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dc.contributor.advisorZhou, Haomin
dc.contributor.authorLu, Jun
dc.date.accessioned2015-06-08T18:10:54Z
dc.date.available2015-06-09T05:30:07Z
dc.date.created2014-05
dc.date.issued2014-04-07
dc.date.submittedMay 2014
dc.identifier.urihttp://hdl.handle.net/1853/53428
dc.description.abstractThis thesis proposes a novel and efficient method (Method of Evolving Junctions) for solving optimal control problems with path constraints, and whose optimal paths are separable. A path is separable if it is the concatenation of finite number of subarcs that are optimal and either entirely constraint active or entirely constraint inactive. In the case when the subarcs can be computed efficiently, the search for the optimal path boils down to determining the junctions that connect those subarcs. In this way, the original infinite dimensional problem of finding the entire path is converted into a finite dimensional problem of determine the optimal junctions. The finite dimensional optimization problem is then solved by a recently developed global optimization strategy, intermittent diffusion. The idea is to add perturbations (noise) to the gradient flow intermittently, which essentially converts the ODE's (gradient descent) into a SDE's problem. It can be shown that the probability of finding the globally optimal path can be arbitrarily close to one. Comparing to existing methods, the method of evolving junctions is fundamentally faster and able to find the globally optimal path as well as a series of locally optimal paths. The efficiency of the algorithm will be demonstrated by solving path planning problems, more specifically, finding the optimal path in cluttered environments with static or dynamic obstacles.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectSDEs
dc.subjectShortest path
dc.subjectDynamic environment
dc.titleMethod of evolving junctions: a new approach to path planning and optimal control
dc.typeDissertation
dc.description.degreePh.D.
dc.contributor.departmentMathematics
dc.embargo.terms2015-05-01
thesis.degree.levelDoctoral
dc.contributor.committeeMemberChow, Shui-Nee
dc.contributor.committeeMemberDieci, Luca
dc.contributor.committeeMemberEgerstedt, Magnus
dc.contributor.committeeMemberKang, Sung Ha
dc.date.updated2015-06-08T18:10:54Z


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