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Linear operator perturbation method in minimax control of linear dynamic systems

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Abstract

A perturbation method is proposed for solving some minimax control problems. The method is based on perturbation of eigenvalues of linear operators in a Hilbert space and Raleigh formulas. An explicit solution of the control problem under uncertainty is obtained.

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Literature cited

  1. M. F. Kirichenko, “Analytical construction of minimax controllers in linear systems,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 7, 591–594 (1977).

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  2. A. G. Nakonechnyi and A. I. Vladimirova, Perturbation Method in Minimax Estimation Problems [in Russian], Preprint No. 82–53, Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1982).

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  3. Functional Analysis [in Russian], Nauka, Moscow (1972).

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Authors and Affiliations

  1. Kiev Polytechnical Institute, Kiev

    A. I. Vladimirova

Authors
  1. A. I. Vladimirova
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Additional information

Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 103–106, 1985.

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Vladimirova, A.I. Linear operator perturbation method in minimax control of linear dynamic systems. J Math Sci 54, 844–847 (1991). https://doi.org/10.1007/BF01097598

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  • DOI: https://doi.org/10.1007/BF01097598

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