Publication detail

# Numerical Solution of Fractional Control Problems via Fractional Differential Transformation

REBENDA, J. ŠMARDA, Z.

Original Title

Numerical Solution of Fractional Control Problems via Fractional Differential Transformation

English Title

Numerical Solution of Fractional Control Problems via Fractional Differential Transformation

Type

conference paper

Language

en

Original Abstract

In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new algorithm convenient for numerical approximation of a solution of the studied problem. The method consists of the fractional differential transformation in combination with general methods of steps. The original system is transformed to a system of recurrence relations. Approximation of the solution is given in the form of truncated fractional power series. The choice of order of the fractional power series is discussed and the order is determined in relation to the order of the system. An application on a two-dimensional fractional system is shown. Exact solution is found for the first two intervals of the method of steps. The result for Caputo derivative of order 1 coincides with the solution of first-order system with classical derivative. We conclude that the algorithm is applicable, efficient and gives reliable results.

English abstract

In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new algorithm convenient for numerical approximation of a solution of the studied problem. The method consists of the fractional differential transformation in combination with general methods of steps. The original system is transformed to a system of recurrence relations. Approximation of the solution is given in the form of truncated fractional power series. The choice of order of the fractional power series is discussed and the order is determined in relation to the order of the system. An application on a two-dimensional fractional system is shown. Exact solution is found for the first two intervals of the method of steps. The result for Caputo derivative of order 1 coincides with the solution of first-order system with classical derivative. We conclude that the algorithm is applicable, efficient and gives reliable results.

Keywords

fractional control problem; differential transformation method

Released

17.11.2017

ISBN

978-1-5386-2085-4

Book

Proceedings of European Conference on Electrical Engineering and Computer Science 2017

Pages from

107

Pages to

111

Pages count

5

BibTex

``````
@inproceedings{BUT149810,
author="Josef {Rebenda} and Zdeněk {Šmarda}",
title="Numerical Solution of Fractional Control Problems via Fractional Differential Transformation",
annote="In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new algorithm convenient for numerical approximation of a solution of the studied problem. The method consists of the fractional differential transformation in combination with general methods of steps. The original system is transformed to a system of recurrence relations. Approximation of the solution is given in the form of truncated fractional power series. The choice of order of the fractional power series is discussed and the order is determined in relation to the order of the system. An application on a two-dimensional fractional system is shown. Exact solution is found for the first two intervals of the method of steps. The result for Caputo derivative of order 1 coincides with the solution of first-order system with classical derivative. We conclude that the algorithm is applicable, efficient and gives reliable results.",
booktitle="Proceedings of European Conference on Electrical Engineering and Computer Science 2017",
chapter="149810",
doi="10.1109/EECS.2017.29",
howpublished="online",
year="2017",
month="november",
pages="107--111",
type="conference paper"
}``````