The regular waterfilling(WF) policy maximizes the mutual information of parallel channels, when the inputs are Gaussian. However, Gaussian input is ideal, which does not exist in reality. Discrete constellations are usually used instead, such as $ M $-PAM and $ M $-QAM. As a result, the mercury/waterfilling (MWF) policy is introduced, which is a generalization of the regular WF. The MWF applies to inputs with arbitrary distributions, while the regular WF only applies to Gaussian inputs. The MWF-based optimal power allocation (OPA) is presented, for which an algorithm called the internal/external bisection method is introduced. The constellation-constrained capacity is discussed in the thesis, where explicit expressions are presented. The expression contains an integral, which does not have a closed-form solution. However, it can be evaluated via the Monte Carlo method. An approximation of the constellation-constrained capacity based on the sphere packing method is introduced, whose OPA is a convex optimization problem. The CVX was used initially, but it did not generate satisfactory results. Therefore, the bisection method is used instead. Capacities of the MWF and its sphere packing approximation are evaluated for various cases, and compared with each other. It turns out the sphere packing approximation has similar performances to the MWF, which validates the approximation. Unlike the MWF, the sphere packing approximation does not suffer from the loss of precision due to the structure of MMSE functions, which demonstrates its robustness.

Localization and motion control (navigation) are two major tasks for a successful mobile robot navigation. The motion controller determines the appropriate action for the robot’s actuator based on its current state in an operating environment. A robot recognizes its environment through some sensors and executes physical actions through actuation mechanisms. However, sensory information is noisy and hence actions generated based on this information may be non-deterministic. Therefore, a mobile robot provides actions to its actuators with a certain degree of uncertainty. Moreover, when no prior knowledge of the environment is available, the problem becomes even more difficult, as the robot has to build a map of its surroundings as it moves to determine the position. Skilled navigation of a differential drive mobile robot (DDMR) requires solving these tasks in conjunction, since they are inter-dependent. Having resolved these tasks, mobile robots can be employed in many contexts in indoor and outdoor environments such as delivering payloads in a dynamic environment, building safety, security, building measurement, research, and driving on highways. This dissertation exploits the use of the emerging Radio Frequency IDentification (RFID) technology for the design and implementation of cost-effective and modular control techniques for navigating a mobile robot in an indoor environment. A successful realization of this process has been addressed with three separate navigation modules. The first module is devoted to the development of an indoor navigation system with a customized RFID reader. This navigation system is mainly pioneered by mounting a multiple antenna RFID reader on the robot and placing the RFID tags in three dimensional workspace, where the tags’ orthogonal position on the ground define the desired positions that the robot is supposed to reach. The robot generates control actions based on the information provided by the RFID reader for it to navigate those pre-defined points. On the contrary, the second and third navigation modules employ custom-made RFID tags (instead of the RFID reader) which are attached at different locations in the navigation environment (on the ceiling of an indoor office, or on posts, for instance). The robot’s controller generates appropriate control actions for it’s actuators based on the information provided by the RFID tags in order to reach target positions or to track pre-defined trajectory in the environment. All three navigation modules were shown to have the ability to guide a mobile robot in a highly reverberant environment with variant degrees of accuracy.

The purpose of this research was to identify the contributors to optimal sexual experiences. At present, there is a lack of clinical knowledge, research knowledge and in-depth public discourse concerning the nature of healthy sexuality. The theoretical and research literature in this area has focused almost exclusively on defining and conceptualizing sexual dysfunctions with little attention paid to either normal or satisfactory experiences. Very little theory exists on the nature and components of optimal sexuality. To date, no empirical investigations have been done to determine the contributors to optimal sexual experiences. In order to identify the contributors to optimal sexual experiences, semi-structured interviews were conducted with 12 individuals who reported having experienced “great sex”. A phenomenologically-oriented content analysis was performed on interview transcripts to determine the contributors to optimal sexual experiences. Analysis led to the identification of seven major contributors, two pathways towards optimal sexual experiences and two minor contributors. The major contributors included developmental contributors, individual qualities overall, individual qualities in-the moment, skills, relationship qualities overall, relationship qualities in-the-moment and environmental, situational and preparatory contributors. Each of these larger themes was also characterized by a variety of more specific themes. The two pathways that led to optimal sexual experiences included individual qualities that facilitated relationship qualities and relationship qualities that facilitated individual qualities. Finally, the minor contributors consisted of personal proclivities and miscellaneous contributors. Noteworthy findings of this investigation are discussed and then compared and contrasted with existing research and theory. The implications of this work for the general public, sex therapy, sex education, theory and research are considered as well as the strengths and limitations of this study.

Pseudo-spectral optimal solvers are used to optimize numerically a performance index of a dynamical system with differential constraints. Although these solvers are commonly used for space vehicles and space launchers for trajectory optimization, few experimental papers exist on optimal control of small airships. The objective of this thesis is to evaluate the use of a pseudo-spectral optimal control solver for generating dynamically constrained, minimal time trajectories. A dynamical model of a small airship is presented, with its experimental virtual mass, drag and motor experimentally modeled. The problems are solved in PSOPT, a pseudo-spectral optimal control code. Experimental tests with a small scale model are performed to evaluate the generated paths. Although drift occurs, as a consequence of an open loop control, the vehicle is capable of following the path. This results of this thesis may find uses in verifying how close to optimal discreet path planners are, to plan complex trajectories on short distances, or to generate dynamic maneuverer such as take-off or landing. Ultimately, improving path planning of small airships will improve their safety, maneuverability and flight-time, which makes them fit for scientific monitoring, for search and rescue, or as mobile telecommunications platforms.

The conceptual evolution of smart cities is highly motivated by the advancement of information and communication technologies (ICTs). The purpose of a smart city is to facilitate the best quality of life to its inhabitants. Its implementation has to be supported by the compliant utilities and networked infrastructures. In the current world, it can only be achieved by applying ICTs in an extensive manner. The move towards the smart city's seamless connectivity widens the scope of cyber security concerns. Smart city infrastructures to face a high risk of targeted attacks due to extended cyber-physical vulnerabilities. This creates many challenging research issues relevant to the design and implementation of cyber security solutions. Networks associated with city infrastructures vary from a small indoor one to a large geographically distributed one. The context of a network is an essential consideration for security solutions. This thesis investigates a set of optimal security placement problems for enhancing monitoring in smart city infrastructures. It develops solutions to such placement problems from a resource management perspective. Economy and quality-of-security service (QoSS) are two major design goals. Such goals are translated into three basic performance metrics: (i) coverage, (ii) tolerance, and (iii) latency. This thesis studies security placement problems pertaining to three different types of networks: (i) wireless sensor network (WSN), (ii) supervisory control and data acquisition (SCADA) backbone, and (iii) advanced metering infrastructure (AMI) wide area network (WAN). In a smart city, WSNs are deployed to support real time monitoring and safety alert (RTMSA) applications. They are highly resource constrained networks. For WSNs, placement problems for an internally configured security monitor named watchdog have been studied. On the other hand, a smart grid is a key driver for smart cities. SCADA and AMI are two major components of a smart grid. They are associated with two different types of geographically distributed networks. For SCADA backbones, placement problems for a specially designed security device named trust system have been studied. For AMI-WANs, placement problems for a cloud-based managed security service have been studied. This thesis proposes a number of promising solution schemes to such placement problems. It includes evaluation results that demonstrate the enhancements of the proposed schemes.

Almost every medium and large company has to deal with an optimal placing of administrative workers. This thesis focuses on solving a problem of dislocation of employees of the Ministry of Finance of the Czech Republic (MFCR) and it proposes a possible solution of the current situation. The basis for finding the optimal solutions are integer programming tasks. The structure of the MFCR and the description of the current/future state of dislocations has been defined in cooperation with the MFCR. Therefore, the solution fully meets the MFCR specifications. The thesis also outlines another optional solution for dislocations within MFCR. Finally, there are summarized other aspects of optimal dislocation of employees that can further improve the solution given in this thesis, especially in terms of efficiency, satisfaction and health of the employees.

Companies dependent on commodities for their production have to deal with volatile commodity prices and should employ measures for risk reduction as unfavourable spot price development may cause significant losses. A useful tool for diminishing the risk is hedging on futures market; however, this approach faces a crucial question of optimal hedge ratio determination (ratio between spot and futures units). Our thesis examines nine different ways of optimal hedge ratio estimation (naive, Sharpe, mean extended Gini coefficient, generalized semivariance, value at risk, and minimum variance through OLS, error correction, GARCH, and bivariate GARCH models) and evaluates their efficiency using the data on eight different commodities. The results differ across the respective commodities and cannot be generalized. Two conclusions resulting from the analysis refer to performance of naive and OLS hedge ratios and constant vs time varying hedge ratios. We find that complex hedge ratios, such as bivariate GARCH or VaR hedge ratios, do not outperform naive and OLS hedge ratios and that the results of constant hedge ratios are mostly as good as results of time-varying hedge ratios.

Local electricity markets can be defined broadly as 'future electricity market designs involving domestic customers, demand-side response and energy storage'. Like current deregulated electricity markets, these localised derivations present specific stochastic optimisation problems in which the dynamic and random nature of the market is intertwined with the physical needs of its participants. Moreover, the types of contracts and constraints in this setting are such that 'games' naturally emerge between the agents. Advanced modelling techniques beyond classical mathematical finance are therefore key to their analysis. This thesis aims to study contracts in these local electricity markets using the mathematical theories of stochastic optimal control and games. Chapter 1 motivates the research, provides an overview of the electricity market in Great Britain, and summarises the content of this thesis. It introduces three problems which are studied later in the thesis: a simple control problem involving demand-side management for domestic customers, and two examples of games within local electricity markets, one of them involving energy storage. Chapter 2 then reviews the literature most relevant to the topics discussed in this work. Chapter 3 investigates how electric space heating loads can be made responsive to time varying prices in an electricity spot market. The problem is formulated mathematically within the framework of deterministic optimal control, and is analysed using methods such as Pontryagin's Maximum Principle and Dynamic Programming. Numerical simulations are provided to illustrate how the control strategies perform on real market data. The problem of Chapter 3 is reformulated in Chapter 4 as one of optimal switching in discrete-time. A martingale approach is used to establish the existence of an optimal strategy in a very general setup, and also provides an algorithm for computing the value function and the optimal strategy. The theory is exemplified by a numerical example for the motivating problem. Chapter 5 then continues the study of finite horizon optimal switching problems, but in continuous time. It also uses martingale methods to prove the existence of an optimal strategy in a fairly general model. Chapter 6 introduces a mathematical model for a game contingent claim between an electricity supplier and generator described in the introduction. A theory for using optimal switching to solve such games is developed and subsequently evidenced by a numerical example. An optimal switching formulation of the aforementioned game contingent claim is provided for an abstract Markovian model of the electricity market. The final chapter studies a balancing services contract between an electricity transmission system operator (SO) and the owner of an electric energy storage device (battery operator or BO). The objectives of the SO and BO are combined in a non-zero sum stochastic differential game where one player (BO) uses a classic control with continuous effects, whereas the other player (SO) uses an impulse control (discontinuous effects). A verification theorem proving the existence of Nash equilibria in this game is obtained by recursion on the solutions to Hamilton-Jacobi-Bellman variational PDEs associated with non-zero sum controller-stopper games.

Trinidad and Tobago is a small open economy that faces macroeconomic policy challenges which are related to imperfections in the financial sector and volatility of energy sector revenues. Specifically, two of the key issues policymakers are grappling with are high levels of excess reserves and the optimal management of the economy's resource revenues—in the face of domestic and external shocks to the energy sector. This thesis uses a general equilibrium modeling approach to examine the dynamic effects of these policy challenges on the Trinidad and Tobago economy. In the first case, this study examines the financial and real effects of excess reserves in a New Keynesian Dynamic Stochastic General Equilibrium model with monopoly banking, credit market imperfections and a cost channel. The model explicitly accounts for the fact that banks in Trinidad and Tobago hold excess reserves and they incur costs in holding these assets. Simulations of a shock to required reserves show that although raising reserve requirements is successful in sterilizing excess reserves, it creates a procyclical effect for real economic activity. This result implies that financial stability may come at a cost of macroeconomic stability. The findings also indicate that using an augmented Taylor rule in which the policy interest rate is adjusted in response to changes in excess reserves reduces volatility in output and inflation but increases fluctuations in financial variables. To the contrary, using a countercyclical reserve requirement rule helps to mitigate fluctuations in excess reserves, but increases volatility in real variables. Moreover, this research uses an open economy Dynamic Stochastic General Equilibrium model to analyze the transmission of resource price shocks and a shock to resource production in the Trinidad and Tobago economy. It also applies alternative fiscal rules to determine the optimal allocation of resource windfalls between spending today and saving in a sovereign wealth fund. The results show that spending all the resource windfall on consumption and investment creates more volatility and amplifies Dutch disease effects, when compared to the case where all the excess revenues are saved. Also, neither a policy of full spending nor full saving of the surplus revenue inflows is optimal if the government is concerned about both household welfare and fiscal stability. In order to minimize deviations from both objectives, the optimal fiscal response suggests that a larger fraction of the resource windfalls should be saved, than what the government is presently saving.

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