This thesis investigates the use of control theory as a means to study and ultimately control the psychological dynamics of people in a crowd. Gustav LeBon's suggestibility theory, a well-known account of collective behaviour, is used to develop a discrete-time nonlinear model of psychological crowd behavior that, consistent with suggestibility theory, is open-loop unstable. As a first attempt to stabilize the dynamics, linear observer-based output-feedback techniques and a collection of simple nonlinear control strategies are pursued. The poor performance afforded by these schemes motivates an agent-oriented control strategy in which authoritative figures, termed control agents, are interspersed within the crowd and, similar to the technique of feedback linearization, use knowledge of the system dynamics to issue signals that propagate through the crowd to drive specific components of the state to zero. It is shown that if these states are chosen judiciously then it follows that a collection of other state signals are, themselves, zero. This realization is used to develop a stability result for a simple crowd structure and this result is, in turn, used as a template to develop similar results for crowds of greater complexity. Simulations are used to verify the functionality of the reported schemes and the advantages of using multiple control agents, instead of a single control agent, are emphasized. While the mathematical study of complex social phenomena, including crowds, is prefixed by an assortment of unique challenges, the main conclusion of this thesis is that control theory is a potentially powerful framework to study the underlying dynamics at play in such systems.

The proliferation and universal adoption of the Internet has made it become the key information transport platform of our time. Congestion occurs when resource demands exceed the capacity, which results in poor performance in the form of low network utilization and high packet loss rate. The goal of congestion control mechanisms is to use the network resources as efficiently as possible. The research work in this thesis is centered on finding ways to address these types of problems and provide guidelines for predicting and controlling network performance, through the use of suitable mathematical tools and control analysis. The first congestion collapse in the Internet was observed in 1980's. To solve the problem, Van Jacobson proposed the Transmission Control Protocol (TCP) congestion control algorithm based on the Additive Increase and Multiplicative Decrease (AIMD) mechanism in 1988. To be effective, a congestion control mechanism must be paired with a congestion detection scheme. To detect and distribute network congestion indicators fairly to all on-going flows, Active Queue Management (AQM), e.g., the Random Early Detection (RED) queue management scheme has been developed to be deployed in the intermediate nodes. The currently dominant AIMD congestion control, coupled with the RED queue in the core network, has been acknowledged as one of the key factors to the overwhelming success of the Internet. In this thesis, the AIMD/RED system, based on the fluid-flow model, is systematically studied. In particular, we concentrate on the system modeling, stability analysis and bounds estimates. We first focus on the stability and fairness analysis of the AIMD/RED system with a single bottleneck. Then, we derive the theoretical estimates for the upper and lower bounds of homogeneous and heterogeneous AIMD/RED systems with feedback delays and further discuss the system performance when it is not asymptotically stable. Last, we develop a general model for a class of multiple-bottleneck networks and discuss the stability properties of such a system. Theoretical and simulation results presented in this thesis provide insights for in-depth understanding of AIME/RED system and help predict and control the system performance for the Internet with higher data rate links multiplexed with heterogeneous flows.

Driven by economic, technical, and environmental reasons, the energy sector is moving into an era where large portions of increases in electrical energy demand will be met through widespread installation of distributed resources or what's known as distributed generation (DG). DG units can operate in parallel to the main grid or in a micro-grid mode. The later is formed by a cluster of DG units connected to a distribution network to maintain the reliability of critical loads, mainly when the grid supply is not available. Distributed resources include variable frequency sources, high frequency sources, and direct energy conversion sources producing dc voltages or currents. The majority of distributed resources are interfaced to the utility grid or to the customer load via dc-ac pulse-width-modulated (PWM) voltage source inverter (VSI) systems. However, these interfaces introduce new issues, such as the absence of the physical inertia, wide-band of dynamics, limited overload capability, susceptibility to parameters variation, and switching harmonics generation. In addition, the uncertain and dynamic nature of the distribution network challenges the stability and control effectiveness of a grid-connected inverter-based DG interface. Generally, difficulties appear in the form of grid impedance and interfacing parameter variations, fast and slow grid-voltage disturbances, grid distortion and unbalance, and interactions between the inverter ac-side filter and the grid. On the other hand, a micro-grid system will be dominated by inverter-based DG units. Unlike conventional power system generators, inverter-based DG units have no physical inertia. This fact makes the micro-grid system potentially susceptible to oscillations resulting from system disturbances. Severe and random disturbances might be initiated in a micro-grid system, due to load changes, the power sharing mechanism of the inverters and other generators, and interactions between the DG interface and the network. Motivated by the aforementioned difficulties, this thesis presents new control algorithms for the DG interface that guarantee stable and high power quality injection under the occurrence of network disturbances and uncertainties, in both the grid-connected and micro-grid systems. The control architecture of the proposed DG interface relies on the following subsystems. First, a newly designed deadbeat current regulation scheme is proposed. The proposed design guarantees high power quality current injection under the presence of different disturbing parameters such as grid voltage distortion, interfacing parameter variation, and inverter system delays. Further, it utilizes the maximum dynamic performance of the inverter in a way that provides a high bandwidth and decoupled control performance for the outer control loops. Different topologies of the ac-side filter are considered for the current control design. Second, a novel adaptive discrete-time grid-voltage sensorless interfacing scheme for DG inverters is proposed. The adaptive interface relies on a new interface-monitoring unit that is developed to facilitate accurate and fast estimation of the interfacing impedance parameters and the grid voltage vector (magnitude and position) at the point of common coupling. The estimated grid voltage is utilized to realize a grid-voltage sensorless interfacing scheme, whereas the interfacing parameters are utilized for the self-tuning control and interface-parameter monitoring. Further, a simple and robust synchronization algorithm and a voltage-sensorless average power control loop are proposed to realize an adaptive voltage-sensorless DG interface. The voltage-sensorless interface positively contributes to the elimination of the residual negative sequence and voltage feed-forward compensation errors, and to the robustness of the power sharing mechanism in paralleled inverter systems, where the power-sharing mechanism is generally based on open-loop controllers. Third, a new voltage control scheme for the DG interface featuring fast load voltage regulation and effective mitigation of fast voltage disturbances is proposed. The proposed voltage control scheme targets the problem of fast and large-signal-based voltage disturbances, which is common in typical distribution feeders. A hybrid voltage controller combining a linear with a variable-structure-control element is proposed for the DG interface. Positive and dual-sequence versions of the proposed voltage controller are developed to address the issue of unbalanced voltage disturbances. The proposed voltage controller successfully embeds a wide band of frequency modes through an equivalent internal model. Subsequently, wide range of balanced and unbalanced voltage perturbations, including capacitor-switching disturbances, can be effectively mitigated. Fourth, to constrain the drift of the low frequency modes in a conventional droop-controlled micro-grid, a new transient-based droop controller with adaptive transient-gains is proposed. The proposed power-sharing controller offers an active damping feature that is designed to preserve the dynamic performance and stability of each inverter unit at different loading conditions. Unlike conventional droop controllers, the proposed droop controller yields two-degree of freedom tunable controller. Subsequently, the dynamic performance of the power-sharing mechanism can be adjusted, without affecting the static droop gain, to damp the oscillatory modes of the power-sharing controller. The overall robust DG interface facilitates a robust micro-grid operation and safe plug-and-play integration of DG units on existing distribution systems; hence increasing the system penetration of DG. The direct result of this development is huge financial saving for utilities by capturing the salient features of deploying DG into existing utility networks. Further, these developments are significant to the industry as they provide the blue print for reliable control algorithms in future DG units, which are expected to operate under challenging system conditions.

Columns subjected to time varying axial load may exhibit dynamic instability due to parametric resonance. This type of instability is inherent in structures; it is not due to material or geometrical imperfections, and can occur even in perfectly constructed structures. This characteristic makes parametric resonance a very difficult to predict and therefore dangerous phenomenon. In this thesis the stability of a structural column under bounded noise axial load is studied by use of Lyapunov exponents. Bounded noise is especially useful as a loading because it may be used to represent both wide and narrow band processes, making the stability equations developed general enough to handle a wide variety of real world probabilistic loadings. The equation of motion of the first mode of vibration for this system is a second-order nonlinear stochastic ordinary differential equation. The nonlinearity makes the system exhibit bifurcating behaviour where stability shifts from the trivial solution to a non-zero mean stationary solution. The stability of the trivial and non-trivial solutions is important in obtaining a complete picture of the dynamical behaviour of the system. The effect that damping, the amplitude of noise, and the level of nonlinearity have on the stability of a structural column is studied using both analytical and numerical approaches. The largest Lyapunov exponent of the trivial solution is determined analytically by using time averaged versions of the original equation of motion. The validity of the analytical time averaged equation of motion is also verified with Monte Carlo simulations. Due to the mathematical complexity the largest Lyapunov exponent of the non-trivial stationary solutions is obtained using Monte Carlo simulation only.

The number of large-scale wind farms integrated to the power system in Sweden is increasing. Two generator concepts that are widely used are Doubly-Fed Induction Generators (DFIG) and Full Power Converters (FPC). The study is of a quantitative character and the aim of the Master thesis is to compare DFIG-models with FPC-models integrated in an area with high concentration of hydropower. Then it is possible to examine how the dynamics in the power system change depending on the selection of technology (DFIG or FPC) when connecting a wind farm. The power system is simulated during a summer night, i.e., a low load is connected. The Master thesis covers stability analysis of the power system by using rotor angle stability that are split into small-signal stability and transient stability (time-domain simulations) and finally voltage stability to see how the hydropower generators react when varying the power production in the wind farm. The Master thesis concludes that independently of wind turbine technique, integration of a wind farm has slight impact on the stability in the power system compared to a power system without a wind farm, even though the load is low. Further, an integration of a wind farms affects the reactive power production in neighbouring hydropower plants. Finally, when increasing the size of the wind farm the neighbouring hydropower station consume less reactive power which can induce problem with the voltage stability.

It is widely understood that injection and production activities can induce additional stress fields that will couple with the in situ stress field. An increased shear stress may cause serious casing stability issue, and casing integrity is one of the major issues in the development of an oilfield. In this thesis, I will present a methodology for semi-quantitatively addressing the physical processes, the occurrence, and the key influential factors associated with large-area casing shear issues in Daqing Oilfield. In the research, I will investigate reservoir heterogeneity and the far-field stress field in the Daqing Oilfield, China; I will review fundamental theories of rock strength, rock failure, casing shear, and techniques for coupling fluid flow and mechanical response of the reservoirs; and I will present mathematical simulations of large-area casing shear in one typical area (X1-3B) in Daqing Oilfield, under different regimes of water-affected shale area ratio and block pressure difference. Heterogeneity in Daqing Oilfield varies according to the scale. Mega-heterogeneity is not too serious: the geometry of the oilfield is simple, the structure is flat, and faults are numerous and complex, but distributed evenly. Macro-heterogeneity is, however, intense. Horizontal macro-heterogeneity is associated with lateral variations because of different depositional facies. Vertical macro-heterogeneity of Daqing Oilfield because of layering is typified by up to 100 individual sand layers with thickness ranging from 0.2 to 20 m and permeability ranging from 20 to 1600 mD (average 230 mD). Furthermore, there are a number of stacked sand-silt-shale (clastic lithofacies) sequences. Mercury porosimetry and photo-micro-graphic analyses were used to investigate the micro-heterogeneity of Daqing Oilfield. This method yields a complete pore size distribution, from several nanometers to several thousands of micro-meters as well as cumulative pore volume distributions, pore-throat aspect ratios, and fractal dimensions. The fractal dimension can be used to describe the heterogeneity at the pore scale; for sandstones, the larger the fractal dimension of a specific pore structure, the more heterogeneous it is. Reservoir sandstones of Daqing Oilfield have similar porosity and mineralogy, so their micro-heterogeneity lies in a micro-structure of considerable variability. Differences in micro-structure affect permeability, which also varies considerably and evidences a considerable amount of micro-scale anisotropy. Finally, the number and nature of faults in the oilfield make the macro-scale heterogeneity more complex. Rock strength is affected by both intrinsic factors and external factors. Increased water saturation affects rock strength by decreasing both rock cohesion and rock friction angle. In Daqing Oilfield, is seems that a 5% increase of water content in shale can decrease the maximum shearing resistance of shale by approximately 40%. Hysteretic behavior leads to porosity and permeability decreases during the compaction stage of oilfield development (increasing σ'). Also, injection pressures are inevitably kept as high as possible in the pursuit of greater production rates. These lead to non-homogeneous distributions of pressures as well as in changes of material behavior over time. Loss of shear strength with water content increase, inherent reservoir heterogeneity, and long periods of high-pressure water injection from a number of wells are three key factors leading to casing shear occurring over large areas in Daqing Oilfield. Reservoir heterogeneity and structural complexity foster uneven formation pressure distribution, leading to inter-block pressure differences. Sustained long-term elevated pressures affect overburden shale mechanical strength as well as reducing normal stresses, and the affected area increases with time under high-pressure injection so that the affected areas overlap at the field scale and alter the in situ stress field. Once the maximum compressive stress parallels or nearly parallels the differential pressure, and the water-affected shale area is big enough, the shear stability of the interface between the shale and the sandstone is severely compromised, and when the thrust stress imposed exceeds the shearing resistance, the strata will slip in a direction corresponding to the vector from high-pressure to low-pressure areas. The change in this slip and creep displacement field is the major reason for the serious casing deformation damage in Daqing Oilfield. To quantify the scale effect of the water-affected shale area on casing stability, coupled non-linear poroelastic fluid flow was simulated for a typical area. The Daqing Oilfield simulation result is in coincidence with the in situ observation of disturbed stress fields and casing displacement. The water-affected area has a scale effect on the casing stability. The ratio of the water-affected shale formation area to the total area influences the stability coefficient much more than the block pressure difference. In the studied area, under conditions of injection pressure of 12.7 MPa and no more than 2.5 MPa block pressure difference, the water-affected ratio should be smaller than 0.50 or so in order to maintain areal casing stability. By history matching, in the studied area under current development condition and considering the water-affected ratio, so long as the injection pressure and pressure differential between blocks are controlled to be less than 12.7 MPa and 0.86 MPa respectively, formation shear slip along a horizontal surface will no longer occur.

A major function of the central nervous system (CNS) during locomotion is the ability to maintain dynamic stability during threats to balance. The CNS uses reactive, predictive, and anticipatory mechanisms in order to accomplish this. Previously, stability has been estimated using single measures. Since the entire body works as a system, dynamic stability should be examined by integrating kinematic, kinetic, and electromyographical measures of the whole body. This thesis examines three threats to stability (recovery from a frontal plane surface translation, stepping onto and walking on a compliant surface, and obstacle clearance on a compliant surface). These threats to stability would enable a full body stability analysis for reactive, predictive, and anticipatory CNS control mechanisms. From the results in this study, observing various biomechanical variables provides a more precise evaluation of dynamic stability and how it is achieved. Observations showed that different methods of increasing stability (eg. Lowering full body COM, increasing step width) were controlled by differing CNS mechanisms during a task. This provides evidence that a single measure cannot determine dynamic stability during a locomotion task and the body must be observed entirely to determine methods used in the maintenance of dynamic stability.

Overloading of the back can cause instability such that buttressing the instability is a primary objective of many of the leading edge therapeutic approaches. However, a challenge lies in determining the location of the instability or the least stable vertebral joint. A mathematical analysis, based on a commonly used approach in engineering for determining structural stability, has been developed for the lumbar spine. The purpose of this investigation was to determine the feasibility of a method for mathematically locating potential areas of instability within a computer-based model of the lumbar spine. To validate this method, the eigenvector from the stability analysis was compared to the output from a geometric equation that approximated individual vertebral joint rotational stiffness with the idea that the entry in the eigenvector with the largest absolute value would correspond to the vertebral joint and axis with the lowest stiffness. Validation of the eigenvector was not possible due to computational similarities between the stability analysis and the geometric rotational stiffness method. However, it has been previously demonstrated that the eigenvector can be useful for locating instability, and thus warrants future study. Determining the least stable vertebral joint and axis can be used to guide proper motor pattern training as a clinical intervention. It was also shown in this investigation that an even distribution of fascicle force and stiffness generated stability. This supports the idea that well-coordinated efforts of muscle activation are beneficial for improving stability of the lumbar spine.

This thesis investigates the use of control theory as a means to study and ultimately control the psychological dynamics of people in a crowd. Gustav LeBon's suggestibility theory, a well-known account of collective behaviour, is used to develop a discrete-time nonlinear model of psychological crowd behavior that, consistent with suggestibility theory, is open-loop unstable. As a first attempt to stabilize the dynamics, linear observer-based output-feedback techniques and a collection of simple nonlinear control strategies are pursued. The poor performance afforded by these schemes motivates an agent-oriented control strategy in which authoritative figures, termed control agents, are interspersed within the crowd and, similar to the technique of feedback linearization, use knowledge of the system dynamics to issue signals that propagate through the crowd to drive specific components of the state to zero. It is shown that if these states are chosen judiciously then it follows that a collection of other state signals are, themselves, zero. This realization is used to develop a stability result for a simple crowd structure and this result is, in turn, used as a template to develop similar results for crowds of greater complexity. Simulations are used to verify the functionality of the reported schemes and the advantages of using multiple control agents, instead of a single control agent, are emphasized. While the mathematical study of complex social phenomena, including crowds, is prefixed by an assortment of unique challenges, the main conclusion of this thesis is that control theory is a potentially powerful framework to study the underlying dynamics at play in such systems.

The proliferation and universal adoption of the Internet has made it become the key information transport platform of our time. Congestion occurs when resource demands exceed the capacity, which results in poor performance in the form of low network utilization and high packet loss rate. The goal of congestion control mechanisms is to use the network resources as efficiently as possible. The research work in this thesis is centered on finding ways to address these types of problems and provide guidelines for predicting and controlling network performance, through the use of suitable mathematical tools and control analysis. The first congestion collapse in the Internet was observed in 1980's. To solve the problem, Van Jacobson proposed the Transmission Control Protocol (TCP) congestion control algorithm based on the Additive Increase and Multiplicative Decrease (AIMD) mechanism in 1988. To be effective, a congestion control mechanism must be paired with a congestion detection scheme. To detect and distribute network congestion indicators fairly to all on-going flows, Active Queue Management (AQM), e.g., the Random Early Detection (RED) queue management scheme has been developed to be deployed in the intermediate nodes. The currently dominant AIMD congestion control, coupled with the RED queue in the core network, has been acknowledged as one of the key factors to the overwhelming success of the Internet. In this thesis, the AIMD/RED system, based on the fluid-flow model, is systematically studied. In particular, we concentrate on the system modeling, stability analysis and bounds estimates. We first focus on the stability and fairness analysis of the AIMD/RED system with a single bottleneck. Then, we derive the theoretical estimates for the upper and lower bounds of homogeneous and heterogeneous AIMD/RED systems with feedback delays and further discuss the system performance when it is not asymptotically stable. Last, we develop a general model for a class of multiple-bottleneck networks and discuss the stability properties of such a system. Theoretical and simulation results presented in this thesis provide insights for in-depth understanding of AIME/RED system and help predict and control the system performance for the Internet with higher data rate links multiplexed with heterogeneous flows.