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On a Solution of an Optimal Control Problem for a Linear Fractional-Order System

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Advanced, Contemporary Control

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1196))

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Abstract

We consider an optimal control problem for a dynamical system described by a linear differential equation with the Caputo fractional derivative of an order \(\alpha \in (0, 1)\). A cost functional to be minimized evaluates a deviation of a system’s terminal state from a given target point. In order to construct a solution, we turn from the considered problem to an auxiliary optimal control problem for a first-order linear system with concentrated delays, which approximates the original system and, after that, we reduce this auxiliary problem to an optimal control problem for an ordinary differential system. Moreover, on this basis, we propose a feedback scheme of optimal control of the original system. The efficiency of the approach is illustrated by an example, and the results of numerical simulations are presented.

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Author information

Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, The Ural Branch of the Russian Academy of Sciences, Ekaterinburg, 620990, Russia

    Mikhail I. Gomoyunov

  2. Ural Federal University, Ekaterinburg, 620002, Russia

    Mikhail I. Gomoyunov

Authors
  1. Mikhail I. Gomoyunov
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Correspondence to Mikhail I. Gomoyunov .

Editor information

Editors and Affiliations

  1. Institute of Automatic Control, Lodz University of Technology, Lodz, Poland

    Andrzej Bartoszewicz

  2. Institute of Automatic Control, Lodz University of Technology, Lodz, Poland

    Jacek Kabziński

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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Gomoyunov, M.I. (2020). On a Solution of an Optimal Control Problem for a Linear Fractional-Order System. In: Bartoszewicz, A., Kabziński, J., Kacprzyk, J. (eds) Advanced, Contemporary Control. Advances in Intelligent Systems and Computing, vol 1196. Springer, Cham. https://doi.org/10.1007/978-3-030-50936-1_70

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