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<p>In this paper, we consider the optimal control of nonlinear systems of fractional-order with control delay, where the fractional derivatives are expressed in the Caputo sense. For this problem, we first obtained the necessary first-order optimality condition in the form of the Pontryagin maximum principle. For a control that is singular in the sense of the Pontryagin maximum principle, a higher-order necessary optimality condition is obtained. Further, in one particular case, a multipoint necessary second-order optimality condition is obtained. The effectiveness of the results obtained is illustrated by specific examples.</p>

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Necessary Optimality Conditions for Singular Controls of Caputo Fractional Systems with Delay in Control

  • 期刊论文

  • 发表日期：

    2025年1月27日

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  • Shakir Sh. Yusubov,
  • Elimhan N. Mahmudov

摘要

In this paper, we consider the optimal control of nonlinear systems of fractional-order with control delay, where the fractional derivatives are expressed in the Caputo sense. For this problem, we first obtained the necessary first-order optimality condition in the form of the Pontryagin maximum principle. For a control that is singular in the sense of the Pontryagin maximum principle, a higher-order necessary optimality condition is obtained. Further, in one particular case, a multipoint necessary second-order optimality condition is obtained. The effectiveness of the results obtained is illustrated by specific examples.