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Sensitivity Analysis of Value Functional of Fractional Optimal Control Problem with Application to Feedback Construction of Near Optimal Controls

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Abstract

We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation of order \(\alpha \in (0, 1)\) and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of this problem has a property of directional differentiability of order \(\alpha \). As an application of this result, we propose a new method for constructing an optimal positional (feedback) control strategy, which allows us to generate \(\varepsilon \)-optimal controls for any predetermined accuracy \(\varepsilon > 0\).

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Acknowledgements

This work was supported by RSF, project no. 19–11–00105.

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  1. N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, 620108, Russia

    Mikhail Gomoyunov

  2. Ural Federal University, Ekaterinburg, 620002, Russia

    Mikhail Gomoyunov

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  1. Mikhail Gomoyunov
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Correspondence to Mikhail Gomoyunov.

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Gomoyunov, M. Sensitivity Analysis of Value Functional of Fractional Optimal Control Problem with Application to Feedback Construction of Near Optimal Controls. Appl Math Optim 88, 41 (2023). https://doi.org/10.1007/s00245-023-10022-4

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