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Stability analysis of networked dynamical systems has been of interest in many disciplines such as biology and physics and chemistry with applications such as LASER cooling and plasma stability. These large networks are often modeled to have a completely random (Erdös-Rényi) or semi-random (Small-World) topologies. The former model is often used due to mathematical tractability while the latter has been shown to be a better model for most real life networks. The recent emergence of cyber physical systems, and in particular the smart grid, has given rise to a number of engineering questions regarding the control and optimization of such networks. Some of the these questions are: How can the stability of a random network be characterized in probabilistic terms? Can the effects of network topology and system dynamics be separated? What does it take to control a large random network? Can decentralized (pinning) control be effective? If not, how large does the control network needs to be? How can decentralized or distributed controllers be designed? How the size of control network would scale with the size of networked system? Motivated by these questions, we began by studying the probability of stability of synchronization in random networks of oscillators. We developed a stability condition separating the effects of topology and node dynamics and evaluated bounds on the probability of stability for both Erdös-Rényi (ER) and Small-World (SW) network topology models. We then turned our attention to the more realistic scenario where the dynamics of the nodes and couplings are mismatched. Utilizing the concept of ε-synchronization, we have studied the probability of synchronization and showed that the synchronization error, ε, can be arbitrarily reduced using linear controllers. We have also considered the decentralized approach of pinning control to ensure stability in such complex networks. In the pinning method, decentralized controllers are used to control a fraction of the nodes in the network. This is different from traditional decentralized approaches where all the nodes have their own controllers. While the problem of selecting the minimum number of pinning nodes is known to be NP-hard and grows exponentially with the number of nodes in the network we have devised a suboptimal algorithm to select the pinning nodes which converges linearly with network size. We have also analyzed the effectiveness of the pinning approach for the synchronization of oscillators in the networks with fast switching, where the network links disconnect and reconnect quickly relative to the node dynamics. To address the scaling problem in the design of distributed control networks, we have employed a random control network to stabilize a random plant network. Our results show that for an ER plant network, the control network needs to grow linearly with the size of the plant network.

This thesis develops theoretical and computational methods for the robustness analysis of uncertain systems. The considered systems are linearized and depend rationally on random parameters with an associated probability distribution. The uncertainty is tackled by applying a polynomial chaos expansion (PCE), a series expansion for random variables similar to the well-known Fourier series for periodic time signals. We consider the linear perturbations around a system's operating point, i.e., reference trajectory, both from a probabilistic and worst-case point of view. A chief contribution is the polynomial chaos series expansion of uncertain linear systems in linear fractional representation (LFR). This leads to significant computational benefits when analyzing the probabilistic perturbations around a system's reference trajectory. The series expansion of uncertain interconnections in LFR further delivers important theoretical insights. For instance, it is shown that the PCE of rational parameter-dependent linear systems in LFR is equivalent to applying Gaussian quadrature for numerical integration. We further approximate the worst-case performance of uncertain linear systems with respect to quadratic performance metrics. This is achieved by approximately solving the underlying parametric Riccati differential equation after applying a polynomial chaos series expansion. The utility of the proposed probabilistic robustness analysis is demonstrated on the example of an industry-sized autolanding system for an Airbus A330 aircraft. Mean and standard deviation of the stochastic perturbations are quantified efficiently by applying a PCE to a linearization of the system along the nominal approach trajectory. Random uncertainty in the aerodynamic coefficients and mass parameters are considered, as well as atmospheric turbulence and static wind shear. The approximate worst-case analysis is compared with Monte Carlo simulations of the complete nonlinear model. The methods proposed throughout the thesis rapidly provide analysis results in good agreement with the Monte Carlo benchmark, at reduced computational cost.

Previous research has shown that sensemaking structures within organizations are not only present, but vital in project settings. Informal individually produced sensemaking structures, such as task lists, are a mean to formulate ones' own project work into individual actions. These have shown to be essential, but some drawbacks have also been shown to exist. However, the lens has previously been mainly on the individual level, and organizational implications have got little attention in research. This study aims to explore projects' implications when such individual structures are dominant in the process. To do so, the reasons for production of said structures are analysed as well as the source of them. As a mean to identify such implications, a qualitative single-case study was performed at a Swedish consultancy company, where in total 16 interviews were held with employees at various positions and hierarchical levels. As expected, sensemaking structures were widely used in several formats, produced both for individual and collective purposes. The study further reveals that depending on the source of inspiration for the task lists, there is a risk that multiple views of the projects' goal are formed, which in turn affects the projects' progress. Also, the responsibility of the project leaders was shown to be of importance as a mean to minimize individual prioritization and instead build a uniform perception of projects' priorities, thus through communication and transparency. As the study finds a clear connection between individuals' sensemaking structures and organizational implications, further and more broad research on sensemaking structures through an organizational lens is suggested. / Tidigare forskning visar på att meningsskapande strukturer [eng: sensemaking structures] i organisationer existerar och håller en avgörande del i projektsammanhang. Informella individuella strukturer, så som uppgiftslistor, används och produceras för att bryta ner projektarbetet till mindre uppgifter. Dessa strukturer har visat sig vara av stor betydelse, men nackdelar har även visat sig förekomma. Tidigare forskning har huvudsakligen fokuserats kring individen, men mindre uppmärksamhet har lagts på organisatoriska aspekter. Denna studie syftar till att utforska de konsekvenser projekt kan erhålla då individuella strukturer är dominanta i projektarbetet. I ett försök att finna dessa konsekvenser så har både skälen till produktionen av dessa strukturer samt dess källa analyserats. För att identifiera dessa konsekvenser har en kvalitativ fallstudie utförts på ett svenskt konsultföretag, där resultatet samlades in genom att intervjua 16 anställda verksamma på olika positioner och hierarkiska nivåer. Användandet av meningsskapande strukturer var som väntat stort, då syftet till dess användning både var individuellt och kollektivt. Studien visar att källan till de individuella listorna skiljer sig åt,vilket bidrar till risken att det formas flertalet synsätt på projektets mål, vilket i sin tur påverkar projektets utveckling. Projektledarens ansvar att kommunicera och vara transparent har visat sig vara av betydelse i syfte att minimera individuella prioriteringar och därav bör det byggas en mer enhetlig syn på projektets prioriteringar. Då författarna av studien finner tydliga kopplingar mellan individuella meningsskapande strukturer och organisatoriska implikationer föreslås vidare forskning på meningsskapande processer genom en organisatorisk lins.

Due to advances in digital computing much of the baseband signal processing of a communication system has moved into the digital domain from the analog domain. Within the domain of digital communication systems, Software Defined Radios (SDRs) allow for majority of the signal processing tasks to be implemented in reconfigurable digital hardware. However this comes at a cost of higher power and resource requirements. Therefore, highly efficient custom hardware implementations for SDRs are needed to make SDRs feasible for practical use. Efficient custom hardware motivates the use of fixed point arithmetic in the implementation of Digital Signal Processing (DSP) algorithms. This conversion to finite precision arithmetic introduces quantization noise in the system, which significantly affects the performance metrics of the system. As a result, characterizing quantization noise and its effects within a DSP system is an important challenge that needs to be addressed. Current models to do so significantly over-estimate the quantization effects, resulting in an over-allocation of hardware resources to implement a system. Polynomial Chaos Expansion (PCE) is a method that is currently gaining attention in modelling uncertainty in engineering systems. Although it has been used to analyze quantization effects in DSP systems, previous investigations have been limited to simple examples. The purpose of this thesis is to therefore introduce new techniques that allow the application of PCE to be scaled up to larger DSP blocks with many noise sources. Additionally, the thesis introduces design space exploration algorithms that leverage the accuracy of PCE simulations to estimate bitwidths for fixed point implementations of DSP systems. The advantages of using PCE over current modelling techniques will be presented though its application to case studies relevant to practice. These case studies include Sine Generators, Infinite Impulse Response (IIR) filters, Finite Impulse Response (FIR) filters, FM demodulators and Phase Locked Loops (PLLs). / Thesis / Master of Applied Science (MASc)

This thesis is a critical review of two central theories in the modern sustainability paradigm – namely… (1) the theory that the Earth’s geosphere, hydrosphere, biosphere and atmosphere form a complex adaptive system – the Earth system, and (2) the theory that all human activities are intrinsically dependent on, and constrained by, non-anthropogenic states and processes in the Earth system. The thesis explains the origins and the logic of these theories, and subjects them to formal, semi-formal and comparative criticism. Ultimately, it refutes both on formal and comparative grounds. Most importantly, it shows that theories 1 and 2 are in conflict with the theory of evolution by natural selection, and with the hypothetico-deductive model of scientific research. It also shows that they are in conflict – both directly and indirectly – with the known laws of physics. While it is true that all human activities rely on biospheric resources today, there are no physical, or natural laws that make it impossible for us to break those dependencies over time. In fact, the thesis shows that it is possible in principle to satisfy any human need by strictly artificial means, and abiotic resources that exist in abundance both inside and outside of the Earth system. An important corollary to this finding is that social and economic progress is not inextricably tied – as the modern sustainability literature suggests – to the exploitation of finite and rapidly diminishing resources here on Earth. Theories 1 and 2 both contribute to this confusion, and hence, to the bleak and irrational Malthusianism that still permeates so much of the sustainability domain. In addition, they appear to blind many researchers to the ecological benefits of technological development. That humanity can break its dependence on the biosphere is a very good thing for its non-human inhabitants. As we become more technologically advanced, we will find it easier and easier to sustain ourselves without destabilizing the world's ecosystems. The Earth’s biosphere is an oasis of beauty, complexity and connection in a Universe that is overwhelmingly empty and boring. As the only animals capable of appreciating this fact, we have a clear moral duty to protect and preserve it. And we can protect and preserve it. If we just let go of the religious ideas that have dominated our field since its inception, we will find that our potential to do good in the world is far greater than we previously imagined.

The aim of this thesis is to simulate stochastic models that are driven by a fractional Brownian motion process and to apply these methods to financial applications related to yield rate and asset price modelling. Several rough volatility processes are used to model the asset price and yield dynamics. Firstly fractional processes of Cox-Ingersoll-Ross, CEV and Vasicek types are introduced as models for volatility and yield data. In this framework it holds that the Hurst parameter that determines the covariance structure of the fBM process can be directly estimated from observed data series using a least squares log-periodogram approach. The remaining parameters in the model are estimated using a combination of Maximum Likelihood estimates and expectation estimations. In the modelling and pricing of assets one model that is studied is the fractional Heston model, that is used to model an asset price process using both observed asset and volatility data. Similarly two other similar rough volatility models are also studied, which are constructed so as to have log-Normal returns. These processes which in the thesis are called the exponential models 1 and 2 have rough volatility that are characterized by the CEV and Vasicek processes. Additionally the first order Wiener Chaos Expansion is implemented and explored in two ways. Firstly the Chaos Expansion is applied to a parametric fractional stochastic model which is used to generate a Wick product process, which is found to resemble the underlying process. It is also used to generate an approximate expansion of real yield rate data using a bootstrap sampling approach. / Den här uppsatsen syftar till att simulera stokastiska modeller som drivs av fraktionell Brownsk rörelse och att använda dessa modeller i finansiella tillämpningar relaterade till räntor och finansiella tillgångar. Flera volatilitetsprocesser som är rough används för att modellera ränte- och aktiedynamiken. Först introduceras de fraktionella varianterna av Cox-Ingersoll-Ross, CEV och Vasicek processer, vilka används för att modellera volatilitet och ränteprocesser. Med detta tillvägagångssätt gäller det att Hurstparametern, vilken bestämmer covariansstrukturen för den fraktionella Brownska rörelsen, kan uppskattas direkt från observerad data med en minsta kvadrat log-periodogram-metod. Samtliga andra parametrar i modellen uppskattas med en kombination av Maximum Likelihood och uppskattning av väntevärden. I modelleringen och prissättningen av finansiella tillgångar är en model som studeras den fraktionella Hestonmodellen, som används för att modellera en tillgång baserat på både volatilitets- och aktiedata. Ytterligare två liknande modeller studeras, vilka också har volatilitet som är rough och är konstruerade så att deras avkastning är log-Normal. Dessa processer, vilka i uppsatsen är benämnda som de exponentiella modellerna 1 och 2 har volatilitet som karaktäriseras av CEV- och Vasicekprocesser. Ytterligare är Wiener's Kaosexpansion av första ordningen också implementerad och undersöks från två håll. Först används den på en parameterbestämd fraktionell stokastisk modell, vilken används för att generera en Wickproduktprocess. Expansionen används även med hjälp av en bootstrap-metod för att generera en process från observerad data.

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