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

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


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.


Optimal control problem Linear system Caputo fractional derivative Approximation Feedback control Numerical method 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Krasovskii Institute of Mathematics and Mechanics, The Ural Branch of the Russian Academy of SciencesEkaterinburgRussia
  2. 2.Ural Federal UniversityEkaterinburgRussia

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