On application of Rothe's fixed point theorem to study the controllability of fractional semilinear systems with delays

Beata Sikora

Kybernetika (2019)

  • Volume: 55, Issue: 4, page 675-689
  • ISSN: 0023-5954

Abstract

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The paper presents finite-dimensional dynamical control systems described by semilinear fractional-order state equations with multiple delays in the control and nonlinear function f . The relative controllability of the presented semilinear system is discussed. Rothe’s fixed point theorem is applied to study the controllability of the fractional-order semilinear system. A control that steers the semilinear system from an initial complete state to a final state at time t > 0 is presented. A numerical example is provided to illustrate the obtained theoretical results and a practical example is given to show a possible application of the study.

How to cite

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Sikora, Beata. "On application of Rothe's fixed point theorem to study the controllability of fractional semilinear systems with delays." Kybernetika 55.4 (2019): 675-689. <http://eudml.org/doc/295056>.

@article{Sikora2019,
abstract = {The paper presents finite-dimensional dynamical control systems described by semilinear fractional-order state equations with multiple delays in the control and nonlinear function $f$. The relative controllability of the presented semilinear system is discussed. Rothe’s fixed point theorem is applied to study the controllability of the fractional-order semilinear system. A control that steers the semilinear system from an initial complete state to a final state at time $t>0$ is presented. A numerical example is provided to illustrate the obtained theoretical results and a practical example is given to show a possible application of the study.},
author = {Sikora, Beata},
journal = {Kybernetika},
keywords = {fractional systems; semilinear control systems; Rothe's fixed point theorem; delays in control; pseudo-transition matrix; the Caputo derivative},
language = {eng},
number = {4},
pages = {675-689},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On application of Rothe's fixed point theorem to study the controllability of fractional semilinear systems with delays},
url = {http://eudml.org/doc/295056},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Sikora, Beata
TI - On application of Rothe's fixed point theorem to study the controllability of fractional semilinear systems with delays
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 4
SP - 675
EP - 689
AB - The paper presents finite-dimensional dynamical control systems described by semilinear fractional-order state equations with multiple delays in the control and nonlinear function $f$. The relative controllability of the presented semilinear system is discussed. Rothe’s fixed point theorem is applied to study the controllability of the fractional-order semilinear system. A control that steers the semilinear system from an initial complete state to a final state at time $t>0$ is presented. A numerical example is provided to illustrate the obtained theoretical results and a practical example is given to show a possible application of the study.
LA - eng
KW - fractional systems; semilinear control systems; Rothe's fixed point theorem; delays in control; pseudo-transition matrix; the Caputo derivative
UR - http://eudml.org/doc/295056
ER -

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