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The design of an optical communication link must plan for the random effects of atmospheric turbulence. This study analyses data from an experiment which transmitted from a laser located 8 meters above ground over a 13 Km range to coherent detection devices approximately 162 meters above ground. The effects of a fading and surging beam wave were considered in regards to code techniques for error correction, amplitude modulation and hardware architecture schemes. This study simulated the use of arrays and large apertures for the receiving devices, and compared the resultant scintillation index with the theoretical calculations.

A flapping-wing micro-air-vehicle (FWMAV) represents a complex multi-disciplinary system whose analysis invokes the frontiers of the aerospace engineering disciplines. From the aerodynamic point of view, a nonlinear, unsteady flow is created by the flapping motion. In addition, non-conventional contributors, such as the leading edge vortex, to the aerodynamic loads become dominant in flight. On the other hand, the flight dynamics of a FWMAV constitutes a nonlinear, non-autonomous dynamical system. Furthermore, the stringent weight and size constraints that are always imposed on FWMAVs invoke design with minimal actuation. In addition to the numerous motivating applications, all these features of FWMAVs make it an interesting research point for engineers. In this Dissertation, some challenging points related to FWMAVs are considered. First, an analytical unsteady aerodynamic model that accounts for the leading edge vortex contribution by a feasible computational burden is developed to enable sensitivity and optimization analyses, flight dynamics analysis, and control synthesis. Second, wing kinematics optimization is considered for both aerodynamic performance and maneuverability. For each case, an infinite-dimensional optimization problem is formulated using the calculus of variations to relax any unnecessary constraints induced by approximating the problem as a finite-dimensional one. As such, theoretical upper bounds for the aerodynamic performance and maneuverability are obtained. Third, a design methodology for the actuation mechanism is developed. The proposed actuation mechanism is able to provide the required kinematics for both of hovering and forward flight using only one actuator. This is achieved by exploiting the nonlinearities of the wing dynamics to induce the saturation phenomenon to transfer energy from one mode to another. Fourth, the nonlinear, time-periodic flight dynamics of FWMAVs is analyzed using direct and higher-order averaging. The region of applicability of direct averaging is determined and the effects of the aerodynamic-induced parametric excitation are assessed. Finally, tools combining geometric control theory and averaging are used to derive analytic expressions for the textit{Symmetric Products}, which are vector fields that directly affect the acceleration of the averaged dynamics. A design optimization problem is then formulated to bring the maneuverability index/criterion early in the design process to maximize the FWMAV maneuverability near hover. / Ph. D.

An accurate PDF of irradiance for a FSO channel is important when designing a laser radar, active laser imaging, or a communications system to operate over the channel. Parameters such as detector threshold level, probability of detection, mean fade time, number of fades, BER, and SNR are derived from the PDF and determine the design constraints of the receiver, transmitter, and corresponding electronics. Current PDF models of irradiance, such as the Gamma-Gamma, do not fully capture the effect of aperture averaging; a reduction in scintillation as the diameter of the collecting optic is increased. The Gamma-Gamma PDF of irradiance is an attractive solution because the parameters of the distribution are derived strictly from atmospheric turbulence parameters; propagation path length, Cn2, l0, and L0. This dissertation describes a heuristic physics-based modeling technique to develop a new PDF of irradiance based upon the optical field. The goal of the new PDF is three-fold: capture the physics of the turbulent atmosphere, better describe aperture averaging effects, and relate parameters of the new model to measurable atmospheric parameters. The modeling decomposes the propagating electromagnetic field into a sum of independent random-amplitude spatial plane waves using an approximation to the Karhunen-Loeve expansion. The scattering effects of the turbulence along the propagation path define the random-amplitude of each component of the expansion. The resulting PDF of irradiance is a double finite sum containing a Bessel function. The newly developed PDF is a generalization of the Gamma-Gamma PDF, and reduces to such in the limit. An experiment was setup and performed to measure the PDF of irradiance for several receiver aperture sizes under moderate to strong turbulence conditions. The propagation path was instrumented with scintillometers and anemometers to characterize the turbulence conditions. The newly developed PDF model and the GG model were compared to histograms of the experimental data. The new PDF model was typically able to match the data as well or better than the GG model under conditions of moderate aperture averaging. The GG model fit the data better than the new PDF under conditions of significant aperture averaging. Due to a limiting scintillation index value of 3, the new PDF was not compared to the GG for point apertures under strong turbulence; a regime where the GG is known to fit data well.

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In this thesis a number of models for recommender systems are explored, all using collaborative filtering to produce their recommendations. Extra focus is put on two models: Matrix Factorization, which is a linear model and Multi-Layer Perceptron, which is a non-linear model. With an additional purpose of training the models without collecting any sensitive data from the users, both models were implemented with a learning technique that does not require the server's knowledge of the users' data, called federated learning. The federated version of Matrix Factorization is already well-researched, and has proven not to protect the users' data at all; the data is derivable from the information that the users communicate to the server that is necessary for the learning of the model. However, on the federated Multi-Layer Perceptron model, no research could be found. In this thesis, such a model is therefore designed and presented. Arguments are put forth in support of the privacy preservability of the model, along with a proof of the user data not being analytically derivable for the central server.    In addition, new ways to further put the protection of the users' data on the test are discussed. All models are evaluated on two different data sets. The first data set contains data on ratings of movies and is called MovieLens 1M. The second is a data set that consists of anonymized fund transactions, provided by the Swedish bank SEB for this thesis. Test results suggest that the federated versions of the models can achieve similar recommendation performance as their non-federated counterparts.

<p dir="ltr">Distributed optimization problems defined over mesh networks are ubiquitous in signal processing, machine learning, and control. In contrast to centralized approaches where all information and computation resources are available at a centralized server, agents on a distributed system can only use locally available information. As a result, efforts have been put into the design of efficient distributed algorithms that take into account the communication constraints and make coordinated decisions in a fully distributed manner from a pure optimization perspective. Given the massive sample size and high-dimensionality generated by distributed systems such as social media, sensor networks, and cloud-based databases, it is essential to understand the statistical and computational guarantees of distributed algorithms to solve such high-dimensional problems over a mesh network.</p><p dir="ltr">A goal of this thesis is a first attempt at studying the behavior of distributed methods in the high-dimensional regime. It consists of two parts: (I) distributed LASSO and (II) distributed stochastic sparse recovery.</p><p dir="ltr">In Part (I), we start by studying linear regression from data distributed over a network of agents (with no master node) by means of LASSO estimation, in high-dimension, which allows the ambient dimension to grow faster than the sample size. While there is a vast literature of distributed algorithms applicable to the problem, statistical and computational guarantees of most of them remain unclear in high dimensions. This thesis provides a first statistical study of the Distributed Gradient Descent (DGD) in the Adapt-Then-Combine (ATC) form. Our theory shows that, under standard notions of restricted strong convexity and smoothness of the loss functions--which hold with high probability for standard data generation models--suitable conditions on the network connectivity and algorithm tuning, DGD-ATC converges globally at a linear rate to an estimate that is within the centralized statistical precision of the model. In the worst-case scenario, the total number of communications to statistical optimality grows logarithmically with the ambient dimension, which improves on the communication complexity of DGD in the Combine-Then-Adapt (CTA) form, scaling linearly with the dimension. This reveals that mixing gradient information among agents, as DGD-ATC does, is critical in high-dimensions to obtain favorable rate scalings. </p><p dir="ltr">In Part (II), we focus on addressing the problem of distributed stochastic sparse recovery through stochastic optimization. We develop and analyze stochastic optimization algorithms for problems over a network, modeled as an undirected graph (with no centralized node), where the expected loss is strongly convex with respect to the Euclidean norm, and the optimum is sparse. Assuming agents only have access to unbiased estimates of the gradients of the underlying expected objective, and stochastic gradients are sub-Gaussian, we use distributed stochastic dual averaging (DSDA) as a building block to develop a fully decentralized restarting procedure for recovery of sparse solutions over a network. We show that with high probability, the iterates generated by all agents linearly converge to an approximate solution, eliminating fast the initial error; and then converge sublinearly to the exact sparse solution in the steady-state stages owing to observation noise. The algorithm asymptotically achieves the optimal convergence rate and favorable dimension dependence enjoyed by a non-Euclidean centralized scheme. Further, we precisely identify its non-asymptotic convergence rate as a function of characteristics of the objective functions and the network, and we characterize the transient time needed for the algorithm to approach the optimal rate of convergence. We illustrate the performance of the algorithm in application to classical problems of sparse linear regression, sparse logistic regression and low rank matrix recovery. Numerical experiments demonstrate the tightness of the theoretical results.</p>

Quick and reliable computational methods for optimized orbital transfers are crucial for projects at preliminary stages. They enable an initial, realistic sizing of the propulsion subsystem, one of the major components of satellite design. This thesis work, conducted at ReOrbit Oy, presents a minimum-time optimal trajectory for the orbit raising of a micro-satellite from GTO to GEO, assuming continuous firing by electric propulsion. The Delta-v requirements resulting from this simulation lead to the selection of an appropriate electric propulsion system, elaborating on the design of its configuration in terms of fuel and thrust requirements. This is done by taking into account, other than the major contribution given by the orbit raising, additions due to in-orbit maneuvers performed twice a day over a 10-year lifetime, like station-keeping corrections and reaction wheels desaturation. The optimization method is a direct-indirect hybrid for low-thrust orbital maneuvers, employing Pontryagin’s Minimum Principle for the transcription into a nonlinear programming problem. The initial guess required to start the optimizer is obtained with Lyapunov control theory. An orbital averaging technique is implemented, enabling fast computation of multiple trajectories during the optimization. Disturbances from the J2 zonal harmonic, solar radiation pressure, third-body effects of the Sun and Moon, and atmospheric drag up to 1500 km of altitude are included in the dynamic model. Eclipse conditions are assessed with a cylindrical shadow model, as the solar electric propulsion experiences a zero thrust period when in Earth’s shadow. The electric propulsion system configuration is determined with trade-off studies and comparisons between different suppliers. The chosen outline includes 4 Xenon thrusters, with complementary power processing units and propellant management systems, resulting in a total transfer time of less than 4 months. The same propulsion system is employed both for the transfer trajectory and the in-orbit maneuvers, by changing the thruster’s configuration once in GEO. / Snabba och pålitliga beräkningsmetoder för optimerade växlingar mellan omloppsbanor är avgörande för projekt i preliminära skeden. De möjliggör en initial, realistisk dimensionering av framdrivningssystemet, ett av huvudkomponenterna i satellitdesign. Detta examensarbete, utfört vid ReOrbit Oy, presenterar en tidsoptimerad bana för en mikrosatellits banhöjning från GTO till GEO, förutsatt kontinuerlig avfyring med elektrisk framdrivning. Simuleringens resulterande Delta-v-krav leder till valet av ett lämpligt elektriskt framdrivningssystem, med utarbetande av dess konfiguration vad gäller bränsle- och drivkraftskrav. Detta uppnås genom att ta hänsyn till (förutom bidraget från växlingen av omloppsbanan) tillägg från manövrar i omloppsbana som utförs två gånger om dagen under en 10-årig livstid, som t.ex. korrigeringar för stationshållning och avmättning av svänghjul. Optimeringsmetoden är en direkt-indirekt hybrid för manövrar i omloppsbanor med låg drivkraft, som använder Pontryagins minimiprincip för omskrivning till ett icke-linjärt programmeringsproblem. Den första gissningen som krävs för att starta optimeraren erhålls med Lyapunovs reglerteori. En teknik for omloppsutjämning implementeras, vilket möjliggör snabb beräkning av flera banor under optimeringen. Störningar från zonövertonen J2, solstrålningstryck, tredjekroppseffekter från solen och månen och luftmotstånd upp till 1500 km höjd ingår i den dynamiska modellen. Förmörkelseförhållanden uppskattas med en cylindrisk skuggmodell, då den elektriska solframdrivningen undergår ett skede utan drivkraft inom jordens skugga. Det elektriska framdrivningssystemets konfiguration bestäms med avvägningsundersökningar och jämförelser mellan olika leverantörer. Förslaget på utformning inkluderar 4 Xenon raketmotorer, med kompletterande kraftbearbetningsenheter och drivmedelshanteringssystem, vilket resulterar i en total överföringstid på mindre än 4 månader. Samma framdrivningssystem används både för överföringsbanan och manövrarna inom omloppsbanorna, genom att ändra motorns konfiguration när satelliten är i GEO.