| Summary: | Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2016. === Cataloged from PDF version of thesis. === Includes bibliographical references (pages 99-100). === 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. === by Christopher Lee Grimm Jr. === S.M.
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