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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Jun, Chanyoung

Contributors dc:contributor

• Alexander, Stephanie B.
• Bishop, Richard L.
• Ghrist, Robert
• Berg, I. David
• Kapovitch, Ilia
• Leininger, Christopher J.

• CAT(K) spaces
• Time-dependent gradient curves

Statement dc:rights

• Copyright 2012 Chanyoung Jun

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/31092

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/31092