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

Jun, Chanyoung

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Description

Title

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

Author(s)

Jun, Chanyoung

Issue Date

2012-05-22T00:27:23Z

Director of Research (if dissertation) or Advisor (if thesis)

Alexander, Stephanie B.

Doctoral Committee Chair(s)

Bishop, Richard L.

Committee Member(s)

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

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2012-05

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

Copyright and License Information

Copyright 2012 Chanyoung Jun

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