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On a linear problem of tracing a given motion

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Abstract

In the present paper, we consider the problem on the optimal tracing of a given vector function with the use of a generalized projection of the trajectory of a linear plant. The deviation of a given motion is measured in the metric C m[0, T] of continuous vector functions of the corresponding dimension m. We suggest an efficient method for the construction of an approximate solution of this optimization problem with given accuracy.

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References

  1. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (The Mathematical Theory of Optimal Processes), Moscow: Nauka, 1976.

    Google Scholar 

  2. Lee, E.B. and Markus, L., Foundations of Optimal Control Theory, New York, 1967. Translated under the title Osnovy teorii optimal’nogo upravleniya, Moscow: Nauka, 1972.

  3. Blagodatskikh, V.I., Vvedenie v optimal’noe upravlenie (Introduction to Optimal Control), Moscow: Vysshaya Shkola, 2001.

    Google Scholar 

  4. Vasil’ev, F.P., Metody optimizatsii (Optimization Methods), Moscow: Faktorial Press, 2002.

    Google Scholar 

  5. Barbashin, E.A., Vvedenie v teoriyu ustoichivosti (Introduction to the Theory of Stability), Moscow: Nauka, 1967.

    Google Scholar 

  6. Dubovitskii, A.Ya. and Milyutin, A.A., Problems on the Extremum in the Presence of Constraints, Zh. Vychisl. Mat. Mat. Fiz., 1965, vol. 5, no. 3, pp. 395–453.

    Google Scholar 

  7. Pshenichnyi, B.N., Neobkhodimye usloviya ekstremuma (Necessary Conditions for an Extremum), Moscow: Nauka, 1969.

    Google Scholar 

  8. Shablinskaya, I.R., Nonsmooth Problems of Optimal Control Theory, Cand. Sci. (Phys.-Math.) Dissertation, Leningrad, 1983.

  9. Dem’yanov, V.F. and Malozemov, V.N., Vvedenie v minimaks (Introduction to Minimax), Moscow: Nauka, 1972.

    MATH  Google Scholar 

  10. Fedorov, V.V., Chislennye metody maksimina (Numerical Methods of Maximin), Moscow: Nauka, 1979.

    Google Scholar 

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    M. S. Nikol’skii

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  1. M. S. Nikol’skii
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Original Russian Text © M.S. Nikol’skii, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 11, pp. 1646–1650.

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Nikol’skii, M.S. On a linear problem of tracing a given motion. Diff Equat 45, 1681–1685 (2009). https://doi.org/10.1134/S0012266109110135

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  • DOI: https://doi.org/10.1134/S0012266109110135

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