The presented thesis project is a study on train energy consumption calculation and optimal train driving strategies for minimum energy consumption. This study is divided into three parts; the first part is a proposed model for energy consumption calculation for trains based on driving resistances. The second part is a presentation of a method based on dynamic programming and the Hamilton-Jacobi-Bellman equation (Bellman’s backward approach) for obtaining optimal speed and control profiles leading to minimum energy consumption. The third part is a case study for a Bombardier Transportation case. It includes the presentation of a preliminary algorithm developed within this thesis project; an algorithm based on the HJB equation that can be further improved in order to be used online in real-time as an advisory system for train drivers.

This study develops a discrete search-based optimization method for path planning in a highly nonlinear dynamical system. The method enables real-time trajectory improvement and singular configuration avoidance in satellite rotation using Control Moment Gyroscopes. By streamlining a legacy optimization method and combining it with a local singularity management scheme, this optimization method reduces the computational burden and advances the capability of satellites to make autonomous look-ahead decisions in real-time. Current optimization methods plan offline before uploading to the satellite and experience high sensitivity to disturbances. Local methods confer autonomy to the satellite but use only blind decision-making to avoid singularities. This thesis' method seeks near-optimal trajectories which balance between the optimal trajectories found using computationally intensive offline solvers and the minimal computational burden of non-optimal local solvers. The new method enables autonomous guidance capability for satellites using discretization and stage division to minimize the computational burden of real-time optimization.

Optimal control methods are applied to mechanical models in order to predict the control strategies in human arm movements. Optimality criteria are used to determine unique controls for a biomechanical model of the human upper-limb with redundant actuators. The motivation for this thesis is to provide a non-task-specific method of motion prediction as a tool for movement researchers and for controlling human models within virtual prototyping environments. The current strategy is based on determining the muscle activation levels (control signals) necessary to perform a task that optimizes several physical determinants of the model such as muscular and joint stresses, as well as performance timing. Currently, the initial and final location, orientation, and velocity of the hand define the desired task. Several models of the human arm were generated using a graph-theoretical method in order to take advantage of similar system topology through the evolution of arm models. Within this framework, muscles were modelled as non-linear actuator components acting between origin and insertion points on rigid body segments. Activation levels of the muscle actuators are considered the control inputs to the arm model. Optimization of the activation levels is performed via a hybrid genetic algorithm (GA) and a sequential quadratic programming (SQP) technique, which provides a globally optimal solution without sacrificing numerical precision, unlike traditional genetic algorithms. Advantages of the underlying genetic algorithm approach are that it does not require any prior knowledge of what might be a 'good' approximation in order for the method to converge, and it enables several objectives to be included in the evaluation of the fitness function. Results indicate that this approach can predict optimal strategies when compared to benchmark minimum-time maneuvers of a robot manipulator. The formulation and integration of the aforementioned components into a working model and the simulation of reaching and lifting tasks represents the bulk of the thesis. Results are compared to motion data collected in the laboratory from a test subject performing the same tasks. Discrepancies in the results are primarily due to model fidelity. However, more complex models are not evaluated due to the additional computational time required. The theoretical approach provides an excellent foundation, but further work is required to increase the computational efficiency of the numerical implementation before proceeding to more complex models.

Optimal control methods are applied to mechanical models in order to predict the control strategies in human arm movements. Optimality criteria are used to determine unique controls for a biomechanical model of the human upper-limb with redundant actuators. The motivation for this thesis is to provide a non-task-specific method of motion prediction as a tool for movement researchers and for controlling human models within virtual prototyping environments. The current strategy is based on determining the muscle activation levels (control signals) necessary to perform a task that optimizes several physical determinants of the model such as muscular and joint stresses, as well as performance timing. Currently, the initial and final location, orientation, and velocity of the hand define the desired task. Several models of the human arm were generated using a graph-theoretical method in order to take advantage of similar system topology through the evolution of arm models. Within this framework, muscles were modelled as non-linear actuator components acting between origin and insertion points on rigid body segments. Activation levels of the muscle actuators are considered the control inputs to the arm model. Optimization of the activation levels is performed via a hybrid genetic algorithm (GA) and a sequential quadratic programming (SQP) technique, which provides a globally optimal solution without sacrificing numerical precision, unlike traditional genetic algorithms. Advantages of the underlying genetic algorithm approach are that it does not require any prior knowledge of what might be a 'good' approximation in order for the method to converge, and it enables several objectives to be included in the evaluation of the fitness function. Results indicate that this approach can predict optimal strategies when compared to benchmark minimum-time maneuvers of a robot manipulator. The formulation and integration of the aforementioned components into a working model and the simulation of reaching and lifting tasks represents the bulk of the thesis. Results are compared to motion data collected in the laboratory from a test subject performing the same tasks. Discrepancies in the results are primarily due to model fidelity. However, more complex models are not evaluated due to the additional computational time required. The theoretical approach provides an excellent foundation, but further work is required to increase the computational efficiency of the numerical implementation before proceeding to more complex models.

As technological advances allow us to peer into and beyond microscopic phenomena, new theoretical developments are necessary to facilitate this exploration. In particular, the potential afforded by utilizing quantum resources promises to dramatically affect scientific research, communications, computation, and material science. Control theory is the field dedicated to the manipulation of systems, and quantum control theory pertains to the manoeuvring of quantum systems. Due to the inherent sensitivity of quantum ensembles to their environment, time-optimal solutions should be found in order to minimize exposure to external sources. Furthermore, the complexity of the Schr\"odinger equation in describing the evolution of a unitary operator makes the analytical discovery of time-optimal solutions rare, motivating the development of numerical algorithms. The seminal result of classical control is the Pontryagin Maximum Principle, which implies that a restriction to bounded control amplitudes admits two classifications of trajectories: bang-bang and singular. Extensions of this result to generalized control problems yield the same classification and hence arise in the study of quantum dynamics. While singular trajectories are often avoided in both classical and quantum literature, a full optimal synthesis requires that we analyze the possibility of their existence. With this in mind, this treatise will examine the issue of time-optimal quantum control. In particular, we examine the results of existing numerical algorithms, including Gradient Ascent Pulse Engineering and the Kaya-Huneault method. We elaborate on the ideas of the Kaya-Huneault algorithm and present an alternative algorithm that we title the Real-Embedding algorithm. These methods are then compared when used to simulate unitary evolution. This is followed by a brief examination on the conditions for the existence of singular controls, as well possible ideas and developments in creating geometry based numerical algorithms.

This thesis contains three essays on topics in agricultural economics. Essays one and two share a focus on international trade and economic development, and essays two and three apply dynamic tools to agricultural economic policy issues.<p>Essay one analyses trade-related implications of a developing country's decision to adopt genetically-modified crop technology. A fixed-proportions model is constructed that evaluates the welfare implications of a range of adoption policies and export market responses. The model in this essay illustrates the importance of the prospective adopter formulating a projection of probable export market effects before making an adoption decision and of the role that high transaction costs may play in a developing country's adoption decision. The model also considers the effects of a new policy tool; a check-off style levy on genetically-modified technology in place of a technology-use agreement. A levy could be useful tool in developing countries, which are characterised by high transaction costs. <p>Essay two models the effects of emergency food aid on a recipient country's agricultural industry. This essay formulates a definition of needed aid in the context of a food emergency and constructs an optimal control model that solves a path of aid shipments that best meets that need. The effects of a range of food aid paths on recipient-country agricultural production are illustrated through numerical simulations. There are two key results. First, a non-optimal amount of aid can hinder a recipient-country's recovery from an exogenous food shock. Second, an exogenous shock can affect farmer revenue and therefore impact planting decisions. This effect must be considered in aid allocation policies. <p>Essay three uses time-series econometric techniques to develop a demand model that assesses the effectiveness of commodity advertising. This essay describes the importance of considering long-run and dynamic effects in demand systems, especially in the case of closely substitutable commodities. A demand system that tests for and accommodates dynamic and time-series properties is developed and applied to US meat data. The results of this model are compared to a traditional static demand system. The dynamic model produces econometrically and theoretically sound results and generates some more intuitively appealing estimates.

The H_infinity control problem is studied for linear constant coefficient descriptor systems. Necessary and sufficient optimality conditions as well as controller formulas are derived in terms of deflating subspaces of even matrix pencils for problems of arbitrary index. A structure preserving method for computing these subspaces is introduced. In combination these results allow the derivation of a numerical algorithm with advantages over the classical methods.

Sensor network coverage refers to the quality of service provided by a sensor network surveilling a region of interest. So far, coverage problems have been formulated to address area coverage or to maintain line-of-sight visibility in the presence of obstacles (i.e., art-gallery problems). Although very useful in many sensor applications, none of the existing formulations address coverage as it pertains to target tracking by means of multiple sensors, nor do they provide a closed-form function that can be applied to the problem of allocating sensors for the surveilling objective of maximizing target detection while minimizing false alarms. This dissertation presents a new coverage formulation addressing the quality of service of sensor networks that cooperatively detect targets traversing a region of interest, and is readily applicable to the current sensor network coverage formulations. The problem of track coverage consists of finding the positions of <em>n</em> sensors such that the amount of tracks detected by at least <em>k</em> sensors is optimized. This dissertation studies the geometric properties of the network, addressing a deterministic track-coverage formulation and binary sensor models. It is shown that the tracks detected by a network of heterogeneous omnidirectional sensors are the geometric transversals of non-translates families of disks. A novel methodology based on cones and convex analysis is presented for representing and measuring sets of transversals as closed-form functions of the sensors positions and ranges. As a result, the problem of optimally deploying a sensor network with the aforementioned objectives can be formulated as an optimization problem subject to mission dynamics and constraints. The sensor placement problem, in which the sensors are placed such that track coverage is maximized for a fixed sensor network, is formulated as a nonlinear program and solved using sequential quadratic programming. The sensor deployment, involving a dynamic sensor network installed on non-maneuverable sonobuoys deployed in the ocean, is formulated as an optimization problem subject to inverse dynamics. Both a finite measure of the cumulative coverage provided by a sensor network over a fixed period of time and the oceanic-induced current velocity field are accounted for in order to optimize the dynamic sensor network configuration. It is shown that a state-space representation of the motions of the individual sensors subject to the current vector field can be derived from sonobuoys oceanic drift models and obtained from CODAR measurements. Also considered in the sensor model are the position-dependent acoustic ranges of the sensors due to the effects from heterogenous environmental conditions, such as ocean bathymetry, surface temporal variability, and bottom properties. A solution is presented for the initial deployment scheme of the non-maneuverable sonobuoys subject to the ocean's current, such that sufficient track coverage is maintained over the entire mission. As sensor networks are subject to random disturbances due to unforseen heterogenous environmental conditions propagated throughout the sensors trajectories, the optimal initial positions solution is evaluated for robustness through Monte Carlo simulations. Finally, the problem of controlling a network of maneuverable underwater vehicles, each equipped with an onboard acoustic sensor is formulated using optimal control theory. Consequently, a new optimal control problem is presented that integrates sensor objectives, such as track coverage, with cooperative path planning of a mobile sensor network subject to time-varying environmental dynamics. / Dissertation

<p>In recent years, government aid agencies and international organizations have increased their financial commitments to controlling and eliminating malaria from the planet. This renewed emphasis on elimination is reminiscent of a previous worldwide campaign to eradicate malaria in the 1960s, a campaign which ultimately failed. To avoid a repeat of the past, mechanisms must be developed to sustain effective malaria control programs.</p><p>A number of sociobehavioral, economic, and biophysical challenges exist for sustainable malaria control, particularly in high-burden areas such as sub-Saharan Africa. Sociobehavioral challenges include maintaining high long-term levels of support for and participation in malaria control programs, at all levels of society. Reasons for the failure of the previous eradication campaign included a decline in donor, governmental, community, and household-level support for control programs, as malaria prevalence ebbed due in part to early successes of these programs.</p><p>Biophysical challenges for the sustainability of national malaria control programs (NMCPs) encompass evolutionary challenges in controlling the protozoan parasite and the mosquito vector, as well as volatile transmission dynamics which can lead to epidemics. Evolutionary challenges are particularly daunting due to the rapid generational turnover of both the parasites and the vectors: The reliance on a handful of insecticides and antimalarial drugs in NMCPs has placed significant selection pressures on vectors and parasites respectively, leading to a high prevalence of genetic mutations conferring resistance to these biocides.</p><p>The renewed global financing of malaria control makes research into how to effectively surmount these challenges arguably more salient now than ever. Economics has proven useful for addressing the sociobehavioral and biophysical challenges for malaria control. A necessary next step is the careful, detailed, and timely integration of economics with the natural sciences to maximize and sustain the impact of this financing.</p><p>In this dissertation, I focus on 4 of the challenges identified above: In the first chapter, I use optimal control and dynamic programming techniques to focus on the problem of insecticide resistance in malaria control, and to understand how different models of mosquito evolution can affect our policy prescriptions for dealing with the problem of insecticide resistance. I identify specific details of the biological model--the mechanisms for so-called "fitness costs" in insecticide-resistant mosquitoes--that affect the qualitative properties of the optimal control path. These qualitative differences carry over to large impacts on the economic costs of a given control plan.</p><p>In the 2nd chapter, I consider the interaction of parasite resistance to drugs and mosquito resistance to insecticides, and analyze cost-effective malaria control portfolios that balance these 2 dynamics. I construct a mathematical model of malaria transmission and evolutionary dynamics, and calibrate the model to baseline data from a rural Tanzanian district. Four interventions are jointly considered in the model: Insecticide-spraying, insecticide-treated net distribution, and the distribution of 2 antimalarial drugs--sulfadoxine pyramethamine (SP) and artemisinin-based combination therapies (ACTs). Strategies which coordinate vector controls and treatment protocols should provide significant gains, in part due to the issues of insecticide and drug resistance. In particular, conventional vector control and ACT use should be highly complementary, economically and in terms of disease reductions. The ongoing debate concerning the cost-effectiveness of ACTs should thus consider prevailing (and future) levels of conventional vector control methods, such as ITN and IRS: If the cost-effectiveness of widespread ACT distribution is called into question in a given locale, scaling up IRS and/or ITNs probably tilts the scale in favor of distributing ACTs. </p><p>In the 3rd chapter, I analyze results from a survey of northern Ugandan households I oversaw in November 2009. The aim of this survey was to assess respondents' perceptions about malaria risks, and mass indoor residual spraying (IRS) of insecticides that had been done there by government-sponsored health workers. Using stated preference methods--specifically, a discrete choice experiment (DCE)--I evaluate: (a) the elasticity of household participation levels in IRS programs with respect to malaria risk, and (b) households' perceived value of programs aimed at reducing malaria risk, such as IRS. Econometric results imply that the average respondent in the survey would be willing to forego a $10 increase in her assets for a permanent 1% reduction in malaria risk. Participation in previous IRS significantly increased the stated willingness to participate in future IRS programs. However, I also find that at least 20% of households in the region perceive significant transactions costs from IRS. One implication of this finding is that compensation for these transactions costs may be necessary to correct theorized public good aspects of malaria prevention via vector control.</p><p>In the 4th chapter, I further study these public goods aspects. To do so, I estimate a welfare-maximizing system of cash incentives. Using the econometric models estimated in the 3rd chapter, in conjunction with a modified version of the malaria transmission models developed and utilized in the first 2 chapters, I calculate village-specific incentives aimed at correcting under-provision of a public good--namely, malaria prevention. This under-provision arises from incentives for individual malaria prevention behavior--in this case the decision whether or not to participate in a given IRS round. The magnitude of this inefficiency is determined by the epidemiological model, which dictates the extent to which households' prevention decisions have spillover effects on neighbors. </p><p>I therefore compute the efficient incentives in a number of epidemiological contexts. I find that non-negligible monetary incentives for participating in IRS programs are warranted in situations where policymakers are confident that IRS can effectively reduce the incidence of malaria cases, and not just exposure rates. In these cases, I conclude that the use of economic incentives could reduce the incidence of malaria episodes by 5%--10%. Depending on the costs of implementing a system of incentives for IRS participation, such a system could provide an additional tool in the arsenal of malaria controls.</p> / Dissertation

The goal of the proposed research is to provide efficient methods for defining, selecting and encoding multi-modal control programs. To this end, modes are recovered from system observations, i.e. quantized input-output strings are converted into consistent mode sequences within the Motion Description Language (MDL) framework. The design of such modes can help identify and predict the behaviors of complex systems (e.g. biological systems such as insects) and inspire the design and control of robust semi-autonomous systems (e.g. navigating robots). In this work, the efficiency of a method will be defined by the complexity and expressiveness of specific control programs. The insistence on low-complexity programs is originally motivated by communication constraints on the computer control of semi-autonomous systems, but also by our belief that, as complex as they may look, natural systems indeed use short motion schemes with few basic behaviors. The attention is first focused on the design of such short-length, few-distinct-modes mode sequences within the MDL framework. Optimal control problems are then addressed. In particular, given a mode sequence, the question of deciding when the system should switch from one mode to another in order to achieve some reachability requirements is studied. Finally, we propose to investigate how sampling strategies affect complexity and reachability, and how an acceptable trade-off between these conflicting entities can be reached.