Anar Huseyin, Nesir Huseyin, Khalik G. Guseinov
Abstract:
This article studies approximations to the set of trajectories, attainable sets and
integral funnel of a control system described by an ordinary differential equation.
It is assumed that the equation is nonlinear with respect to the phase state vector
and affine with respect to the control vector.
The system includes control functions, some of which satisfy the \(L_p\)
\((p\in (1,\infty))\) norm constraint, while the others satisfy the
\(L_{\infty}\) norm constraint. Step by step, the set of admissible control functions
is replaced by a set consisting of a finite number of piecewise-constant control
functions that generate a finite number of trajectories.
Error evaluations are provided for the Hausdorff distances between the set of
trajectories, attainable sets, integral funnel, and their approximations,
which depend on discretization parameters.
Submitted December 7, 2025. Published April 13, 2026.
Math Subject Classifications: 93B03, 93C10, 34H05, 49M25.
Key Words: Control system; geometric constraint; integral constraint; trajectories;
attainable set; integral funnel; approximation.
DOI: 10.58997/ejde.2026.27
Show me the PDF file (449 KB), TEX file for this article.
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Anar Huseyin Department of Statistics and Computer Sciences Faculty of Science, Cumhuriyet University Sivas 58140, Turkey email: ahuseyin@cumhuriyet.edu.tr |
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Nesir Huseyin Department of Mathematics and Science Education Faculty of Education, Cumhuriyet University Sivas 58140, Turkey email: nhuseyin@cumhuriyet.edu.tr |
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Khalik G. Guseinov Krasovskii Institute of Mathematics and Mechanics Ural Branch of the Russian Academy of Sciences Yekaterinburg 620108, Russia email: k.g.guseinov@gmail.com |
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