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Pursuit-evasion and time-dependent gradient flow in singular spaces

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Title: Pursuit-evasion and time-dependent gradient flow in singular spaces
Author(s): Jun, Chanyoung
Director of Research: Alexander, Stephanie B.
Doctoral Committee Chair(s): Bishop, Richard L.
Doctoral Committee Member(s): Alexander, Stephanie B.; Ghrist, Robert; Berg, I. David; Kapovich, Ilya; Leininger, Christopher J.
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): CAT(K) spaces Time-dependent gradient curves
Abstract: In this dissertation, we consider an applied problem, namely, pursuit-evasion games. These problems are related to robotics, control theory and computer simulations. We want to find the solution curves of differential equations for pursuit-evasion games, and investigate the properties of solution curves. First, we define CAT(0) and CAT(K) spaces, and explain why they are suitable playing fields, that vastly generalize the usual playing field in the pursuit-evasion literature. Then we prove our existence and uniqueness theorems for continuous pursuit curves in CAT(K) spaces, as well as our convergence estimates and regularity theorem. Pursuit curves are downward gradient curves for the distance from a moving evader, that is, for a time-dependent gradient flow. We consider not only pursuit curves, but also more general time-dependent gradient flow.
Issue Date: 2012-05-22
URI: http://hdl.handle.net/2142/31092
Rights Information: Copyright 2012 Chanyoung Jun
Date Available in IDEALS: 2012-05-22
Date Deposited: 2012-05
 

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