Application of Numerical Methods to the Hamilton-Jacobi-Isaacs Equation in Various Dynamical Systems

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dc.contributorMulani, Sameer B
dc.contributorBranam, Richard
dc.contributorMelkonyan, Tigran
dc.contributorFlory, John
dc.contributor.advisorSood, Rohan
dc.contributor.authorLedbetter, William Gordon
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2021-11-23T14:34:12Z
dc.date.available2021-11-23T14:34:12Z
dc.date.issued2021
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractThe field of differential games has broad applicability to topics of economics, engineering, business, and warfare. Given the increasing levels of autonomy implemented in man-made systems in these fields, competition-based analysis may be the best option for understanding behavioral bounds when such systems interact. Differential games are governed by the Hamilton-Jacobi-Isaacs PDE, and many solution techniques are explored before identifying a gap in the existing literature. This dissertation develops a new approach to analyzing differential games based on a saddle-point solution technique. In a 2D system, the standard algorithmic approach produces both a value function interpolation and an approximate control map. Additionally, analysis of the observation error indicates that future analysis should prefer a problem formulation with relative motion. In the Circular Restricted Three-Body Problem, the same algorithms are applied to a system with real-world implications. The value and control interpolations produce a near-optimal trajectory, but the radial basis function approach suffered from high data density and did not exactly recreate the nominal solution. A perturbation analysis indicated that any mid-flight disturbance to the game state is most likely to benefit the pursuer, extending the works of Isaacs to a new domain. Ultimately, the proposed method is demonstrated to be a valuable tool for future differential games research.en_US
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otherhttp://purl.lib.ua.edu/181491
dc.identifier.otheru0015_0000001_0003930
dc.identifier.otherLedbetter_alatus_0004D_14586
dc.identifier.urihttp://ir.ua.edu/handle/123456789/8162
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.titleApplication of Numerical Methods to the Hamilton-Jacobi-Isaacs Equation in Various Dynamical Systemsen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Aerospace Engineering and Mechanics
etdms.degree.disciplineAerospace Engineering
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.

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