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Asymptotic Solution of a Singularly Perturbed Linear-Quadratic Problem in Critical Case with Cheap Control

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  • Nguyen Thi Hoai

    (VNU, University of Science)

Abstract

Using the direct scheme method, we construct an asymptotic expansion for the solution of a singularly perturbed optimal problem in critical case with cheap control and two fixed end-points. The asymptotic solution contains the outer series and two boundary-layer series in the vicinities of the two end-points. The error estimates for state and control variables and the functional are obtained. It is shown that the value of minimized functional does not increase when a higher-order approximation to the optimal control is used. An illustrative example is given.

Suggested Citation

  • Nguyen Thi Hoai, 2017. "Asymptotic Solution of a Singularly Perturbed Linear-Quadratic Problem in Critical Case with Cheap Control," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 324-340, November.
    • Handle: RePEc:spr:joptap:v:175:y:2017:i:2:d:10.1007_s10957-017-1156-6
    DOI: 10.1007/s10957-017-1156-6
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    References listed on IDEAS

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    1. Kurina, Galina & Hoai, Nguyen Thi, 2014. "Asymptotic solution of a linear-quadratic problem with discontinuous coefficients and cheap control," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 347-364.
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    Cited by:

    1. Thi Hoai Nguyen, 2021. "Asymptotic Solution of a Singularly Perturbed Optimal Problem with Integral Constraint," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 931-950, September.

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