Engineering Commons^™

Algebraic, Computational, And Data-Driven Methods For Control-Theoretic Analysis And Learning Of Ensemble Systems, Wei Miao

McKelvey School of Engineering Theses & Dissertations

In this thesis, we study a class of problems involving a population of dynamical systems under a common control signal, namely, ensemble systems, through both control-theoretic and data-driven perspectives. These problems are stemmed from the growing need to understand and manipulate large collections of dynamical systems in emerging scientific areas such as quantum control, neuroscience, and magnetic resonance imaging. We examine fundamental control-theoretic properties such as ensemble controllability of ensemble systems and ensemble reachability of ensemble states, and propose ensemble control design approaches to devise control signals that steer ensemble systems to desired profiles. We show that these control-theoretic properties …

Computational Modelling Enables Robust Multidimensional Nanoscopy, Matthew D. Lew

Electrical & Systems Engineering Publications and Presentations

The following sections are included:

• Present State of Computational Modelling in Fluorescence Nanoscopy

• Recent Contributions to Computational Modelling in Fluorescence Nanoscopy

• Outlook on Computational Modelling in Fluorescence Nanoscopy

• Acknowledgments

• References

A Computationally-Efficient Bound For The Variance Of Measuring The Orientation Of Single Molecules, Tingting Wu, Tianben Ding, Hesam Mazidi, Oumeng Zhang, Matthew D. Lew

Electrical & Systems Engineering Publications and Presentations

Modulating the polarization of excitation light, resolving the polarization of emitted fluorescence, and point spread function (PSF) engineering have been widely leveraged for measuring the orientation of single molecules. Typically, the performance of these techniques is optimized and quantified using the Cramér-Rao bound (CRB), which describes the best possible measurement variance of an unbiased estimator. However, CRB is a local measure and requires exhaustive sampling across the measurement space to fully characterize measurement precision. We develop a global variance upper bound (VUB) for fast quantification and comparison of orientation measurement techniques. Our VUB tightly bounds the diagonal elements of the …

Systemic Risk In Financial Networks, Tathagata Banerjee

McKelvey School of Engineering Theses & Dissertations

In this dissertation, I have used the network model based approach to study systemic risk in financial networks. In particular, I have worked on generalized extensions of the Eisenberg--Noe [2001] framework to account for realistic financial situations viz. pricing of corporate debt while accounting for network effects, asset liquidation mechanisms during fire sales, dynamic clearing and impact of contingent payments such as insurance and credit default swaps. First, I present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. I demonstrate that the comonotonic setting provides a lower bound to the price …

Sufficient Conditions For Optimal Control Problems With Terminal Constraints And Free Terminal Times With Applications To Aerospace, Sankalp Kishan Bhan

McKelvey School of Engineering Theses & Dissertations

Motivated by the flight control problem of designing control laws for a Ground Collision Avoidance System (GCAS), this thesis formulates sufficient conditions for a strong local minimum for a terminally constrained optimal control problem with a free-terminal time. The conditions develop within the framework of a construction of a field of extremals by means of the method of characteristics, a procedure for the solution of first-order linear partial differential equations, but modified to apply to the Hamilton-Jacobi-Bellman equation of optimal control. Additionally, the thesis constructs these sufficient conditions for optimality with a mathematically rigorous development. The proof uses an approach …

Robust Engineering Of Dynamic Structures In Complex Networks, Walter Botongo Bomela

McKelvey School of Engineering Theses & Dissertations

Populations of nearly identical dynamical systems are ubiquitous in natural and engineered systems, in which each unit plays a crucial role in determining the functioning of the ensemble. Robust and optimal control of such large collections of dynamical units remains a grand challenge, especially, when these units interact and form a complex network. Motivated by compelling practical problems in power systems, neural engineering and quantum control, where individual units often have to work in tandem to achieve a desired dynamic behavior, e.g., maintaining synchronization of generators in a power grid or conveying information in a neuronal network; in this dissertation, …

Numerical Methods For Nonlinear Optimal Control Problems And Their Applications In Indoor Climate Control, Runxin He

McKelvey School of Engineering Theses & Dissertations

Efficiency, comfort, and convenience are three major aspects in the design of control systems for residential Heating, Ventilation, and Air Conditioning (HVAC) units. In this dissertation, we study optimization-based algorithms for HVAC control that minimizes energy consumption while maintaining a desired temperature, or even human comfort in a room. Our algorithm uses a Computer Fluid Dynamics (CFD) model, mathematically formulated using Partial Differential Equations (PDEs), to describe the interactions between temperature, pressure, and air flow. Our model allows us to naturally formulate problems such as controlling the temperature of a small region of interest within a room, or to control …

A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, Jimmie Harold Lenz

Doctor of Business Administration Dissertations

At heart every trader loves volatility; this is where return on investment comes from, this is what drives the proverbial “positive alpha.” As a trader, understanding the probabilities related to the volatility of prices is key, however if you could also predict future prices with reliability the world would be your oyster. To this end, I have achieved three goals with this dissertation, to develop a model to predict future short term prices (direction and magnitude), to effectively test this by generating consistent profits utilizing a trading model developed for this purpose, and to write a paper that anyone with …

A General Framework Of Large-Scale Convex Optimization Using Jensen Surrogates And Acceleration Techniques, Soysal Degirmenci

McKelvey School of Engineering Theses & Dissertations

In a world where data rates are growing faster than computing power, algorithmic acceleration based on developments in mathematical optimization plays a crucial role in narrowing the gap between the two. As the scale of optimization problems in many fields is getting larger, we need faster optimization methods that not only work well in theory, but also work well in practice by exploiting underlying state-of-the-art computing technology.

In this document, we introduce a unified framework of large-scale convex optimization using Jensen surrogates, an iterative optimization method that has been used in different fields since the 1970s. After this general treatment, …

Dynamic Pricing And Inventory Management: Theory And Applications, Renyu Zhang

Arts & Sciences Electronic Theses and Dissertations

We develop the models and methods to study the impact of some emerging trends in technology, marketplace, and society upon the pricing and inventory policy of a firm. We focus on the situation where the firm is in a dynamic, uncertain, and (possibly) competitive market environment. The market trends of particular interest to us are: (a) social networks, (b) sustainability concerns, and (c) customer behaviors. The two main running questions this dissertation aims to address are: (a) How these emerging market trends would influence the operations decisions and profitability of a firm; and (b) What pricing and inventory strategies a …

Acoustic Firearm Discharge Detection And Classification In An Enclosed Environment, Lorenzo Luzi, Eric Gonzalez, Paul Bruillard, Matthew Prowant, James Skorpik, Michael Hughes, Scott Child, Duane Kist, John E. Mccarthy

Mathematics Faculty Publications

Two different signal processing algorithms are described for detection and classification of acoustic signals generated by firearm discharges in small enclosed spaces. The first is based on the logarithm of the signal energy. The second is a joint entropy. The current study indicates that a system using both signal energy and joint entropy would be able to both detect weapon discharges and classify weapon type, in small spaces, with high statistical certainty.