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Asymptotic solution of a linear-quadratic problem with discontinuous coefficients and cheap control

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  • Kurina, Galina
  • Hoai, Nguyen Thi

Abstract

This paper is devoted to a linear-quadratic problem with cheap control and discontinuous coefficients. Using the direct scheme, consisting of an immediate substitution of a postulated asymptotic expansion of a solution into the problem condition and finding a family of control problems to define the terms of the asymptotic expansion, the asymptotic solution of the considered problem is obtained. The proximity of the exact solution to the approximate asymptotic one is estimated for the control, trajectory, and functional. It is shown that the minimized functional does not increase when a higher order asymptotic approximation to the optimal control is used. An illustrative example is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:347-364
    DOI: 10.1016/j.amc.2013.12.097
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    Cited by:

    1. Kurina, Galina & Hoai, Nguyen Thi, 2017. "First asymptotic approximations to a solution of singularly perturbed optimal control problem with intersecting solutions of degenerate problem," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 356-374.
    2. 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.

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