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Asymptotic methods in the theory of optimum correction for systems with slowly varying parameters

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Abstract

This paper deals with the problem of optimum control for the case where the constraints are linear differential equations and the functional is of quadratic type. It is assumed that the matrix of these simultaneous equations dependsslowly on the time. The paper describes a method which permits to construct effectively asymptotic solutions of such a problem when the matrix of the characteristic equation which corresponds to Pontryagin's set of equations does not have any simple elementary divisors.

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References

  1. Tamarkin, Ya. D.,General Problems in the Theory of Ordinary Differential Equations (in Russian), Frolova Publishing House, Leningrad, USSR, 1917.

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  2. Moiseev, N. N.,Asymptotic Representation of the Solutions of Linear Differential Equations with Multiple Elementary Divisors of the Characteristic Equation (in Russian), Doklady AN SSSR, Vol. 170, No. 4, 1966.

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Authors and Affiliations

  1. Computing Center, Academy of Sciences of the USSR, Moscow, USSR

    N. N. Moiseev (Professor) & A. G. Shmidt (Research Scientist)

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  1. N. N. Moiseev
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  2. A. G. Shmidt
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Communicated by R. E. Kalaba

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Moiseev, N.N., Shmidt, A.G. Asymptotic methods in the theory of optimum correction for systems with slowly varying parameters. J Optim Theory Appl 3, 141–152 (1969). https://doi.org/10.1007/BF00929439

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  • DOI: https://doi.org/10.1007/BF00929439

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