Negative-imaginary systems are broadly speaking stable and square (equal number of inputs and outputs) systems whose Nyquist plot lies underneath (never touches for strictly negative-imaginary systems) the real axis when the frequency varies in the open interval 0 to ∞. This class of systems appear quite often in engineering applications, for example, in lightly damped flexible structures with collocated position sensors and force actuators, multi-link robots, DC machines, active filters, etc. In this thesis, robustness analysis and controller synthesis methods for uncertain negative-imaginary systems are explored. Two new reformulation techniques are proposed that facilitate both the robustness analysis and controller synthesis for uncertain negative-imaginary systems. These reformulations are based on the transformation from negative-imaginary systems to a bounded-real framework via the positive-real property. In the presence of strictly negative-imaginary uncertainty, the robust stabilization problem is posed in an equivalent H∞ control framework; similarly, a negative-imaginary robust performance analysis problem is cast into an equivalent μ-framework. The latter framework also allows robust stability analysis when the perturbations are a mixture of bounded-real and negative-imaginary uncertainties. The proposed two techniques pave the way for existing H∞ control and μ theory to be applied to robustness analysis and controller synthesis for negative-imaginary systems. In addition, a static state-feedback synthesis method is proposed to achieve robust stability of a system in the presence of strictly negative-imaginary uncertainties. The method is developed in the LMI framework, which can be solved efficiently using convex optimization techniques. The controller synthesis method is based on the negative-imaginary stability theorem: a positive feedback interconnection of two negative-imaginary systems is internally stable if and only if the DC loop gain is contractive and at least one of the systems in the interconnected loop is strictly negative-imaginary. Also, in order to handle non-strict negative-imaginary uncertainties, a strongly strictly negative-imaginary lemma is proposed that helps to ensure the strictly negative-imaginary property of the nominal closed-loop system for robustness. To this end, a state-space characterization for strictly negative-imaginary property is given for non-minimal systems where the conditions are convex and hence numerically attractive. The results in this thesis hence facilitate both the robustness analysis and controller synthesis for negative-imaginary systems that quite often arise in practical scenarios. In addition, they can be applied to quantify the worse-case performance for this class of systems. Therefore, the proposed results have important implications in controller synthesis for uncertain negative-imaginary systems that achieve not only robust stabilization but also robust performance.

Les systèmes micro mécatroniques intègrent dans un volume très réduit des fonctions de natures différentes (électrique, mécanique, thermique, magnétique ou encore optique). Ces systèmes sont des produits finaux ou sont dans des systèmes de taille macroscopique. La tendance à la miniaturisation et à la complexité des fonctions à réaliser conduit à des microsystème en trois dimensions et constitué´es de composants provenant de processus de (micro)fabrication parfois incompatibles. L’assemblage microbotique est une réponse aux challenges de leur réalisation. Pour assurer les opérations d’ assemblage avec des précisions et des résolutions élevées, des capteurs adaptés au micro monde et des outils particuliers de manipulation doivent être utilisés. Les éléments principaux constituants les systèmes de micromanipulation sont les micro-actionneurs.Ces derniers sont souvent faits à base de matériaux actifs parmi lesquels les matériaux Piézoélectriques . Les actionneurs piézoélectriques sont caractérisés par leur très haute résolution (souvent nanométrique), leur grande bande-passante (plus du kHz pour certains micro-actionneurs) et leur grande densité de force. Tout ceci en fait des actionneurs particulièrement intéressants pour le micro-assemblage et la micromanipulation. Cependant,ces actionneurs présentent, en plus de leur comportement non-linéaire, une forte dépendance à l’environnement et aux tâches considérées. De plus, ces tâches de micromanipulation et de micro-assemblage sont confrontées à un manque de capteurs précis et compatibles avec les dimensions du micromonde. Ceci engendre des incertitudes sur les paramètres du élaboré lors de l’identification. En présence du verrou technologique lié à la réalisation des capteurs et des propriétés complexes des actionneurs, il est difficile d’obtenir les performances de haut niveau requises pour réussir les tâches de micromanipulation et de micro-assemblage. C’est notamment la mise au point d’outils de commande convenables qui permet d’atteindre les niveaux de précision et de résolution nécessaires.Les travaux de cette thèse s’inscrivent dans ce cadre. Afin de réussir les tâches de micromanipulation et de micro-assemblage, plusieurs méthodes de commande prenant en compte des incertitudes liées au modèle, comme les approches de commande robustes de type H-inf ont déjà utilisées pour commander les actionneurs piézoélectriques.L’un des inconvénients majeurs de ces méthodes est la dérivation de régulateurs d’ordre élevé qui sont coûteux en calcul et peuvent difficilement être embarqués dans les microsystèmes. Afin de prendre en compte les incertitudes paramétriques des modèles des Systèmes à commander, nous proposons une solution alternative basée sur l’utilisation du calcul par intervalles. Ces techniques du calcul par intervalles sont combinées avec les outils de l’automatique pour modéliser et commander les microsystèmes. Nous chercherons également à montrer que l’utilisation de ces techniques permet d’associer la robustesse et la simplicité des correcteurs dérivés / Micromechatronic systems integrate in a very small volume functions with differentnatures. The trend towards miniaturization and complexity of functions to achieve leadsto 3-dimensional microsystems. These 3-dimensional systems are formed by microroboticassembly of various microfabricated and incompatible components. To achieve theassembly operations with high accuracy and high resolution, adapted sensors for themicroworld and special tools for the manipulation are required. The microactuators arethe main elements that constitute the micromanipulation systems. These actuators areoften based on smart materials, in particular piezoelectric materials. The piezoelectricmaterials are characterized by their high resolution (nanometric), large bandwidth (morethan kHz) and high force density. This why the piezoelectric actuators are widely usedin the micromanipulation and microassembly tasks. However, the behavior of the piezoelectricactuators is non-linear and very sensitive to the environment. Moreover, thedeveloppment of the micromanipulation and the microassembly tasks is limited by thelack of precise and compatible sensors with the microworld dimensions. In the presenceof the difficulties related to the sensors realization and the complex characteristics ofthe actuators, it is difficult to obtain the required performances for the micromanipulationand the microassembly tasks. For that, it is necessary to develop a specific controlapproach that achieves the wanted accuracy and resolution.The works in this thesis deal with this problematic. In order to success the micromanipulationand the microassembly tasks, robust control approaches such as H∞ havealready been tested to control the piezoelectric actuators. However, the main drawbacksof these methods is the derivation of high order controllers. In the case of embedded microsystems,these high order controllers are time consuming which limit their embeddingpossibilities. To address this problem, we propose in our work an alternative solutionto model and control the microsystems by combining the interval techniques with theautomatic tools. We will also seek to show that the use of these techniques allows toderive robust and low-order controllers.

The distributed nature of Federated Learning (FL) creates security-related vulnerabilities including training-time attacks. Recently, it has been shown that well-known Byzantine-resilient aggregation schemes are indeed vulnerable to an informed adversary who has access to the aggregation scheme and updates sent by clients. Therefore, it is a significant challenge to establish successful defense mechanisms against such an adversary. To the best of our knowledge, most current aggregators are immune to single or partial attacks and none of them is expandable to defend against new attacks. We frame the robust distributed learning problem as a game between a server and an adversary that tailors training-time attacks. We introduce RobustTailor, a simulation-based algorithm that prevents the adversary from being omniscient. RobustTailor is a mixed strategy and has good expandability for any deterministic Byzantine-resilient algorithm. Under a challenging setting with information asymmetry between two players, we show that our method enjoys theoretical guarantees in terms of regret bounds. RobustTailor preserves almost the same privacy guarantees as standard FL and robust aggregation schemes. Simulation improves robustness to training-time attacks significantly. Empirical results under challenging attacks validate our theory and show that RobustTailor preforms similar to an upper bound which assumes the server has perfect knowledge of all honest clients over the course of training. / Den distribuerade karaktären hos federerade maskininlärnings-system gör dem sårbara för cyberattacker, speciellt under tiden då systemen tränas. Nyligen har det visats att många existerande Byzantine-resilienta aggregeringssystem är sårbara för attacker från en välinformerad motståndare som har tillgång till aggregeringssystemet och uppdateringarna som skickas av klienterna. Det är därför en stor utmaning att skapa framgångsrika försvarsmekanismer mot en sådan motståndare. Såvitt vi vet är de flesta nuvarande aggregatorer immuna mot enstaka eller partiella attacker och ingen av dem kan på ett enkelt sätt utvidgas för att försvara sig mot nya attacker. Vi utformar det robusta distribuerade inlärningsproblemet som ett spel mellan en server och en motståndare som skräddarsyr attacker under träningstiden. Vi introducerar RobustTailor, en simuleringsbaserad algoritm som förhindrar att motståndaren är allvetande. RobustTailor är en blandad strategi med god expanderbarhet för alla deterministiska Byzantine-resilienta algoritmer. I en utmanande miljö med informationsasymmetri mellan de två spelarna visar vi att vår metod har teoretiska garantier i form av gränser för ånger. RobustTailor har nästan samma integritetsgarantier som standardiserade federerade inlärnings- och robusta aggregeringssystem. Vi illustrerar även hur simulering förbättrar robustheten mot attacker under träningstiden avsevärt. Empiriska resultat vid utmanande attacker bekräftar vår teori och visar att RobustTailor presterar på samma sätt som en övre gräns som förutsätter att servern har perfekt kunskap om alla ärliga klienter under utbildningens gång.

Social media has provided a way for music artists to reach many people with their music, without having to rely on record labels to perform marketing tasks. Most previous research within the area has focused on how already established music artists can use social media as part of their marketing strategies and how digital technologies have transformed the music industry. This study focuses on how unsigned music artists’ followers and fans on social media have an impact on their music streaming numbers. The main research question of the study is: how does unsigned artists’ social media performance affect the number of streams of their music? To investigate this, a robust regression model was defined with the aim of predicting the number of artists’ music streams based on their social media data. The robust regression model showed that the social media variables did not have significant effects on the number of streams. Therefore, an analysis of each individual artist in the data was conducted. The results showed that the social media data in this study could not be used to explain changes in the number of streams for unsigned music artists. An analysis based on each individual artist and the content that each individual artist is posting on the different social media channels, is suggested instead. An information visualization tool was developed with the purpose of allowing analysts to get an overview of the social media data as well as allow analysts to look at each artist’s social media feeds to understand how artists’ social media activities affect their music streaming data. / Sociala medier har gjort det möjligt för musikartister att nå många människor med sin musik utan att behöva förlita sig på skivbolag. Tidigare forskning inom området har fokuserat på hur redan etablerade musikartister kan använda sociala medier som en del av sina marknadsstrategier och hur digital teknik har förändrat musikbranschen. Denna studie fokuserar på hur osignerade musikartisters antal anhängare och fans på sociala medier påverkar antalet streams av artisternas musik. Studiens huvudsakliga forskningsfråga är: Hur påverkar osignerade artisters prestationer på sociala medier antalet streams av deras musik? För att undersöka detta definierades en robust regressionsmodell i syfte att förutse antalet streams av artisternas musik baserat på deras sociala mediedata. Den robusta regressionsmodellen visade att socialamedievariablerna inte hade signifikanta effekter på antalet streams av artisternas musik. Därför genomfördes en analys av varje enskild artist i datan. Resultaten visade att sociala mediedatan i denna studie inte kunde användas för att förklara förändringar i antalet streams för osignerade musikartister. En analys baserad på varje enskild artist och innehållet som varje enskild artist lägger ut på de olika sociala mediekanalerna föreslås istället. Ett informationsvisualiseringsverktyg utvecklades med syftet att ge analytiker en möjlighet att få en överblick över sociala mediedatan samt låta analytiker titta på varje artists sociala medieflöden för att förstå hur artisternas sociala medier påverkar deras musikstreamingdata.

Cancer is a group of diseases that are characterized by abnormal cell growth and is considered a leading cause of death globally. There are a number of different cancer treatment modalities, one of which is radiation therapy. In radiation therapy treatment planning, it is important to make sure that enough radiation is delivered to the tumor and that healthy organs are spared, while also making sure to account for uncertainties such as misalignment of the patient during treatment. To reduce the workload on clinics, data-driven automated treatment planning can be used to generate treatment plans for new patients based on previously delivered plans. In this thesis, we propose a novel method for robust automated treatment planning where a deep learning model is trained to deform a dose in accordance with a set of potential scenarios that account for the different uncertainties while maintaining certain statistical properties of the input dose. The predicted scenario doses are then used in a robust optimization problem with the goal of finding a treatment plan that is robust to these uncertainties. The results show that the proposed method for deforming doses yields realistic doses of high quality and that the proposed pipeline can potentially generate doses that conform better to the target than the current state of the art but at the cost of dose homogeneity. / Cancer är ett samlingsnamn för sjukdomar som karaktäriseras av onormal celltillväxt och betraktas som en ledande dödsorsak globalt. Det finns olika typer av cancerbehandling, varav en är strålterapi. Inom strålterapiplanering är det viktigt att säkerställa att tillräckligt med strålning ges till tumören, att friska organ skonas, och att osäkerheter som felplacering av patienten under behandlingen räknas med. För att minska arbetsbelastningen på kliniker används data-driven automatisk strålterapiplanering för att generera behandlingsplaner till nya patienter baserat på tidigare levererade behandlingar. I denna uppsats föreslår vi en ny metod för robust automatisk strålterapiplanering där en djupinlärningsmodell tränas till att deformera en dos i enlighet med en mängd potentiella scenarion som motsvarar de olika osäkerheterna medan vissa statistiska egenskaper bibehålls från originaldosen. De predicerade scenariodoserna används sedan i ett robust optimeringsproblem där målet är att hitta en behandlingsplan som är robust mot dessa osäkerheter. Resultaten visar att den föreslagna metoden för dosdeformation ger realistiska doser av hög kvalitet, vilket i sin tur kan leda till robusta doser med högre doskonformitet än tidigare metoder men på bekostnad av doshomogenitet.

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Pumped hydro energy storages commonly plan their operations on short-term forecasts of the upcoming electricity prices, meaning that errors in these forecasts would entail suboptimal operations of the energy storage. Despite the high investment costs of pumped hydro energy storages, few studies take a holistic approach to the uncertainties involved in such investment decisions. The aim of this study is to investigate how forecast errors in electricity prices affect the chosen size configuration in investment decisions for pumped hydro energy storages. Moreover, sizing decisions are made in the long-term and involve long-term uncertainties in electricity prices. A robust decision-making framework including long-term electricity price scenarios is therefore used to evaluate the effects of including forecast errors in the sizing decision. By simulating the day-to-day operation of the energy storage with short-term forecasts, the effects of including the errors are compared to using perfect information. Using this approach, the most robust capacity is shown to increase by 25 MW, from 2 375 MW to 2 400 MW, when including forecast errors instead of assuming perfect information in the simulations. This indicates that the deviations in short-term forecasts require the pumped hydro energy storage operator to be more flexible in their operations, thus requiring a higher capacity. In addition, the profitability of the energy storage decreased significantly when including forecast errors in the simulations, showing the importance of taking the short-term forecast errors into account in sizing and investment decisions of pumped hydro energy storage. / Driften av pumpkraftverk optimeras med hjälp av kortsiktiga prognoser av elpriser, vilket innebär att fel i dessa prognoser leder till suboptimal drift. Trots att investeringar i pumpkraftverk är kostsamma, har få studier ett holistisk synsätt kring osäkerheter i investeringsbeslutet. Målet med denna studie är att undersöka hur kortsiktiga prognosfel i elpriser påverkar den optimala dimensionering av pumpkraftverk. Investeringsbeslut i pumpkraftverk är långsiktiga och kräver estimat av framtida elpriser, vars karakteristik är osäker. Ett ramverk som bygger på robust beslutstagande, med scenarier över framtida elpriser, används därför för att bedöma effekten av att inkludera kortsiktiga prognosfel i investeringsbeslutet. Genom att simulera den dagliga driften av energilager, undersöks effekten av att inkludera prognosfel jämfört med perfekt information. Med detta tillvägagångsätt ökade den mest robusta kapaciteten med 25 MW, från 2 375 MW till 2 400 MW, när prognosfel inkluderades. Detta visar på att fel i kortsiktiga prognoser kräver pumpkraftverket av vara mer flexibelt, vilket ges av höjdkapacitet. Lönsamheten minskade också signifikant när prognosfel inkluderades, vilket visar på vikten av att ta hänsyn till kortsiktiga prognosfel i beslut kring dimensionering och investering av pumpkraftverk.

The enhancement of the reliability, security, and resiliency of electric power systems depends on the availability of fast, accurate, and robust dynamic state estimators. These estimators should be robust to gross errors on the measurements and the model parameter values while providing good state estimates even in the presence of large dynamical system model uncertainties and non-Gaussian thick-tailed process and observation noises. It turns out that the current Kalman filter-based dynamic state estimators given in the literature suffer from several important shortcomings, precluding them from being adopted by power utilities for practical applications. To be specific, they cannot handle (i) dynamic model uncertainty and parameter errors; (ii) non-Gaussian process and observation noise of the system nonlinear dynamic models; (iii) three types of outliers; and (iv) all types of cyber attacks. The three types of outliers, including observation, innovation, and structural outliers are caused by either an unreliable dynamical model or real-time synchrophasor measurements with data quality issues, which are commonly seen in the power system. To address these challenges, we have pioneered a general theoretical framework that advances both robust statistics and robust control theory for robust dynamic state and parameter estimation of a cyber-physical system. Specifically, the generalized maximum-likelihood-type (GM)-estimator, the unscented Kalman filter (UKF), and the H-infinity filter are integrated into a unified framework to yield various centralized and decentralized robust dynamic state estimators. These new estimators include the GM-iterated extended Kalman filter (GM-IEKF), the GM-UKF, the H-infinity UKF and the robust H-infinity UKF. The GM-IEKF is able to handle observation and innovation outliers but its statistical efficiency is low in the presence of non-Gaussian system process and measurement noise. The GM-UKF addresses this issue and achieves a high statistical efficiency under a broad range of non-Gaussian process and observation noise while maintaining the robustness to observation and innovation outliers. A reformulation of the GM-UKF with multiple hypothesis testing further enables it to handle structural outliers. However, the GM-UKF may yield biased state estimates in presence of large system uncertainties. To this end, the H-infinity UKF that relies on robust control theory is proposed. It is shown that H-infinity is able to bound the system uncertainties but lacks of robustness to outliers and non-Gaussian noise. Finally, the robust H-infinity filter framework is proposed that leverages the H-infinity criterion to bound system uncertainties while relying on the robustness of GM-estimator to filter out non-Gaussian noise and suppress outliers. Furthermore, these new robust estimators are applied for system bus frequency monitoring and control and synchronous generator model parameter calibration. Case studies of several different IEEE standard systems show the efficiency and robustness of the proposed estimators. / Ph. D.

Doctor of Philosophy / Department of Statistics / Weixin Yao and Kun Chen / Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. In this proposal, we first review and describe some available and popular robust techniques, including some recent developed ones, and compare them in terms of breakdown point and efficiency. In addition, we also use a simulation study and a real data application to compare the performance of existing robust methods under different scenarios. Finite mixture models are widely applied in a variety of random phenomena. However, inference of mixture models is a challenging work when the outliers exist in the data. The traditional maximum likelihood estimator (MLE) is sensitive to outliers. In this proposal, we propose a Robust Mixture via Mean shift penalization (RMM) in mixture models and Robust Mixture Regression via Mean shift penalization (RMRM) in mixture regression, to achieve simultaneous outlier detection and parameter estimation. A mean shift parameter is added to the mixture models, and penalized by a nonconvex penalty function. With this model setting, we develop an iterative thresholding embedded EM algorithm to maximize the penalized objective function. Comparing with other existing robust methods, the proposed methods show outstanding performance in both identifying outliers and estimating the parameters.

Doctor of Philosophy / Department of Statistics / Kun Chen and Weixin Yao / This proposal contains two projects that are related to robust mixture models. In the robust project, we propose a new robust mixture of regression models (Bai et al., 2012). The existing methods for tting mixture regression models assume a normal distribution for error and then estimate the regression param- eters by the maximum likelihood estimate (MLE). In this project, we demonstrate that the MLE, like the least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust estimation procedure and an EM-type algorithm to estimate the mixture regression models. Using a Monte Carlo simulation study, we demonstrate that the proposed new estimation method is robust and works much better than the MLE when there are outliers or the error distribution has heavy tails. In addition, the proposed robust method works comparably to the MLE when there are no outliers and the error is normal. In the second project, we propose a new robust mixture of linear mixed-effects models. The traditional mixture model with multiple linear mixed effects, assuming Gaussian distribution for random and error parts, is sensitive to outliers. We will propose a mixture of multiple linear mixed t-distributions to robustify the estimation procedure. An EM algorithm is provided to and the MLE under the assumption of t- distributions for error terms and random mixed effects. Furthermore, we propose to adaptively choose the degrees of freedom for the t-distribution using profile likelihood. In the simulation study, we demonstrate that our proposed model works comparably to the traditional estimation method when there are no outliers and the errors and random mixed effects are normally distributed, but works much better if there are outliers or the distributions of the errors and random mixed effects have heavy tails.