IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i12p2102-d840933.html
   My bibliography  Save this article

Observer-Based Finite-Time H ∞ Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model

Author

Listed:
  • Zhiguo Yan

    (School of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Zhiwei Zhang

    (School of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Guolin Hu

    (School of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Baolong Zhu

    (School of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

Abstract

This paper studies the problem of the finite-time H ∞ 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 H ∞ 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 H ∞ 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.

Suggested Citation

  • Zhiguo Yan & Zhiwei Zhang & Guolin Hu & Baolong Zhu, 2022. "Observer-Based Finite-Time H ∞ Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model," Mathematics, MDPI, vol. 10(12), pages 1-15, June.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2102-:d:840933
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/12/2102/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/12/2102/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mohsen Bakouri & Ahmed Alassaf & Khaled Alshareef & Saleh Abdelsalam & Husham Farouk Ismail & Ali Ganoun & Abdul-Hakeem Alomari, 2022. "An Optimal H-Infinity Controller for Left Ventricular Assist Devices Based on a Starling-like Controller: A Simulation Study," Mathematics, MDPI, vol. 10(5), pages 1-17, February.
    2. Flávio Faria & Geraldo Silva & Vilma Oliveira, 2013. "Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(10), pages 1956-1969.
    3. Zhou, Jianping & Park, Ju H. & Ma, Qian, 2016. "Non-fragile observer-based H∞ control for stochastic time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 69-83.
    4. Xiao-Heng Chang & Guang-Hong Yang & Haibo Wang, 2011. "Observer-based -control for discrete-time T–S fuzzy systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(10), pages 1801-1809.
    5. Hakim Achour & Djamel Boukhetala & Hilal Labdelaoui, 2020. "An observer-based robust H∞ controller design for uncertain Takagi–Sugeno fuzzy systems with unknown premise variables using particle swarm optimisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(14), pages 2563-2581, October.
    6. Guolin Hu & Jian Zhang & Zhiguo Yan, 2022. "An improved approach to fuzzy dynamic output feedback H∞ control of continuous-time Takagi–Sugeno fuzzy systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(7), pages 1529-1544, May.
    7. Yan, Zhiguo & Zhang, Min & Chang, Gaizhen & Lv, Hui & Park, Ju H., 2022. "Finite-time annular domain stability and stabilization of Itô stochastic systems with Wiener noise and Poisson jumps-differential Gronwall inequality approach," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    8. Joby, Maya & Santra, Srimanta & Anthoni, S. Marshal, 2021. "Finite-time contractive boundedness of extracorporeal blood circulation process," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guolin Hu & Jian Zhang & Zhiguo Yan, 2022. "Local H ∞ Control for Continuous-Time T-S Fuzzy Systems via Generalized Non-Quadratic Lyapunov Functions," Mathematics, MDPI, vol. 10(19), pages 1-13, September.
    2. Mohammad Hassan Asemani & Vahid Johari Majd, 2015. "A robust -tracking design for uncertain Takagi–Sugeno fuzzy systems with unknown premise variables using descriptor redundancy approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(16), pages 2955-2972, December.
    3. Jing Sheng & Yunhai Geng & Min Li & Baolong Zhu, 2023. "Finite-Time Contractive Control of Spacecraft Rendezvous System," Mathematics, MDPI, vol. 11(8), pages 1-14, April.
    4. You, Luyao & Yang, Xueyan & Wu, Shuchen & Li, Xiaodi, 2023. "Finite-time stabilization for uncertain nonlinear systems with impulsive disturbance via aperiodic intermittent control," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    5. Sakthivel, R. & Joby, Maya & Wang, Chao & Kaviarasan, B., 2018. "Finite-time fault-tolerant control of neutral systems against actuator saturation and nonlinear actuator faults," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 425-436.
    6. Luo, Jinnan & Tian, Wenhong & Zhong, Shouming & Shi, Kaibo & Chen, Hao & Gu, Xian-Ming & Wang, Wenqin, 2017. "Non-fragile asynchronous H∞ control for uncertain stochastic memory systems with Bernoulli distribution," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 109-128.
    7. Vimal Kumar, S. & Raja, R. & Marshal Anthoni, S. & Cao, Jinde & Tu, Zhengwen, 2018. "Robust finite-time non-fragile sampled-data control for T-S fuzzy flexible spacecraft model with stochastic actuator faults," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 483-497.
    8. Zhou, Yu & Pan, Yingnan & Li, Shubo & Liang, Hongjing, 2020. "Event-triggered cooperative containment control for a class of uncertain non-identical networks," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    9. Zhou, Jianping & Sang, Chengyan & Li, Xiao & Fang, Muyun & Wang, Zhen, 2018. "H∞ consensus for nonlinear stochastic multi-agent systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 41-58.
    10. Harshavarthini, S. & Sakthivel, R. & Ma, Yong-Ki & Muslim, M., 2020. "Finite-time resilient fault-tolerant investment policy scheme for chaotic nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    11. Wu, Kai-Ning & Sun, Han-Xiao & Yang, Baoqing & Lim, Cheng-Chew, 2018. "Finite-time boundary control for delay reaction–diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 52-63.
    12. Liang Zhu & Baolong Zhu & Zhiguo Yan & Guolin Hu, 2022. "Finite-Time Contractively Bounded Control of Positive Linear Systems under H ∞ Performance and Its Application to Pest Management," Mathematics, MDPI, vol. 10(12), pages 1-13, June.
    13. Xiong, Jun & Chang, Xiao-Heng & Yi, Xiaojian, 2018. "Design of robust nonfragile fault detection filter for uncertain dynamic systems with quantization," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 774-788.
    14. Yu, Peng & Ma, Yuechao, 2020. "Observer-based asynchronous control for Markov jump systems," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    15. Kaviarasan, Boomipalagan & Kwon, Oh-Min & Park, Myeong Jin & Sakthivel, Rathinasamy, 2021. "Stochastic faulty estimator-based non-fragile tracking controller for multi-agent systems with communication delay," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    16. Thanh Binh Nguyen & Hyoung-Kyu Song, 2022. "Further Results on Robust Output-Feedback Dissipative Control of Markovian Jump Fuzzy Systems with Model Uncertainties," Mathematics, MDPI, vol. 10(19), pages 1-16, October.
    17. Che, Haochi & Huang, Jun & Zhao, Xudong & Ma, Xiang & Xu, Ning, 2020. "Functional interval observer for discrete-time systems with disturbances," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    18. Long, Shaohua & Wu, Yunlong & Zhong, Shouming & Zhang, Dian, 2018. "Stability analysis for a class of neutral type singular systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 113-131.
    19. Liu, Yanli & Wang, Runzhi & Hao, Li-Ying, 2022. "Adaptive TD control of full-state-constrained nonlinear stochastic switched systems," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    20. Kavikumar, R. & Kwon, O.M. & Sakthivel, R. & Lee, S.H. & Choi, S.G. & Priyanka, S., 2022. "Sliding mode control for IT2 fuzzy semi-Markov systems with faults and disturbances," Applied Mathematics and Computation, Elsevier, vol. 423(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2102-:d:840933. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.