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DOI: 10.23952/cot.2023.13
Received June 4, 2022; Accepted December 5, 2022; Published March 20, 2023
Abstract. The (classical) Elvis problem refers to a particular type of minimum time problem in which the control dynamics are piece-wise constant and isotropic on two mediums separated by an interface. The somewhat impertinent nomenclature refers to an observation by Timothy Pennings [1] whose dog (named Elvis) enjoyed fetching an object thrown from the shore of Lake Michigan into the water. Elvis was observed to retrieve the object by going in a path that resembled how light would refract (according to Snell’s Law) in isotropic mediums. The problem is first generalized to allow for anisotropic velocity sets that are closed, convex, bounded and with 0 in its interior. Tools of Convex Analysis are employed to characterize optimum movement. Further generalizations are then considered with potentially having faster movement on the interface and with more than two mediums.
How to Cite this Article:
Clinten A. Graham, Claire K. Pearson, Peter R. Wolenski, Generalization of the Elvis problem, Commun. Optim. Theory 2023 (2023) 13.