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Optimal Control with Time Delays via the Penalty Method

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  • Mohammed Benharrat
  • Delfim F. M. Torres

Abstract

We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general optimal control problem with time delays is considered. Main result gives a convergence theorem, allowing us to obtain a solution to the delayed optimal control problem by considering a sequence of delayed problems of the calculus of variations.

Suggested Citation

  • Mohammed Benharrat & Delfim F. M. Torres, 2014. "Optimal Control with Time Delays via the Penalty Method," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-9, September.
    • Handle: RePEc:hin:jnlmpe:250419
    DOI: 10.1155/2014/250419
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    Cited by:

    1. Abraha, Teklebirhan & Al Basir, Fahad & Obsu, Legesse Lemecha & Torres, Delfim F.M., 2021. "Pest control using farming awareness: Impact of time delays and optimal use of biopesticides," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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