Observer-Based Finite-Time <i>H</i><sub>∞</sub> Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model
This paper studies the problem of the finite-time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/12/2102 |
| _version_ | 1797484709327929344 |
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| author | Zhiguo Yan Zhiwei Zhang Guolin Hu Baolong Zhu |
| author_facet | Zhiguo Yan Zhiwei Zhang Guolin Hu Baolong Zhu |
| author_sort | Zhiguo Yan |
| collection | DOAJ |
| description | This paper studies the problem of the finite-time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> control of the blood gases system, presented as a T-S fuzzy model with bounded disturbance during extracorporeal circulation. The aim was to design an observer-based fuzzy controller to ensure that the closed-loop system was finite-time bounded with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> performance. Firstly, different from the existing results, the T-S fuzzy model of a blood gas control system was developed and a new method was given to process the time derivatives of the membership functions. Secondly, based on the fuzzy Lyapunov function, sufficient conditions for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> finite-time boundedness of the system were obtained by using Finsler’s lemma and matrix decoupling techniques. Simulation results are provided to demonstrate the effectiveness of the proposed methodology. |
| first_indexed | 2024-03-09T23:08:20Z |
| format | Article |
| id | doaj.art-e9947616088a41c88a25a9144e824b49 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:08:20Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e9947616088a41c88a25a9144e824b492023-11-23T17:49:45ZengMDPI AGMathematics2227-73902022-06-011012210210.3390/math10122102Observer-Based Finite-Time <i>H</i><sub>∞</sub> Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy ModelZhiguo Yan0Zhiwei Zhang1Guolin Hu2Baolong Zhu3School of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, ChinaSchool of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, ChinaSchool of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, ChinaSchool of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, ChinaThis paper studies the problem of the finite-time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> control of the blood gases system, presented as a T-S fuzzy model with bounded disturbance during extracorporeal circulation. The aim was to design an observer-based fuzzy controller to ensure that the closed-loop system was finite-time bounded with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> performance. Firstly, different from the existing results, the T-S fuzzy model of a blood gas control system was developed and a new method was given to process the time derivatives of the membership functions. Secondly, based on the fuzzy Lyapunov function, sufficient conditions for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> finite-time boundedness of the system were obtained by using Finsler’s lemma and matrix decoupling techniques. Simulation results are provided to demonstrate the effectiveness of the proposed methodology.https://www.mdpi.com/2227-7390/10/12/2102observer-based fuzzy controllerfuzzy Lyapunov functionT-S fuzzy modelfinite-time boundedness |
| spellingShingle | Zhiguo Yan Zhiwei Zhang Guolin Hu Baolong Zhu Observer-Based Finite-Time <i>H</i><sub>∞</sub> Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model Mathematics observer-based fuzzy controller fuzzy Lyapunov function T-S fuzzy model finite-time boundedness |
| title | Observer-Based Finite-Time <i>H</i><sub>∞</sub> Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model |
| title_full | Observer-Based Finite-Time <i>H</i><sub>∞</sub> Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model |
| title_fullStr | Observer-Based Finite-Time <i>H</i><sub>∞</sub> Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model |
| title_full_unstemmed | Observer-Based Finite-Time <i>H</i><sub>∞</sub> Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model |
| title_short | Observer-Based Finite-Time <i>H</i><sub>∞</sub> Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model |
| title_sort | observer based finite time i h i sub ∞ sub control of the blood gases system in extracorporeal circulation via the t s fuzzy model |
| topic | observer-based fuzzy controller fuzzy Lyapunov function T-S fuzzy model finite-time boundedness |
| url | https://www.mdpi.com/2227-7390/10/12/2102 |
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