We consider the analysis of the scattering problem. Assume that an incoming time harmonic wave is scattered by a surface of an impenetrable obstacle. The reflected wave is determined by the surface impedance of the obstacle. In this paper we will investigate the problem of choosing the surface impedance so that a desired scattering amplitude is achieved. We formulate this control problem within the framework of the minimization of a Tikhonov functional. In particular, questions of the existence of an optimal solution and the derivation of the optimality conditions will be addressed. / Master of Science

Underwater gliders are robust and long endurance ocean sampling platforms that are increasingly being deployed in coastal regions. This new environment is characterized by shallow waters and significant currents that can challenge the mobility of these efficient (but traditionally slow moving) vehicles. This dissertation aims to improve the performance of shallow water underwater gliders through path planning. The path planning problem is formulated for a dynamic particle (or "kinematic car") model. The objective is to identify the path which satisfies specified boundary conditions and minimizes a particular cost. Several cost functions are considered. The problem is addressed using optimal control theory. The length scales of interest for path planning are within a few turn radii. First, an approach is developed for planning minimum-time paths, for a fixed speed glider, that are sub-optimal but are guaranteed to be feasible in the presence of unknown time-varying currents. Next the minimum-time problem for a glider with speed controls, that may vary between the stall speed and the maximum speed, is solved. Last, optimal paths that minimize change in depth (equivalently, maximize range) are investigated. Recognizing that path planning alone cannot overcome all of the challenges associated with significant currents and shallow waters, the design of a novel underwater glider with improved capabilities is explored. A glider with a pneumatic buoyancy engine (allowing large, rapid buoyancy changes) and a cylindrical moving mass mechanism (generating large pitch and roll moments) is designed, manufactured, and tested to demonstrate potential improvements in speed and maneuverability. / Ph. D.

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

This dissertation investigates advanced concepts in terminal missile guidance. The terminal phase of missile guidance usually lasts less than ten seconds and calls for very accurate maneuvering to ensure intercept. Technological advancements have produced increasingly sophisticated threats that greatly reduce the effectiveness of traditional approaches to missile guidance. Because of this, terminal missile guidance is, and will remain, an important and active area of research. The complexity of the problem and the desire for an optimal solution has resulted in researchers focusing on simplistic, usually linear, models. The fruit of these endeavors has resulted in some of the world's most advanced weapons systems. Even so, the resulting guidance schemes cannot possibly counter the evolving threats that will push the system outside the linear envelope for which they were designed. The research done in this dissertation greatly extends previous research in the area of optimal missile guidance. Herein it is shown that optimal missile guidance is fundamentally a pairing of an optimal guidance strategy and an optimal control strategy. The optimal guidance strategy is determined from a missile's information constraints, which are themselves largely determined from the missile's sensors. The optimal control strategy is determined by the missile's control constraints, and works to achieve a specified guidance strategy. This dichotomy of missile guidance is demonstrated by showing that missiles having different control constraints utilize the same guidance strategy so long as the information constraints are the same. This concept has hitherto been unrecognized because of the difficulty in developing an optimal control for the nonlinear set of equations that result from control constraints. Having overcome this difficulty by indirect means, evidence of the guidance strategy paradigm emerged. The guidance strategy paradigm is used to develop two advanced guidance laws. The new guidance laws are compared qualitatively and quantitatively with existing guidance laws.

The content of this dissertation consists of three parts. In the first part, optimal control strategies are developed for Unified Power Flow Controller (UPFC) following the clearance of fault conditions. UPFC is one of the most versatile Flexible AC Transmission devices (FACTs) that have been implemented thus far. The optimal control scheme is composed of two parts. The first is an optimal stabilization control, which is an open-loop ‘Bang’ type of control. The second is an suboptimal damping control, which consists of segments of ‘Bang’ type control with switching functions the same as those of a corresponding approximate linear system. Simulation results show that the proposed control strategy is very effective in maintaining stability and damping out transient oscillations following the clearance of the fault. In the second part, a new power market structure is proposed. The new structure is based on a two-level optimization formulation of the market. It is shown that the proposed market structure can easily find the optimal solutions for the market while takeing factors such as demand elasticity into account. In the last part, a mathematical programming problem is formulated to obtain the maximum value of the loadibility factor, while the power system is constrained by steady-state dynamic security constraints. An iterative solution procedure is proposed for the problem, and the solution gives a slightly conservative estimate of the loadibility limit for the generation and transmission system.

Approved for public release; distribution in unlimited. / Spray cooling is a promising means of dissipating large steady state heat fluxes in high density power and electronic systems, such as thermophotovoltaic systems. The present study reports on the effectiveness of spray cooling in removing heat fluxes as high as 220 W/cm2. An experiment was designed to determine how the parameters of spray volumetric flow rate and droplet size influence the heat removal capacity of such a system. A series of commercially available nozzles were used to generate full cone water spray patterns encompassing a range of volumetric flow rates (3.79 to 42.32 L/h) and droplet Sauter mean diameters (17.4 to 35.5 micrometers). The non-flooded regime of spray cooling was studied, in which liquid spreading on the heater surface following droplet impact is the key phenomenon that determines the heat transfer rate. The experimental data established a direct proportionality of the heat flux with spray flow rate, and an inverse dependence on the droplet diameter. A correlation of the data was developed to predict heat flux as a function of the studied parameters over the range of values tested in this. / Lieutenant, United States Navy

Mathematical theory of homogenization of partial differential equations is relatively a new area of research (30-40 years or so) though the physical and engineering applications were well known. It has tremendous applications in various branches of engineering and science like : material science ,porous media, study of vibrations of thin structures, composite materials to name a few. There are at present various methods to study homogenization problems (basically asymptotic analysis) and there is a vast amount of literature in various directions. Homogenization arise in problems with oscillatory coefficients, domain with large number of perforations, domain with rough boundary and so on. The latter one has applications in fluid flow which is categorized as oscillating boundaries. In fact ,in this thesis, we consider domains with oscillating boundaries. We plan to study to homogenization of certain optimal control problems with oscillating boundaries. This thesis contains 6 chapters including an introductory Chapter 1 and future proposal Chapter 6. Our main contribution contained in chapters 2-5. The oscillatory domain under consideration is a 3-dimensional cuboid (for simplicity) with a large number of pillars of length O(1) attached on one side, but with a small cross sectional area of order ε2 .As ε0, this gives a geometrical domain with oscillating boundary. We also consider 2-dimensional oscillatory domain which is a cross section of the above 3-dimensional domain. In chapters 2 and 3, we consider the optimal control problem described by the Δ operator with two types of cost functionals, namely L2-cost functional and Dirichlet cost functional. We consider both distributed and boundary controls. The limit analysis was carried by considering the associated optimality system in which the adjoint states are introduced. But the main contribution in all the different cases(L2 and Dirichlet cost functionals, distributed and boundary controls) is the derivation of error estimates what is known as correctors in homogenization literature. Though there is a basic test function, one need to introduce different test functions to obtain correctors. Introducing correctors in homogenization is an important aspect of study which is indeed useful in the analysis, but important in numerical study as well. The setup is the same in Chapter 4 as well. But here we consider Stokes’ Problem and study asymptotic analysis as well as corrector results. We obtain corrector results for velocity and pressure terms and also for its adjoint velocity and adjoint pressure. In Chapter 5, we consider a time dependent Kirchhoff-Love equation with the same domain with oscillating boundaries with a distributed control. The state equation is a fourth order hyperbolic type equation with associated L2-cost functional. We do not have corrector results in this chapter, but the limit cost functional is different and new. In the earlier chapters the limit cost functional were of the same type.

This thesis studies the optimal control of vehicular systems, focusing on the solution of minimum-lap-time problems for a Formula 1 car. The basic optimal control theory is summarised as an infinite-dimensional extension of optimisation theory. The relevant numerical techniques for optimisation and integral approximation are compared in view of the application to vehicle systems. The classical brachistochrone problem is revisited from an optimal control perspective, with two vehicle-relevant generalisations. Closed-form solutions are derived for both the optimal trajectory and transit time. Problems involving a steerable disc rolling on the interior surface of a hemisphere are studied. For three-dimensional problems of this type, which involve rolling bodies and nonholonomic constraints, numerical solutions are used. The identification of 3D race track models from measured GPS data is treated as a problem in the differential geometry of curves and surfaces. Curvilinear coordinates are adopted to facilitate optimal control solutions. The track is specified in terms of three displacement-dependent curvatures and two edge variables. The differential model is smoothed using numerical optimal control techniques. The Barcelona track is considered as an illustrative example. The minimum-lap-time problem for a Formula 1 car on a flat track is solved using direct transcription. The driven line and multiple car setup parameters are optimised simultaneously. It is shown that significant lap-time reductions can be obtained from track-specific setup parameter optimisation. Reduced computing times are achieved using a combination of analytical derivatives, model non-dimensionalisation and problem scaling. The optimal control of the car on a 3D track is studied; the results are compared with flat-track solutions. Contemporary kinetic energy-recovery systems are studied and compared with future hybrid kinetic-thermal energy-recovery systems. It is demonstrated that these systems can produce contemporary lap time using approximately two-thirds of the fuel required by present-day vehicles.

Heavy duty powertrains are complex systems with components from various domains, different response times during transient operations and different efficient operating ranges. To ensure efficient transient operation of a powertrain, e.g. with low fuel consumption or short transient duration, it is important to come up with proper control strategies. In this dissertation, optimal control theory is used to calculate and analyze efficient heavy duty powertrain controls during transient operations in different applications. This is enabled by first developing control ready models, usable for multi-phase optimal control problem formulations, and then using numerical optimal control methods to calculate the optimal transients. Optimal control analysis of a wheel loader operating in a repetitive loading cycle is the first studied application. Increasing fuel efficiency or reducing the operation time in such repetitive loading cycles sums up to large savings over longer periods of time. Load lifting and vehicle traction consume almost all of the power produced by a diesel engine during wheel loader operation. Physical models are developed for these subsystems where the dynamics are described by differential equations. The model parameters are tuned and fuel consumption estimation is validated against measured values from real wheel loader operation. The sensitivity of wheel loader trajectory with respect to constrains such as the angle at which the wheel loader reaches the unloading position is also analyzed. A time and fuel optimal trajectory map is calculated for various unloading positions. Moreover, the importance of simultaneous optimization of wheel loader trajectory and the component transients is shown via a side to side comparison between measured fuel consumption and trajectories versus optimal control results. In another application, optimal control is used to calculate efficient gear shift controls for a heavy duty Automatic Transmission system. A modeling and optimal control framework is developed for a nine speed automatic transmission. Solving optimal control problems using the developed model, time and jerk efficient transient for simultaneous disengagement of off-going and engagement of in-coming shift actuators are obtained and the results are analyzed. Optimal controls of a diesel-electric powertrain during a gear shift in an Automated Manual Transmission system are calculated and analyzed in another application of optimal control. The powertrain model is extended by including driveline backlash angle as an extra state in the system. This is enabled by implementation of smoothing techniques in order to describe backlash dynamics as a single continuous function during all gear shift phases. Optimal controls are also calculated for a diesel-electric powertrain corresponding to a hybrid bus during a tip-in maneuver. It is shown that for optimal control analysis of complex powertrain systems, minimizing only one property such as time pushes the system transients into extreme operating conditions far from what is achievable in real applications. Multi-objective optimal control problem formulations are suggested in order to obtain a compromise between various objectives when analyzing such complex powertrain systems.

Self-assembly is a process of non-intrusive transformation of a system from a disordered to an ordered state. For engineering purposes, self-assembly of microscopic objects can benefit significantly from macroscopic guidance and control. This dissertation is concerned with controlling self-assembly in binary monolayers of electrically charged particles that follow basic laws of statistical mechanics. First, a simple macroscopic model is used to determine an optimal thermal control for self-assembly. The model assumes that a single rate-controlling mechanism is responsible for the formation of spatially ordered structures and that its rate follows an Arrhenius form. The model parameters are obtained using molecular dynamics simulations. The optimal control is derived in an analytical form using classical optimization methods. Two major lessons were learned from that work: (i) isothermal control was almost as effective as optimal time-dependent thermal control, and (ii) neither electrostatic interactions nor thermal control were particularly effective in eliminating voids formed during self-assembly. Accordingly, at the next stage, the focus is on temperature-pressure control under isothermal-isobaric conditions. In identifying optimal temperature and pressure conditions, several assumptions, that allow one to relate the optimal conditions to the phase diagram, are proposed. Instead of verifying the individual assumptions, the entire approach is verified using molecular dynamics simulations. It is estimated that under optimal isothermal-isobaric conditions the rate of self-assembly is about five time faster than that under optimal temperature control conditions. It is argued that the proposed approach of relating optimal conditions to the phase diagram is applicable to other systems. Further, the work reveals numerous and useful parallels between self-assembly and crystal physics, which are important to exploit for developing robust engineering self-assembly processes. / text