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.

Abstract Based upon the Nordhaus' model, we can analyze the political business cycle (PBC) of parliamentarian system. This is our point in this paper. Adding an uncertain factor in the Nordhaus' assumptions, we can get unemployment rate of optimal control path by using the dynamic optimal control theory. Comparing these two results, the model of political business cycle of parliamentarian system has higher elective frequency and lower amplitude in the unemployment rate of optimal control path. From the social welfare point of view, which one is better is hard to say? The social welfare is decided by voters' preferences when voters face these two type of PBC. Keywords: Political business cycle (PBC). Parliamentarian system. The optimal

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With the increase of world population and industrial growth of developing countries, demand for energy, in particular electric power, has gone up at an unprecedented rate over the last decades. To meet the demand, electric power generation by use of fossil fuel has increased enormously thereby producing increased quantity of greenhouse gases. This contributes more and more to atmospheric pollution, which climate scientists believe can adversly affect the global climate, as well as health and the welfare of the world population. In view of these issues, there is global awareness to look for alternate sources of energy such as natural gas, hydropower, wind, solar, geothermal and biomass. It is recognized that this requires replacement of existing infrastructure with new systems, which cannot be achieved overnight. Optimal control theory has been widely used in diverse areas of physical sciences, medicine, engineering and economics. The main motivation of this thesis is to use this theory to find the optimum strategy for integration of all currently available renewable energy sources with the existing electric power generating systems. The ultimate goal is to eliminate fossil fuels. Eight main energy sources namely, Coal, Petroleum, Natural Gas, Conventional Hydro, Wind, Solar, Geothermal and Biomass are considered in a dynamic model. The state of the dynamic model represents the level of energy generation from each of the sources. Different objective functions are proposed in this thesis. These range from meeting the desired target level of power generation from each of the available sources at the end of a given plan period, to reducing the implementation and investment costs; from minimizing the production from polluted energy sources to meeting the electricity demand during a whole plan period. Official released data from the U.S. Energy Information Administration have been used as a case study. Based on real life data and the mathematics of optimal control theory, we present an optimal policy for integration of renewable energy sources to the national power grid.

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.

Covariance assignment theory, introduced in the late 1980s, provided the only means to directly control the steady-state error properties of a linear system subject to Gaussian white noise and parameter uncertainty. This theory, however, does not extend to control of the transient uncertainties and to date there exist no practical engineering solutions to the problem of directly and optimally controlling the uncertainty in a linear system from one Gaussian distribution to another. In this thesis I design a dual-mode Receding Horizon Controller (RHC) that takes a controllable, deterministic linear system from an arbitrary initial covariance to near a desired stationary covariance in finite time. The RHC solves a sequence of free-time Optimal Control Problems (OCP) that directly controls the fundamental solution matrices of the linear system; each problem is a right-invariant OCP on the matrix Lie group GLn of invertible matrices. A terminal constraint ensures that each OCP takes the system to the desired covariance. I show that, by reducing the Hamiltonian system of each OCP from T?GLn to gln? x GLn, the transversality condition corresponding to the terminal constraint simplifies the two-point Boundary Value Problem (BVP) to a single unknown in the initial or final value of the costate in gln?. These results are applied in the design of a dual-mode RHC. The first mode repeatedly solves the OCPs until the optimal time for the system to reach the de- sired covariance is less than the RHC update time. This triggers the second mode, which applies covariance assignment theory to stabilize the system near the desired covariance. The dual-mode controller is illustrated on a planar system. The BVPs are solved using an indirect shooting method that numerically integrates the fundamental solutions on R4 using an adaptive Runge-Kutta method. I contend that extension of the results of this thesis to higher-dimensional systems using either in- direct or direct methods will require numerical integrators that account for the Lie group structure. I conclude with some remarks on the possible extension of a classic result called Lie?s method of reduction to receding horizon control.

With the increase of world population and industrial growth of developing countries, demand for energy, in particular electric power, has gone up at an unprecedented rate over the last decades. To meet the demand, electric power generation by use of fossil fuel has increased enormously thereby producing increased quantity of greenhouse gases. This contributes more and more to atmospheric pollution, which climate scientists believe can adversly affect the global climate, as well as health and the welfare of the world population. In view of these issues, there is global awareness to look for alternate sources of energy such as natural gas, hydropower, wind, solar, geothermal and biomass. It is recognized that this requires replacement of existing infrastructure with new systems, which cannot be achieved overnight. Optimal control theory has been widely used in diverse areas of physical sciences, medicine, engineering and economics. The main motivation of this thesis is to use this theory to find the optimum strategy for integration of all currently available renewable energy sources with the existing electric power generating systems. The ultimate goal is to eliminate fossil fuels. Eight main energy sources namely, Coal, Petroleum, Natural Gas, Conventional Hydro, Wind, Solar, Geothermal and Biomass are considered in a dynamic model. The state of the dynamic model represents the level of energy generation from each of the sources. Different objective functions are proposed in this thesis. These range from meeting the desired target level of power generation from each of the available sources at the end of a given plan period, to reducing the implementation and investment costs; from minimizing the production from polluted energy sources to meeting the electricity demand during a whole plan period. Official released data from the U.S. Energy Information Administration have been used as a case study. Based on real life data and the mathematics of optimal control theory, we present an optimal policy for integration of renewable energy sources to the national power grid.

<p>Alternate power sources in automotive class-8 trucking industry is a major focus of research in recent days. Green house gasses, oxides of Nitrogen(NOx), Oxides of Sulphur(SOx), hydrocarbons and particulate matter are major concerns contributing to the shift in alternate fuel strategies. Another direct relation to move to an alternate power strategy is the reduction in net fuel consumption which in turn implicitly improves the emission components.</p> <p>A holistic approach is needed while designing a modern class-8 vehicle. A variety of system architecture, control algorithms, diagnostic levers are needed to be manipulated to achieve the best of blends amongst Total Cost of Ownership (TCO), Drivability, Fuel</p> <p>Economy, Emissions Compliant, Hauling Capacity, etc. The control and system levers are not mutually exclusive and there is a strong correlation amongst all these control and system components. In order to achieve a consensus amongst all these levers to achieve a common objective, is a challenging and complex problem to solve. It is often required to shift the algorithm strategy to predictive information based rather than reactive logic. Predictively modulating and manipulating control logic can help with better fuel efficient solution along with emissions improvement. A further addition to the above challenge is when we add a fleet of vehicle to the problem. So, the problem now is to optimize a control action for a fleet</p> <p>of vehicles and design/select the correct component size. A lot of research has been done and is still underway to use a 48V hybrid system with a small battery using a simple charge sustaining SOC control strategy. This will make the system light enough not to compromise on the freight carrying capacity as well as give some extra boost during the high torque requirement sections in the route for a better fuel and emissions efficient solution. In this work a P2 type 48V hybrid system is used which is side mounted to the transmission via a gear system. The selection of the system and components enables the usage of different control strategies such as neutral coasting and Engine off coasting. This architecture with a traditional 12-15L Internal combustion engine along with a mild 48V hybrid system provides the most viable selection for a long haul class-8 application and is used in this work. It is also possible to identify other component sizes along with architectures for new configurations. The framework in this research work can help develop the study for different component sizing. While this research work is focused towards building a framework for achieving predictive control in a 3 truck platooning system using multi-agent based control, the other supporting work done also helps understand the optimal behavior of the interacting multiple controls when the corridor information such as road grade and route speed limit are known a-priori, in a single vehicle. The build up of this work analyzes an offline simulation of a 4 control optimal solution for a single hybrid truck and then extend the optimal controls to a 3 truck platoon. In the single truck, this research will help identify the interacting zones in the route where the various control actions will provide the best cost benefits which is fuel economy. These benefits are associated as a function of exogenous look ahead information such as grade and speed limit. Further it is also possible to identify the optimal behavior and the look ahead horizon required for achieving that. In other words the optimal behavior and benefits associated with the global solution can be accomplished by implementing rule based control system with a look ahead horizon of 2-5 km. If this would not have been the case then it is almost impossible to design a predictive controller based on the entire route information which can stretch up to hundreds of kilometers. Optimal algorithms of such prediction horizon are not feasible to be implemented in real time controllers. This research work will also help understand the interaction between different active control actions such as predictive speed modulation, gear shift, coasting and power split with passive control levers such as slow down due to hybrid regeneration, hybrid boost during coasting, etc. This will help in architecting a system involving component specifications, active optimal control, look ahead information, hybrid system strength, etc, working in close interaction with each other. Though we analyze these predictive behavior for a single vehicle as a supporting work the prime objective is to include these predictive levers in a platooning system using an agent based method. This multi-agent based technique will help analyze the behavior of multiple trucks in a platoon in terms of fuel efficient safe operation. The focus of this research work is to not directly come up with a controller or strategy but rather to understand the optimality of this control levers for a multi-vehicle platoon system given a look ahead information is available. The research shows that predictive information will help in gaining fuel economy for a platoon of class-8 mild hybrid trucks. It also highlights the challenges in doing so and what needs to be traded off in order to achieve the net fuel benefit.</p>

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Water heating in a typical home in the U.S. accounts for a significant portion (between 14% and 25%) of the total home's annual energy consumption. The objective of considerably reducing the home's energy consumption from the utilities calls for the use of onsite renewable energy systems. Integral Collector Storage (ICS) solar domestic water heating systems are an alternative to help meet the hot water energy demands in a household. In order to evaluate the potential benefits and contributions from the ICS system, it is important that the parameter values included in the model used to estimate the system's performance are as accurate as possible. The overall heat loss coefficient (Uloss) in the model plays an important role in the performance prediction methodology of the ICS. This work presents a new and improved methodology to determine Uloss as a function of time in an ICS system using a systematic optimal control theoretic approach. This methodology is based on the derivation of a new nonlinear state space model of the system, and the formulation of a quadratic performance function whose minimization yields estimates of Uloss values that can be used in computer simulations to improve the performance prediction of the ICS system, depending on the desired time of the year and hot water draw profile. Simulation results show that predictions of the system's performance based on these estimates of Uloss are considerably more accurate than the predictions based on current existing methods for estimating Uloss.