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A Solution to Fuller’s Problem Using Constructions of Pontryagin’s Maximum Principle

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Abstract

The classical two-dimensional Fuller problem is considered. The boundary value problem of Pontryagin’s maximum principle is considered. Based on the central symmetry of solutions to the boundary value problem, the Pontryagin maximum principle as a necessary condition of optimality, and the hypothesis of the form of the switching line, a solution to the boundary value problem is constructed and its optimality is substantiated. Invariant group analysis is in this case not used. The results are of considerable methodological interest.

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References

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    Yu. N. Kiselev, M. V. Orlov & S. M. Orlov

Authors
  1. Yu. N. Kiselev
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  2. M. V. Orlov
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  3. S. M. Orlov
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Corresponding author

Correspondence to Yu. N. Kiselev.

Additional information

Original Russian Text © Yu.N. Kiselev, M.V. Orlov, S.M. Orlov, 2018, published in Vestnik Moskovskogo Universiteta, Seriya 15: Vychislitel’naya Matematika i Kibernetika, 2018, No. 4, pp. 9–18.

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Kiselev, Y.N., Orlov, M.V. & Orlov, S.M. A Solution to Fuller’s Problem Using Constructions of Pontryagin’s Maximum Principle. MoscowUniv.Comput.Math.Cybern. 42, 152–162 (2018). https://doi.org/10.3103/S0278641918040039

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  • DOI: https://doi.org/10.3103/S0278641918040039

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