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Remarks on stability analysis for delayed systems with applications
Title
Remarks on stability analysis for delayed systems with applications.
Creator
Tiwari, Shanaz, Wang, Yuan, Graduate College
Date Issued
2011-04-08
PURL
http://purl.flvc.org/fcla/dt/3164800
Subject Headings
Nonlinear control theory, Lyapunov functions, Time delay systems
Format
Document (PDF)
Computing Global Decompositions of Dynamical Systems
Title
Computing Global Decompositions of Dynamical Systems.
Creator
Ban, Hyunju, Kalies, William D., Florida Atlantic University
Abstract/Description
In this dissertation we present a computational approach to Conley's Decomposition Theorem, which gives a global decomposition of dynamical systems, and introduce an explicit numerical algorithm with computational complexity bounds for computing global dynamical structures of a continous map including attractorrepeller pairs and Conley's Lyapunov function. The approach is based on finite spatial discretizations and combinatorial multivalued maps. The method is successful in exhibiting...
Show moreIn this dissertation we present a computational approach to Conley's Decomposition Theorem, which gives a global decomposition of dynamical systems, and introduce an explicit numerical algorithm with computational complexity bounds for computing global dynamical structures of a continous map including attractorrepeller pairs and Conley's Lyapunov function. The approach is based on finite spatial discretizations and combinatorial multivalued maps. The method is successful in exhibiting approximations of attractor-repeller pairs, invariant sets, and Conley's Lyapunov function. We used the C++ language to code the algorithm.
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Date Issued
2006
PURL
http://purl.flvc.org/fau/fd/FA00000848
Subject Headings
Lyapunov functions, Control theory, Mathematical optimization, Differentiable dynamical systems
Format
Document (PDF)
Automatic Station Keeping of Small Twin Screw Boats
Title
Automatic Station Keeping of Small Twin Screw Boats.
Creator
VanZwieten, James H., Driscoll, Frederick R., Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
This work details the development of tools and controllers for station keeping control of twin screw vessels. A fundamental analysis is conducted of the dynamics of twin screw displacement hull vessels and their actuator systems, where the response characteristics and maneuverability are quantified through a series of full scale trials conducted in different environmental conditions while recording the environmental conditions, actuator states, and geodetic and inertial measurements. The data...
Show moreThis work details the development of tools and controllers for station keeping control of twin screw vessels. A fundamental analysis is conducted of the dynamics of twin screw displacement hull vessels and their actuator systems, where the response characteristics and maneuverability are quantified through a series of full scale trials conducted in different environmental conditions while recording the environmental conditions, actuator states, and geodetic and inertial measurements. The data from these maneuvers were repeatable from run to run and thus provide valuable benchmarks for several maneuvers and the measured actuator response provides valuable set points of performance characteristics/limitations for control development. A comprehensive general simulation of small twin screw displacement hull boats is developed as a tool to estimate ship and actuator responses in support of developing and tuning of control systems. The model and computer simulation is capable of modeling a wide range of the surface vessels, including their actuators and environmental conditions. This model proved to be accurate, when compared to the sea trial data, and model estimates have rms velocity errors for the various steady maneuvers of 1.2-4.6% for surge, 12.6-17.9% for sway, and 7.6-20.2% for yaw. A path following station keeping controller is developed that uses Lyapunov stability analysis to determine the path the vessel should follow to effectively eliminate position error. This controller showed good performance for several different environmental conditions. Encouraged by these finding, three additional station keeping control methodologies are developed for twin screw surface ships. All four of these controllers are examined for their robustness to environmental conditions, as well as their sensitivity to sensor precision, sensor update rates, and actuator limitations. All controllers are evaluated in sea state 4 yielding rms position errors from 3.3 to 16.2 m, the rms surge and sway accelerations are under 0.62 m/s , and the engine shifting frequencies are between 0.011 and 0.145 Hz. These four controllers are then tested over a wide range of environmental conditions, sensor precisions and update rates, and actuator response rates. The results from these tests give quantitative data that will aid in selecting the appropriate controller for a specific application, and will assist in selecting appropriate sensors.
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Date Issued
2007
PURL
http://purl.flvc.org/fau/fd/FA00012579
Subject Headings
Boats and boating--Design, Actuators--Testing, Fracture mechanics, Lyapunov functions
Format
Document (PDF)
Stability analysis for singularly perturbed systems with time-delays
Title
Stability analysis for singularly perturbed systems with time-delays.
Creator
Yang, Yang, Wang, Yuan, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
Singularly perturbed systems with or without delays commonly appear in mathematical modeling of physical and chemical processes, engineering applications, and increasingly, in mathematical biology. There has been intensive work for singularly perturbed systems, yet most of the work so far focused on systems without delays. In this thesis, we provide a new set of tools for the stability analysis for singularly perturbed control systems with time delays.
Date Issued
2015
PURL
http://purl.flvc.org/fau/fd/FA00004423, http://purl.flvc.org/fau/fd/FA00004423
Subject Headings
Biology -- Mathematical models, Biomathematics, Differentiable dynamical systems, Differential equations, Partial -- Numerical solutions, Global analysis (Mathematics), Lyapunov functions, Nonlinear theories
Format
Document (PDF)