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On Estimates of the Solutions of Inverse Problems of Optimal Control

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

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Abstract

This paper is devoted to the problem of reconstruction of the normal control generating a realized trajectory of a dynamic control system by using known inaccurate measurements of this trajectory. A class of dynamic control systems with dynamics linear in controls and non-linear in state coordinates is considered. A new method, suggested in earlier publications, for solving such problems is discussed. This approach relies on necessary optimality conditions in an auxiliary variational problem on extremum of an integral discrepancy functional. The distinguishing feature of the method is using a functional which is convex in control variables and concave in state variables discrepancy. This form of the functional allows to obtain oscillating solutions. In this paper the estimates of the error of the discussed method are exposed and validated.

This work was supported by the Russian Foundation for Basic Research (project no. 17-01-00074) and by the Ural Branch of the Russian Academy of Sciences (project no. 18-1-1-10).

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Authors and Affiliations

  1. N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences (IMM UB RAS), 16 S. Kovalevskaya Str., Ekaterinburg, 620990, Russia

    Evgenii A. Krupennikov

  2. Ural Federal University named after the first President of Russia B.N.Yeltsin, 19 Mira Street, Ekaterinburg, 620002, Russia

    Evgenii A. Krupennikov

Authors
  1. Evgenii A. Krupennikov
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Correspondence to Evgenii A. Krupennikov .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

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Krupennikov, E.A. (2019). On Estimates of the Solutions of Inverse Problems of Optimal Control. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_39

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

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