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

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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.

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Authors and Affiliations

  1. Faculty of Mathematics, Mechanics and Informatics, VNU, University of Science, Hanoi, Vietnam

    Nguyen Thi Hoai

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  1. Nguyen Thi Hoai
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Correspondence to Nguyen Thi Hoai.

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Communicated by Roberto Triggiani.

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Hoai, N.T. Asymptotic Solution of a Singularly Perturbed Linear-Quadratic Problem in Critical Case with Cheap Control. J Optim Theory Appl 175, 324–340 (2017). https://doi.org/10.1007/s10957-017-1156-6

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  • DOI: https://doi.org/10.1007/s10957-017-1156-6

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