A tensor-train-decomposition-based algorithm for high-dimensional pursuit-evasion games

The research presented in this thesis was inspired by an interest in determining feedback strategies for high-dimensional pursuit-evasion games. When a problem is high-dimensional or involves a state space that is defined by several variables, various methods used to solve pursuit-evasion games often require unrealistic computation time. This problem, called the curse of dimensionality, can be mitigated under certain circumstances by utilizing tensor-train (TT) decomposition. By using this intuition, a new algorithm for solving high dimensional pursuit-evasion problems called Best-Response Tensor-Train-decomposition-based Value Iteration (BR-TT-VI) was developed. BR-TT-VI builds on concepts from game theory, dynamic programming (DP), and tensor-train decomposition. By using TT decomposition, BR-TT-VI greatly reduces the effects of the curse of dimensionality. This work culminates in the application of BR-TT-VI to two different pursuit-evasion problems. First, a four-dimensional problem capable of being solved by traditional value iteration(VI) is tackled by the BR-TT-VI algorithm. This problem allows a direct comparison between VI and BR-TT-VI to demonstrate the reduced computational time of the new algorithm. Finally, BR-TT-VI is used to solve a six-dimensional problem involving two Dubins vehicles that is impractical to solve with VI.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Aeronautics and Astronautics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2016

Author dc:creator

• Grimm, Christopher Lee, Jr

Advisor dc:contributor.advisor

• Sertac Karaman.

• Aeronautics and Astronautics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/105615

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/105615