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This article is cited in 3 scientific papers (total in 3 papers)
Construction of Solutions to Control Problems for Fractional-Order Linear Systems Based on Approximation Models
M. I. Gomoyunovab, N. Yu. Lukoyanovab a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
Abstract:
We consider an optimal control problem for a dynamical system
whose motion is described by a linear differential equation with the Caputo
fractional derivative of order $\alpha \in (0, 1)$. The time interval of the
control process is fixed and finite. The control actions are subject to
geometric constraints. The aim of the control is to minimize a given
terminal-integral performance index. In order to construct a solution,
we develop the following approach. First, from the considered problem,
we turn to an auxiliary optimal control problem for a first-order linear
system with lumped delays, which approximates the original system. After that,
the auxiliary problem is reduced to an optimal control problem for an ordinary
differential system. Based on this, we propose a closed-loop scheme of optimal
control of the original system that uses the approximating system as a guide.
In this scheme, the control in the approximating system is formed with the
help of an optimal positional control strategy from the reduced problem. The
effectiveness of the developed approach is illustrated by a problem in which
the performance index is the norm of the terminal state of the system.
Keywords:
optimal control, linear systems, fractional-order derivatives, approximation, time-delay systems, closed-loop control.
Received: 25.12.2019 Revised: 24.01.2020 Accepted: 27.01.2020
Citation:
M. I. Gomoyunov, N. Yu. Lukoyanov, “Construction of Solutions to Control Problems for Fractional-Order Linear Systems Based on Approximation Models”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 1, 2020, 39–50; Proc. Steklov Inst. Math. (Suppl.), 313, suppl. 1 (2021), S73–S82
Linking options:
https://www.mathnet.ru/eng/timm1698 https://www.mathnet.ru/eng/timm/v26/i1/p39
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Abstract page: | 299 | Full-text PDF : | 67 | References: | 51 | First page: | 14 |
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