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Optimality of Broken Extremals

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Abstract

In this paper, we analyse the optimality of broken Pontryagin extremal for an n-dimensional affine control system with a control parameter, taking values in a k-dimensional closed ball. We prove the optimality of broken normal extremals in many cases that include (but not are exhausted by) the cases of the involutive driftless part of the system for any n > k and of the contact driftless part for n = 3 and k = 2.

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Notes

  1. In the \(\mathcal {C}^{\infty } (M)\) category.

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Acknowledgments

The work of A.A. Agrachev was supported by the Russian Science Foundation under grant No 17-11-01387.

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Authors and Affiliations

  1. SISSA, Via Bonomea 265, 34136, Trieste, Italy

    Andrei A. Agrachev & Carolina Biolo

  2. PSI RAS, Pereslavl-Zalessky, Russia

    Andrei A. Agrachev

Authors
  1. Andrei A. Agrachev
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  2. Carolina Biolo
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Correspondence to Carolina Biolo.

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Agrachev, A.A., Biolo, C. Optimality of Broken Extremals. J Dyn Control Syst 25, 289–307 (2019). https://doi.org/10.1007/s10883-018-9416-9

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  • DOI: https://doi.org/10.1007/s10883-018-9416-9

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