Individuals exhibit different reactions to stress, both between individuals and within individuals at different time points. A person’s current emotional state is one of the primary factors that influences how they handle a stressful situation. Someone who is feelingdepressed or anxious may not cope with stress as well as when they are feeling at peace. Another factor that impacts an individual’s ability to cope with stress is being, or at least feeling, in control of the stressful situation. Uncontrollable stress can cause greater emotional disruption and negatively affect behaviour and motivation. Stress-related psychiatric disorders are common today, and research in this field is essential to help individuals improve their stress-coping abilities. In this study, we measured physiological stress responses (heart rate variability and skin conductance) while participants performed a widelyused stress induction task and a novel stress induction task that systematically varied controllability. Before the tasks, participants reported their baseline levels of depression, anxiety, and stress. Our goal was to investigate if negative emotional states predicted the physiological stress response and if stress reactivity to the well-established task was related to stress reactivity when facing an uncontrollable stressor. We hypothesised that individuals who experience more negative emotional states would exhibit a stronger physiological stress response to both tasks. The data we obtained from 61 participants indicated that participants reacted differently to the two stress tasks, but we did not observe any significant impact of depression, anxiety, or stress levels.

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Alan Turing explored how patterns emerged in embryos. The modelsexplained by Turing describe how two morphogens interact with eachother and develop certain patterns though different conditions. Usingthe differential equation expressed by Turing gives a lot of freedom inthe choice of variables depending on how the variables are chosen, whichwill be explored and simulated in this thesis. Later, a systems theoreticformulation will be used to explore the stability and controllability ofthe homogenous diffusion problem and Turing’s Reaction and Diffusionproblem. It will be found that under the assumptions made in this thesisboth models will be stable and controllable.

In 1952 Alan Turing published his paper "The Chemical Basis of Morphogenesis", which described a model for how naturally occurring patterns, such as the stripes of a zebra and the spots of a leopard, can arise from a spatially homogeneous steady state through diffusion. Turing suggested that the concentration of the substances producing the patterns is determined by the reaction kinetics, how the substances interact, and diffusion.  In this project Turing's model with linear reactions kinetics was studied. The model was first solved using two different numerical methods; the finite difference method (FDM) and the finite element method (FEM) with different boundary conditions. A parameter study was then conducted, investigating the effect on the patterns of changing the parameters of the model. Lastly the controllability of the model and the least energy control was considered. The simulations were found to produce patterns provided the right parameters, as expected. From the investigation of the parameters it could be concluded that the size/tightness of the pattern and similarity of the substance concentration distributions depended on the choice of parameters. As for the controllability, a desired final state could be produced thorough simulations using control of the boundary and the energy cost of producing the pattern increased when decreasing the number of controls.

<p dir="ltr">This dissertation encompasses my research work during my Ph.D. career, focusing on the controllability properties of liquid crystal flow. I have achieved two main results, which are as follows: Firstly, I have established the local exact controllability to the trajectory of the simplified Ericksen-Leslie model and its Ginzburg-Landau approximation. Secondly, I have successfully proven the global null controllability of the simplified Ericksen-Leslie model with Lions boundary condition for u and Neumann boundary condition for d, with the aid of a globally defined magnetic field which is independent of the spatial variable x. </p>

This work addresses two primary topics related to vibrations in structures. The first topic is the use of a spatially distributed sensor network for localization of vibration events. I use a received signal strength (RSS) framework that presumes exponential energy decay with distance to the source. I derive the Cramér-Rao bound (CRB) for this parameter estimation problem, with the unknown parameters being source location, source intensity, and the energy dissipation rate. In this framework, I show that the CRB matches the variance of maximum likelihood estimators (MLEs) in more computationally expensive Monte Carlo trials. I also compare the CRB to the results of physical experiments to test the power of the CRB to predict spatial areas where MLEs show practical evidence of being ill-conditioned. Supported by this evidence, I recommend the CRB as a simple measure of localization accuracy, which may be used to optimize sensor layouts before installation. I demonstrate how this numerical optimization may be performed for some regions of interest with simple geometries. The second topic investigates modal vibrations of multi-body structures built from simple one-dimensional elements, with networks of elastic strings as the primary example. I introduce a method of using a nonlinear eigenvalue problem (NLEVP) to express boundary conditions of the vibrating elements so that the (infinitely many) eigenvalues of the full structure are the eigenvalues of the finite-dimensional NLEVP. The mode shapes of the structure can then be recovered in analytic form (not as a discretization) from the corresponding eigenvectors of the NLEVP. I show some advantages of this method over dynamic stiffness matrices, which is another NLEVP framework for modal analysis. In numerical experiments, I test several contour integration solvers for NLEVPs on sample problems generated from string networks. / Doctor of Philosophy / This work deals with two primary topics related to vibrations in structures. The first topic is the use of vibration sensors to detect movement or impact and to estimate the location of the detected event. Sensors that are close to the event will record a larger amount of energy than the sensors that are farther away, so comparing the signals of several sensors can approximately establish the event location. In this way, vibration sensors might be used to monitor activity in a building without the use of intrusive cameras. The accuracy of location estimates can be greatly affected by the relative positions of the sensors and the event. Generally, location estimates tend to be most accurate if the sensors closely surround the event, and less accurate if the event is outside of the sensor zone. These principles are useful, but not precise. Given a framework for how event energy and noise are picked up by the sensors, the Cramér-Rao bound (CRB) is a formula for the achievable accuracy of location estimates. I demonstrate that the CRB is usefully similar to the location estimate accuracy from experimental data collected from a volunteer walking through a sensor-rigged hallway. I then show how CRB computations may be used to find an optimal arrangement of sensors. The match between the CRB and the accuracy of the experiments suggests that the sensor layout that optimizes the CRB will also provide accurate location estimates in a real building. The other main topic is how the vibrations of a structure can be understood through the structure's natural vibration frequencies and corresponding vibration shapes, called the "modes" of the structure. I connect vibration modes to the abstract framework of "nonlinear eigenvalue problems" (NLEVPs). An NLEVP is a square matrix-valued function for which one wants to find the inputs that make the matrix singular. But these singular matrices are usually isolated---% distributed among the infinitely many matrices of the NLEVP in places that are difficult to predict. After discussing NLEVPs in general and some methods for solving them, I show how the vibration modes of certain structures can be represented by the solutions of NLEVPs. The structures I analyze are multi-body structures that are made of simple interconnected pieces, such as elastic strings strung together into a spider web. Once a multi-body structure has been cast into the NLEVP form, an NLEVP solver can be used to find the vibration modes. Finally, I demonstrate that this method can be computationally faster than many traditional modal analysis techniques.

The NASA Performance Adaptive Aeroelastic Wing (PAAW) project goals include significant reductions in fuel burn, emissions, and noise via efficient aeroelastic design and improvements in propulsion systems. As modern transport airplane designs become increasingly lightweight and incorporate high aspect-ratio wings, aeroservoelastic effects gain prominence in modeling and design considerations. As a result, the influence of the flight dynamics and controls on the optimal structural and aerodynamic design needs to be captured in the design process. There is an increasing interest in more integrated aircraft multidisciplinary design optimization (MDAO) processes that can bring flight control design into the early stage of an aircraft design cycle. So, in this thesis different flight dynamics modeling methodologies are presented that can be integrated within the MDAO framework. MDAO studies are conducted to maximize the controllability and observability of a UAV type aircraft using curvilinear SpaRibs and straight spars and ribs as the internal structural layout. The impulse residues and controllability Gramians are used as surrogates for the control objectives in the MDAO to maximize the controllability and observability of the aircraft. The optimal control designs are compared with those obtained using weight minimization as the design objective. It is found that using the aforementioned control objectives, the resulting aircraft design is more controllable and can be used to expand the flight envelope by up to 50% as compared to the weight minimized design. / Doctor of Philosophy / Over the last two decades, several attempts have been made towards multidisciplinary design analysis and optimization (MDAO) of flexible wings by integrating flight control laws in the wing design so that the aircraft will have sufficient control authority across different flying conditions. However, most of the studies have been restricted to the wing design only using a predefined control architecture approach, which would be very difficult to implement at the conceptual design stage. There is a need for an approach that would be faster and more practical. Including control surface and control law designs at the conceptual design stage is becoming increasingly important, due to the complexity of both the aircraft control laws and that of the actuation and sensing, and the enhanced wing flexibility of future transport aircraft. A key question that arises is, can one design an aircraft that is more controllable and observable? So, in this thesis, a more fundamental approach, in which the internal structural layout of the aircraft is optimized to design an aircraft that is more controllable, is presented and implemented. The approach uses the fundamentals of linear systems theory for maximizing the controllability and observability of the aircraft using an MDAO framework.

Dans cette thèse, nous prouvons des résultats concernant le contrôle et la stabilisation d'équations dispersives étudiées sur un intervalle borné. Pour commencer, nous étudions la stabilisation interne du système de Gear-Grimshaw, qui est un système de deux équations de Korteweg-de-Vries (KdV) couplées. Nous obtenons une décroissance exponentielle de l'énergie totale associée au modèle en introduisant une fonction de Lyapunov convenable. Nous prouvons aussi des résultats de contrôlabilité à zéro et exacte pour l'équation de Korteweg-de Vries avec un contrôle distribué à support dans un sous-intervalle du domaine. Pour la contrôlabilité à zéro du système linéarisé, nous utilisons l'approche classique basée sur la dualité qui ramène le problème à l'étude d'une inégalité d'observabilité qui, dans ce travail, est établie à l'aide d'une inégalité de Carleman. Ensuite, utilisant des fonctions plateau, nous prouvons un résultat de contrôlabilité exacte. Dans les deux cas, le résultat concernant le système non linéaire est obtenu à l'aide d'un argument de point fixe. Enfin, dans la lignée du résultat de contrôlabilité au bord obtenu par L. Rosier pour KdV, nous prouvons que le système linéaire de Boussinesq de type KdV-KdV est exactement contrôlable lorsque des contrôles sont appliqués au bord. Notre méthode repose sur l'utilisation de multiplicateurs et l'approche de la dualité mentionnée ci-dessus. Lorsqu'un mécanisme d'amortissement est introduit au bord, nous montrons que le système non linéaire est aussi exactement contrôlable et que l'énergie associée au modèle décroit exponentiellement / This work is devoted to prove a series of results concerning the control and stabilization properties of dispersive models posed on a bounded interval. Initially, we study the internal stabilization of a coupled system of two Korteweg-de Vries equations (KdV), the so-called Gear-Grimshaw system. Defining a convenient Lyapunov function we obtain the exponential decay of the total energy associated to the model. We also prove results of null and exact controllability for the Korteweg-de Vries equation with a control acting internally on a subset of the domain. In the case of the null controllability for the linear model, we use a classical duality approach which reduces the problem to the study of an observability inequality that, in this work, is proved by means of a Carleman inequality. Then, making use of cut-off functions, the exact controllability is also investigated. In both cases, the result for the nonlinear system is obtained by means of fixed-point argument. Finally, in view of the result of the boundary controllability obtained by L. Rosier for the KdV equation, we prove that the linear Boussinesq system of KdV-KdV type is exactly controllable when the controls act in the boundary conditions. Our analysis is performed using multipliers and the duality approach mentioned above. Adding a damping mechanism in the boundary, it is proved that the nonlinear system is also exactly controllable and that the energy associated to the model decays exponentially

Dans cette thèse on s'intéresse à la contrôlabilité de deux classes de systèmes paraboliques linéaires.On caractérise dans un premier temps la contrôlabilité à zéro de systèmes à coefficients constants en dimension 1 lorsque les contrôles agissent sur différentes parties du domaine ou de sa frontière.On regarde ensuite avec le théorème de Fattorini la contrôlabilité frontière approchée de ces systèmes en dimension quelconque.On obtient notamment que les systèmes de 2 équations sont toujours contrôlables dans un rectangle si la zone de contrôle contient 2 directions.Dans un autre travail sur les systèmes à coefficients constants, on obtient une estimation du coût du contrôle frontière à zéro en dimension 1.On utilise ce résultat pour montrer que la contrôlabilité frontière à zéro dans des domaines cylindrique est réduite à la contrôlabilité frontière à zéro en dimension 1.On étudie ensuite la contrôlabilité approchée de systèmes en cascade avec un couplage d'ordre 1.On prouve que la contrôlabilité interne avec un couplage constant à toujours lieu, quel que soit la dimension et la zone de contrôle.On établit d'autre part une caractérisation de la contrôlabilité frontière en dimension 1 avec un couplage variable.Enfin, dans une dernière partie on s'intéresse à la contrôlabilité interne approchée de systèmes en cascade à coefficients variables en dimension 1.On montre qu'on est ramené à établir une caractérisation de la propriété de continuation unique pour une équation elliptique non-homogène.A l'aide de la caractérisation alors obtenue on montre en particulier comment la géométrie de la zone de contrôle peut influencer la contrôlabilité des systèmes. / This thesis focuses on the controllability of two classes of linear parabolic systems.We start with a caracterization of the null-controllability of systems with constant coefficients in dimension 1 where the controls are acting on different parts of the domain or its boundary.With the help of the theorem of Fattorini we then look at the boundary approximate controllability of these systems in any dimension.We show that a system of 2 equations is always approximately controllable on a rectangle if we assume that the control domain contains 2 directions.In another work on the systems with constant coefficients, we obtain an estimate of the boundary null-control cost in dimension 1.We then use this result to show that the boundary null-controllability in cylindrical domains is reduced to the boundary null-controllability in dimension 1.We then study the approximate controllability of cascade systems with a first order coupling term.We prove the distributed controllability when the coupling is constant, whatever the dimension and control domain are.On the other hand, we establish a caracterisation of the boundary controllability in dimension 1 for space-dependent couplings.Last, we investigate the distributed approximate controllability of cascade systems with space-dependent coefficients in dimension 1.Using the theorem of Fattorini and the structure of the systems under study we are lead to characterize the unique continuation property for a non-homogeneous elliptic equation.With the help of the caracterization then obtained we show in particular how the geometry of the control domain can affect the controllability properties of systems.