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Lower semicontinuous solutions of the Bellman equation for the minimum time problem

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Abstract

The minimum time problem associated with a nonlinear control system is considered, and the unicity of the lower semicontinuous solution of the corresponding Bellman equation is investigated. A main tool in our approach is the Kruzkov transformation that enables us to work on ℝn−{0}, where {0} is the target set, instead of the unknown reachable set.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Iasi, Iasi, România

    O. Carja (Assistant Professor)

  2. Department of Mathematics, University of Genova, Genova, Italy

    F. Mignanego (Assistant Professor)

  3. IDST, Faculty of Architecture, University of Genova, Genova, Italy

    G. Pieri (Assistant Professor)

Authors
  1. O. Carja
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  2. F. Mignanego
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  3. G. Pieri
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Additional information

Communicated by R. Conti

This research was carried out while the first author was visiting the Department of Mathematics, University of Genova, Genova, Italy.

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Carja, O., Mignanego, F. & Pieri, G. Lower semicontinuous solutions of the Bellman equation for the minimum time problem. J Optim Theory Appl 85, 563–574 (1995). https://doi.org/10.1007/BF02193056

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  • DOI: https://doi.org/10.1007/BF02193056

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