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Constructive methods in the nonlinear problems of control theory

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Abstract

We consider nonlinear control problems of transformation of a substance from one state into another given some boundary data. Our goal is to recover the second order differential operators with three time-independent coefficients. Some constructive analytical methods of study are proposed that use, in particular, the Burman-Lagrange inversion formulas for analytic functions. Some formulas are given for solving the control problems in a few particular cases of the initialboundary data. Alongside the theoretical study, we carry out, on the basis of a logical system of symbolic computation, the practical implementation of the algorithms and programs for automatic generation of the formulas that give the solutions of control problems.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    Yu. E. Anikonov & M. V. Neshchadim

  2. Siberian State University of Telecommunications and Informatics, ul. Kirova 86, Novosibirsk, 630102, Russia

    Yu. V. Krivtsov

Authors
  1. Yu. E. Anikonov
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  2. Yu. V. Krivtsov
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  3. M. V. Neshchadim
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Correspondence to Yu. E. Anikonov.

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Original Russian Text © Yu.E. Anikonov, Yu.V. Krivtsov, M.V. Neshchadim, 2010, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2010, Vol. XIII, No. 2, pp. 30–45.

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Anikonov, Y.E., Krivtsov, Y.V. & Neshchadim, M.V. Constructive methods in the nonlinear problems of control theory. J. Appl. Ind. Math. 5, 165–179 (2011). https://doi.org/10.1134/S1990478911020037

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  • DOI: https://doi.org/10.1134/S1990478911020037

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