Non-linear Dynamics Commons^™

Rogue Rotary - Modular Robotic Rotary Joint Design, Sean Wesley Murphy, Tyler David Riessen, Jacob Mark Triplett

Mechanical Engineering

This paper describes the design process from ideation to test validation for a singular robotic joint to be configured into a myriad of system level of robots.

P26. Global Exponential Stabilization On So(3), Soulaimane Berkane

Western Research Forum

Global Exponential Stabilization on SO(3)

Autonomous Quadrotor Collision Avoidance And Destination Seeking In A Gps-Denied Environment, Thomas C. Kirven

Theses and Dissertations--Mechanical and Aerospace Engineering

This thesis presents a real-time autonomous guidance and control method for a quadrotor in a GPS-denied environment. The quadrotor autonomously seeks a destination while it avoids obstacles whose shape and position are initially unknown. We implement the obstacle avoidance and destination seeking methods using off-the-shelf sensors, including a vision-sensing camera. The vision-sensing camera detects the positions of points on the surface of obstacles. We use this obstacle position data and a potential-field method to generate velocity commands. We present a backstepping controller that uses the velocity commands to generate the quadrotor's control inputs. In indoor experiments, we demonstrate that the …

Neutrosophic Operational Research - Vol. 2, Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

Branch Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It …

Self-Correcting Kelly Strategies For Skeptical Traders, Aaron C. Brown

International Conference on Gambling & Risk Taking

The Kelly criterion gives the appropriate bet size in idealized situations with known parameters. In financial trading situations parameters are generally unknown and the mathematical assumptions underlying the Kelly proof are not met precisely. Moreover a risk manager typically must cooperate with a trader who may be skeptical about both the Kelly criterion specifically and the concept of mathematical optimization of bet size in general.

This presentation tackles the problem of designing a Kelly-based system for setting trade risk management parameters that is both self-correcting (the system delivers good results even if initial parameter are misestimated or parameters change) and …

Toward Adaptive Control Of Acute Inflammation, Judy D. Day, Seddik M. Djouadi, Ouassim Bara, Gregory L. Zitelli

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok

Mathematics Honors Papers

This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.

The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided …

A Contribution Toward Better Understanding Of Overbanking Tendency In Fixed-Wing Aircraft, Nihad E. Daidzic

Journal of Aviation Technology and Engineering

The phenomenon of overbanking tendency for a rigid-body, fixed-wing aircraft is investigated. Overbanking tendency is defined as a spontaneous, unbalanced rolling moment that keeps increasing an airplane’s bank angle in steep turns and must be arrested by opposite aileron action. As stated by the Federal Aviation Administration, the overbanking tendency may lead to a loss of control, especially in instrument meteorological conditions. It was found in this study that the speed differential over wing halves in horizontal turns indeed creates a rolling moment that achieves maximum values for bank angles between 45 and 55 degrees. However, this induced rolling moment …

Symmetry And Stability Of Homogeneous Flocks, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

The study of the movement of flocks, whether biological or technological, is motivated by the desire to understand the capability of coherent motion of a large number of agents that only receive very limited information. In a biological flock a large group of animals seek their course while moving in a more or less fixed formation. It seems reasonable that the immediate course is determined by leaders at the boundary of the flock. The others follow: what is their algorithm? The most popular technological application consists of cars on a one-lane road. The light turns green and the lead car …

Stable Motions Of Vehicle Formations, Anca Williams, Gerardo Lafferriere, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We investigate stable maneuvers for a group of autonomous vehicles while moving in formation. The allowed decentralized feeback laws are factored through the Laplacian matrix of the communication graph. We show that such laws allow for stable circular or elliptical motions for certain vehicle dynamics. We find necessary and sufficient conditions on the feedback gains and the dynamic parameters for convergence to formation. In particular, we prove that for undirected graphs there exist feedback gains that stabilize rotational (or elliptical) motions of arbitrary radius (or eceentricity). In the directed graph case we provide necessary and sufficient conditions on the curvature …

On The Empirical Balanced Truncation For Nonlinear Systems, Marissa Condon, Rossen Ivanov

Articles

Novel constructions of empirical controllability and observability gramians for nonlinear systems for subsequent use in a balanced truncation style of model reduction are proposed. The new gramians are based on a generalisation of the fundamental solution for a Linear Time-Varying system. Relationships between the given gramians for nonlinear systems and the standard gramians for both Linear Time-Invariant and Linear Time-Varying systems are established as well as relationships to prior constructions proposed for empirical gramians. Application of the new gramians is illustrated through a sample test-system.

A Mathematical Model And Simulation Of Natural Circulation Loop Thermalhydraulics, Nihad E. Daidzic

Aviation Department Publications

In this work, a simple, nonlinear, seventh-order mathematical model with lumped parameter analysis of the thermalhydraulic processes in a natural circulation steam boiler loop is presented. Digital simulation has been performed in order to predict open loop transients in severe accidental situations. Parts of the circulation loop such as the steam drum, downcomer, and riser were modelled separately on the basis of the integral balance equations. The two-phase flow in the steam drum and in the riser was modelled with the aid of a homogeneous-equilibrium, two-phase flow model. Special care was taken to ensure the stability of the numerical scheme, …