On the robustness of the integrable trajectories of the control systems with limited control resources
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| Title: | On the robustness of the integrable trajectories of the control systems with limited control resources |
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| Authors: | Hüseyin, Nesir, Hüseyin, Anar, Guseinov, Khalik |
| Contributors: | Eğitim Fakültesi, Fen Fakültesi, orcid:0000-0002-3911-2304, orcid:0000-0001-7652-1505 |
| Source: | Archives of Control Sciences, Vol vol. 33, Iss No 3 (2023) |
| Publication Status: | Preprint |
| Publisher Information: | Polish Academy of Sciences Chancellery, 2023. |
| Publication Year: | 2023 |
| Subject Terms: | nonlinear control system, integral equation, integral constraint, integrable trajectory, robustness, 0209 industrial biotechnology, 93C23, 93C35, 45G15, integrable trajectory, nonlinear control system, robustness, Information technology, 02 engineering and technology, T58.5-58.64, 01 natural sciences, integral equation, Optimization and Control (math.OC), 0103 physical sciences, QA1-939, FOS: Mathematics, 0101 mathematics, Mathematics - Optimization and Control, integral constraint, Mathematics |
| Description: | The control system described by Urysohn type integral equation is considered where the system is nonlinear with respect to the phase vector and is affine with respect to the control vector. The control functions are chosen from the closed ball of the space $L_q\left(��;\mathbb{R}^m\right),$ $q>1,$ with radius $r$ and centered at the origin. The trajectory of the system is defined as $p$-integrable multivariable function from the space $L_p\left(��;\mathbb{R}^n\right),$ $\frac{1}{q}+\frac{1}{p}=1,$ satisfying the system's equation almost everywhere. It is shown that the system's trajectories are robust with respect to the remaining control resource. Applying this result it is proved that every trajectory can be approximated by the trajectory obtained by full consumption of the total control resource. |
| Document Type: | Article |
| File Description: | application/pdf |
| Language: | Polish |
| ISSN: | 1230-2384 |
| DOI: | 10.24425/acs.2023.146958 |
| DOI: | 10.48550/arxiv.2105.05967 |
| Access URL: | http://arxiv.org/abs/2105.05967 https://hdl.handle.net/20.500.12418/14132 https://hdl.handle.net/20.500.12418/14128 https://hdl.handle.net/20.500.12418/14153 https://hdl.handle.net/20.500.12418/14134 https://hdl.handle.net/20.500.12418/14133 https://hdl.handle.net/20.500.12418/35248 https://hdl.handle.net/20.500.12418/14130 |
| Rights: | arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....263cce1d504c9449a122b190e31e2a40 |
| Database: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | The control system described by Urysohn type integral equation is considered where the system is nonlinear with respect to the phase vector and is affine with respect to the control vector. The control functions are chosen from the closed ball of the space $L_q\left(��;\mathbb{R}^m\right),$ $q>1,$ with radius $r$ and centered at the origin. The trajectory of the system is defined as $p$-integrable multivariable function from the space $L_p\left(��;\mathbb{R}^n\right),$ $\frac{1}{q}+\frac{1}{p}=1,$ satisfying the system's equation almost everywhere. It is shown that the system's trajectories are robust with respect to the remaining control resource. Applying this result it is proved that every trajectory can be approximated by the trajectory obtained by full consumption of the total control resource. |
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| ISSN: | 12302384 |
| DOI: | 10.24425/acs.2023.146958 |