Trident Scholar Abstracts 2016

Alvin A. Abes
Midshipman First Class
United States Navy

Modeling and Control of the Cobelli Model as a Personalized Prescriptive Tool for Diabetes Treatment

The human body maintains homeostasis with the assistance of hormones secreted by the endocrine system in order to sustain normal bodily functions. Glucose provides energy for these functions; however unhealthy levels lead to various health complications.  In patients with diabetes, the body ineffectively utilizes insulin to assist the uptake and transport of glucose from the blood into the cells. In type I diabetes, the pancreas does not secrete enough insulin to assist the uptake of glucose. Type II diabetes occurs when cells in the body become desensitized to insulin. In both cases, glucose is transferred from the blood to the cells at a lower rate which increases the overall amount of glucose.

Mathematical models of glucose and insulin dynamics within the body allow for a more quantified approach in medicine prescription as well as a deeper understanding of the discrete operations of diabetes. Cobelli et. al. developed a mathematical model of glucose and insulin interactions that illustrate the dynamics from ingestion to absorption within the body. The FDA has approved this model to be a substitute for animal trials in preclinical testing due to its physiological accuracy. A physiological accurate model allows for the use of control theory to investigate applications as a personalized prescription tool.

This research developed a clinically-relevant, personalized algorithm for a diabetic patient that prescribes doses of oral medications, secretagogues and/or sensitizing agents, and inject insulin, slow or fast acting, based on their measured blood glucose levels.  The research expanded upon Cobelli’s mathematical model to include the four different medications and their effects on the body at a physiological level. A cost function was also developed to be utilized with MPC to adequately choose medications for future dosing based on physiological accuracy and convenience. A proof of concept demonstrated the possibility of the use of Model Predictive Control for three medication inputs to control glucose levels. This work provided a framework for data verification once clinical data is obtained.

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In this project we demonstrate two different approaches to speed up the training of neural nets. First, even before training, we demonstrate an informed way of initializing parameters closer to their final, trained values. Second, we introduce a new training algorithm that scales linearly when parallelized, allowing for substantially decreased training times on large datasets. Neural nets are famously unintuitive, and as such, parameters are typically randomly assigned, then adjusted during training. However, by using a cosine activation function, a layer of neurons can be made to approximate the implicit feature space of a kernel. Therefore, intuition on kernel selection can guide initial parameter assignments even before any data observations. We implement this approach and show that it can greatly speed up training, often approaching the final accuracy after only one training iteration.

Our second contribution was in the application of the ADMM algorithm to neural nets. Conventional gradient based optimization methods for neural nets scale poorly which is difficult to avoid with extremely large datasets. The proposed method avoids many of the conditions that typically make gradient based methods slow, allowing for efficient computation without specialized hardware. Our implementation demonstrates strong scalability with linear speedups even up to thousands of cores. We show that for large problems, our approach can converge faster than GPU-based implementations of standard algorithms.

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The emerging field of microrobotics facilitates precise manipulation of objects at the microscale, which has many applications in medicine and microassembly. This project advanced both sensing and motion capabilities of the Naval Academy’s microrobot system, bringing it from a planar system to a three-dimensional system that utilizes an adaptive controller for autonomous operation. Reproducible, robust robot control is particularly challenging at the microscale, where lesser understood surface forces like friction dominate volumetric forces. In such an environment, an adaptive (or “uncalibrated”) controller which can dynamically adjust to changes in the operation environment is essential. While many groups have already demonstrated the ability to control a microrobot in three dimensions through magnetically based actuation methods, very few have attempted to apply uncalibrated control algorithms to these systems. This project focused on first developing a magnetic actuation and visual sensor system for a microrobot in a three-dimensional fluidic environment, and then on the development of an uncalibrated controller, utilizing a Recursive Least Squares (RLS) estimation algorithm. With a given desired position, the adaptive controller drives the microrobot to the target position without any prior knowledge of the system parameters such as electromagnetic field strengths, drag coefficients, or intrinsic and extrinsic camera parameters.

FACULTY ADVISORS
Associate Professor Jenelle A. Piepmeier
Weapons and Systems Engineering Department

Professor Samara L. Firebaugh
Electrical and Computer Engineering Department

Assistant Professor Hatem Elbidweihy
Electrical and Computer Engineering Department

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Spencer C. Shabshab
Midshipman First Class
United States Navy

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FACULTY ADVISORS
Associate Professor Amy E. Ksir
Mathematics Department

Associate Professor LT Brian Stout, USN
Mathematics Department

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Aaron M. Sims
Midshipman First Class
United States Navy

Control of Multi-Vehicle Formation with Coordinated Inter-Vehicle Communication

The expanded role of unmanned systems in military and civilian applications has introduced interesting new questions in multi-vehicle coordination and communication. The goal of this research is to derive steering algorithms utilizing event- and self-triggered control, capable of driving vehicles to a particular formation while simultaneously coordinating inter-agent communication instances (i.e. surfacing times). This goal is broken up into two segments: multi-vehicle control and communication control. By leveraging previous work in tracking control, we show the ability to combine kinematic and vehicle dynamic controllers to create a model that easily adapts to changing vehicle dynamics and time-varying desired configurations. Target and trajectory tracking are demonstrated, both of which are useful in conducting autonomous missions. Additionally, we present a permutation algorithm to optimally assign vehicles to formation positions based on proximity.

This work combines the multi-vehicle and communication-coordinating control to present a framework capable of steering a multi-vehicle system to a time-varying configuration without relying on all-to-all communication. The contributions of this work may enhance the capability of underwater sampling by increasing formation precision subject to intermittent communication. 

FACULTY ADVISORS
Assistant Professor Levi D. DeVries
Weapons and Systems Engineering Department

VADM Charles I. Leidig, USN (ret.)
Mechanical Engineering Department

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With the advent of lasers as weapons, it is necessary to understand how a laser propagates through a complex medium. For the U.S. Navy, the complexity of a maritime environment imposes particular challenges for laser propagation due to high concentrations of water vapor and high probabilities of liquid water in the form of fog, rain, or sea spray along the beam path. Although considerable research has gone into characterizing the maritime environment and simulating laser propagation through water vapor and turbulence, the interactions between a high energy laser (HEL) and liquid water are poorly understood. There are currently no physical or empirical models of HEL propagation through liquid clouds or sprays. Before a useful HEL spray model can be developed, the coupled interactions between an HEL and a single saturated (vaporizing) liquid droplet must be explored. The objective of the proposed work is to uncover the physical phenomena most responsible for controlling laser power and profile transmitted through single water droplets. Experimentation is required to elucidate both the thermodynamics and fluid dynamics in the droplet, and the effects that those thermofluid properties have on beam transmission.  

A project is taking place in the United States Naval Academy’s Directed Energy Research Center to investigate the interaction of a high energy laser and single water droplets. An HEL is used to irradiate droplets of water, and the droplet shape and size, the infrared radiation from the droplet, and the transmitted beam profile are measured and recorded. To control the droplet shape, it will be levitated using a commercial ultrasonic levitator, where the drop is held in place at a node by the pressure from a standing sound wave. Experiments will vary the drop size (initial diameter) and composition (salinity and turbidity). Both infrared and visible spectrum cameras off-axis captured images of the droplet as it is irradiated, facilitating modeling of the optical propagation, the resulting thermofluid effects on the droplet, and determination of time for vaporization. On axis, the beam exits the droplet into a beam profiler, which served to map out the irradiance of the beam, and how it varies over its cross-section. A combination of the heat maps from the beam profiler and the images from the cameras will provide a working knowledge of the effect the droplet has upon the beam as it is transmitted. Furthermore, multi-physics modeling tools will be used to help interpret and understand the experimental results.

The results of this experiment will provide an understanding of the coupled interaction between an HEL and a water droplet. Based upon these results, both offensive and defensive systems can be developed for distinct military applications. Analysis of the beam profile will provide insight into what configuration and number of droplets most effectively blocks directed energy. Similarly, the results can assist in determining when conditions are favorable for using a directed energy weapon, as well as when to expect cover from such attacks.

FACULTY ADVISORS
Associate Professor Cody J. Brownell
Mechanical Engineering Department

Assistant Professor CDR Stuart R. Blair, USN
Mechanical Engineering Department

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Ψ Thomas J. Wester 
Midshipman First Class
United States Navy

Mathematical Modeling: Immune System Dynamics in the Presence of Cancer and Immunodeficiency in vivo

The Human Immunodeficiency Virus (HIV) targets CD4 T-cells which are crucial in regulating the immune system's response to foreign pathogens and cancerous cell development. Furthermore, several studies link HIV infection with the proliferation of specific forms of cancer such as Kaposi Sarcoma and Non-Hodgkin's Lymphoma; HIV infected individuals can be several thousand times more likely to be diagnosed with cancer. While our understanding of both HIV and cancer has increased in the past decade, much remains unknown about the dynamic interaction between cancer development and immunodeficiency. In this project, we seek to apply systems of nonlinear ordinary differential equations to analyze how the dynamics of primary infection affect the proliferation of cancer. We first begin by characterizing the dynamics of HIV infection. During HIV-1 primary infection, we know that the virus concentration increases, reaches a peak, and then decreases until it reaches a set point. We studied longitudinal data from 18 subjects identified as HIV positive during plasma donation screening and applied several models to analyze the dynamics of the systems and determine the most effective model for characterizing the infection. We prove existence, uniqueness, positivity, and boundlessness, investigate the qualitative behavior of the models, and find the conditions that guarantee the asymptotic stability of the equilibria. In addition, we conduct numerical simulations and sensitivity analyses to illustrate and extend the theoretical results. Furthermore, we develop and study a new Tumor-Immunodeficiency model which integrates the effects of an immunodeficiency on cancerous tumor cell development. The obtained results are consistent with the known biological behavior and yield a better understanding of the interaction between cancer and immunodeficiency.

FACULTY ADVISOR
Associate Professor Sonia M. Garcia
Mathematics Department

External Collaborators
Dr. Aaron Lim
School of Social and Community Medicine
University of Bristol

Dr. Ruy Ribeiro
Theoretical Biology and Biophysics Division
Los Alamos National Laboratory

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Michael A. Woulfe
Midshipman First Class
United States Navy

Towards a Theory of a Nearly Two-Dimensional Dipolar Bose Gas

This project develops a theoretical model for gases of bosonic atoms at ultracold, but finite temperatures. Under these circumstances, the gas can undergo a phase transition to a purely quantum mechanical state, a Bose-Einstein condensate (BEC), where the atoms cease to behave like distinguishable entities, and instead form a single macroscopic matter wave. At exactly zero temperature, all of the atoms occupy the BEC; at finite temperatures, a significant fraction of the atoms leave the BEC and form a thermal cloud. Thus, the state of a low, but finite-temperature gas of bosonic atoms involves the coexistence of a BEC and a thermal cloud. Further, the atoms can interact in a variety of different ways, which have important consequences for the state of the gas. We consider both short range contact interactions and dipolar interactions, where the atoms interact via the long-range, anisotropic dipole-dipole force. We develop this model in both three- and two-dimensional geometries.

FACULTY ADVISOR
Assistant Professor Ryan M. Wilson
Physics Department