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

Nguyen Thi Hoai ()
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Nguyen Thi Hoai: VNU, University of Science

Journal of Optimization Theory and Applications, 2017, vol. 175, issue 2, No 2, 324-340

Abstract: 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.

Keywords: Optimal problems; Singular perturbations; Asymptotic expansions; Direct scheme; Critical case; Cheap control; 49J15; 41A60; 34E15 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-017-1156-6

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