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Minimal Time Problem with Impulsive Controls

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Abstract

Time optimal control problems for systems with impulsive controls are investigated. Sufficient conditions for the existence of time optimal controls are given. A dynamical programming principle is derived and Lipschitz continuity of an appropriately defined value functional is established. The value functional satisfies a Hamilton–Jacobi–Bellman equation in the viscosity sense. A numerical example for a rider-swing system is presented and it is shown that the reachable set is enlargered by allowing for impulsive controls, when compared to nonimpulsive controls.

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Authors and Affiliations

  1. Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, 8010, Graz, Austria

    Karl Kunisch

  2. Radon Institute of Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstraße 69, 4040, Linz, Austria

    Karl Kunisch & Zhiping Rao

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  1. Karl Kunisch
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  2. Zhiping Rao
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Correspondence to Zhiping Rao.

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Kunisch, K., Rao, Z. Minimal Time Problem with Impulsive Controls. Appl Math Optim 75, 75–97 (2017). https://doi.org/10.1007/s00245-015-9324-2

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