| Shakir Yusubov, Elimhan Mahmudov, Shikhi Yusubov Some Necessary Conditions for Optimality in Fractional Caputo Systems with Control Delay |
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| Abstract. This paper considers an optimal control problem involving a dynamic system described by a nonlinear fractional differential equation of Caputo type of order 0<α<1 with control delay, associated with a Bolza-type cost functional expressed as the sum of a Mayer cost and a Lagrangian cost given by a Riemann-Liouville fractional integral of order β>0 with control delay. For this problem, an analogue of the Euler equation and the Legendre-Clebsch condition has been obtained. In deriving the analogue of the Legendre-Clebsch condition, a higher-order necessary optimality condition was obtained. |
| Keywords: fractional Caputo derivative, fractional optimal control, necessary optimality condition |
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