximate solution with the FORTRAN packages DIRCOL and NUDOCCCS. The results of this direct approach are used to discern the structure of the optimal solution, i.e. type of constraints active, time of their activation, switching and jump points. This qualitative analysis, employing the results of stage I and optimal control theory, constitutes stage 2. Finally, in stage 3, the insight of stage 2 are made precise by rigorous mathemati cal formulation of the relevant two-point boundary value problems (TPBVPs), using the appropriate theorems of optimal control theory. The TPBVPs obtained from this indirect approach are then solved using the FORTRAN package BNDSCO and the results compared with the appropriate solutions of stage I. For each formulation (minimum altitude and minimum time) the influence of boundary conditions on the structure of the optimal solution and the performance index is investigated. The results are then interpreted from the operational and computational perspectives. Software implementation employing DIRCOL, NUDOCCCS and BNDSCO, which produced the results, is described and documented. Finally, some conclusions are drawn and recommendations made

Improved profile fitting and quantification of uncertainty in experimental measurements of impurity transport coefficients using Gaussian process regression

The need to fit smooth temperature and density profiles to discrete observations is ubiquitous in plasma physics, but the prevailing techniques for this have many shortcomings that cast doubt on the statistical validity of the results. This issue is amplified in the context of validation of gyrokinetic transport models (Holland et al 2009 Phys. Plasmas 16 052301), where the strong sensitivity of the code outputs to input gradients means that inadequacies in the profile fitting technique can easily lead to an incorrect assessment of the degree of agreement with experimental measurements. In order to rectify the shortcomings of standard approaches to profile fitting, we have applied Gaussian process regression (GPR), a powerful non-parametric regression technique, to analyse an Alcator C-Mod L-mode discharge used for past gyrokinetic validation work (Howard et al 2012 Nucl. Fusion 52 063002). We show that the GPR techniques can reproduce the previous results while delivering more statistically rigorous fits and uncertainty estimates for both the value and the gradient of plasma profiles with an improved level of automation. We also discuss how the use of GPR can allow for dramatic increases in the rate of convergence of uncertainty propagation for any code that takes experimental profiles as inputs. The new GPR techniques for profile fitting and uncertainty propagation are quite useful and general, and we describe the steps to implementation in detail in this paper. These techniques have the potential to substantially improve the quality of uncertainty estimates on profile fits and the rate of convergence of uncertainty propagation, making them of great interest for wider use in fusion experiments and modelling efforts.United States. Dept. of Energy. Office of Fusion Energy Sciences (Award DE-FC02-99ER54512)United States. Dept. of Energy. Office of Science (Contract DE-AC05-06OR23177)United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Award DE-SC0007099