IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v410y2021ics0096300321005567.html
   My bibliography  Save this article

Proportional integral observer based tracking control design for Markov jump systems

Author

Listed:
  • Vijayakumar, M.
  • Sakthivel, R.
  • Mohammadzadeh, Ardashir
  • Karthick, S.A.
  • Marshal Anthoni, S.

Abstract

With the use of proportional integral observer, this article intends to discuss an effective output tracking control and disturbance rejection problem for an input time-delayed Markov jump system with state dependent nonlinearities and randomly occurring uncertainties. Notably, the proportional integral observer incorporates both proportional and integral loop, where the presence of additional loop provides unbiased state estimation. Moreover, an improved equivalent input disturbance approach with a gain factor is considered to enhance better disturbance estimation and rejection performance. Naturally, Smith predictor is commenced to handle input time delays. Subsequently, the combination of improved equivalent input disturbance with Smith predictor guarantees the desired tracking performance with input time delays and external disturbances. By endowing Lyapunov stability theory, a set of sufficient conditions is developed in the frame of linear matrix inequalities to promise the asymptotically stability of the closed-loop system. Subsequently, the explicit form of the desired proportional integral gain matrices are parameterized using the matrix inequality techniques. The superiority of our proffered control technique are validated through two numerical examples, which includes a practical model namely RLC circuit.

Suggested Citation

  • Vijayakumar, M. & Sakthivel, R. & Mohammadzadeh, Ardashir & Karthick, S.A. & Marshal Anthoni, S., 2021. "Proportional integral observer based tracking control design for Markov jump systems," Applied Mathematics and Computation, Elsevier, vol. 410(C).
  • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005567
    DOI: 10.1016/j.amc.2021.126467
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321005567
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2021.126467?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Du, Xiao-Kun & Zhao, Hui & Chang, Xiao-Heng, 2015. "Unknown input observer design for fuzzy systems with uncertainties," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 108-118.
    2. Qunxian Zheng & Youzhu Ling & Lisheng Wei & Hongbin Zhang, 2018. "Mixed H∞ and passive control for linear switched systems via hybrid control approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(4), pages 818-832, March.
    3. Liu, Xinmiao & Xia, Jianwei & Huang, Xia & Shen, Hao, 2020. "Generalized synchronization for coupled Markovian neural networks subject to randomly occurring parameter uncertainties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. Hu, Xiaohui & Xia, Jianwei & Wei, Yunliang & Meng, Bo & Shen, Hao, 2019. "Passivity-based state synchronization for semi-Markov jump coupled chaotic neural networks with randomly occurring time delays," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 32-41.
    5. Song, Jia-Sheng & Chang, Xiao-Heng, 2020. "H∞ controller design of networked control systems with a new quantization structure," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    6. Wu, Li-Bing & Park, Ju H. & Xie, Xiang-Peng & Liu, Ya-Juan & Yang, Zhi-Chun, 2020. "Event-triggered adaptive asymptotic tracking control of uncertain nonlinear systems with unknown dead-zone constraints," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xu, Qiyi & Zhang, Ning & Qi, Wenhai, 2023. "Finite-time control for discrete-time nonlinear Markov switching LPV systems with DoS attacks," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    2. Zhang, Ning & Qi, Wenhai & Pang, Guocheng & Cheng, Jun & Shi, Kaibo, 2022. "Observer-based sliding mode control for fuzzy stochastic switching systems with deception attacks," Applied Mathematics and Computation, Elsevier, vol. 427(C).

    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. Huang, Yao & Bao, Haibo, 2020. "Master-slave synchronization of complex-valued delayed chaotic Lur’e systems with sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    2. Zhao, Yongshun & Li, Xiaodi & Cao, Jinde, 2020. "Global exponential stability for impulsive systems with infinite distributed delay based on flexible impulse frequency," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. Li, Xin & Cheng, Kaijie & Zhu, Liangkuan & Wei, Guoliang, 2023. "Outlier-resistant interval observer design for multirate time-delayed systems under the adaptive event-triggered protocols," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    4. Liu, Lizhi & Wang, Yinhe & Gao, Zilin, 2020. "Tracking control for the dynamic links of discrete-time complex dynamical network via state observer," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    5. Wu, Tianyu & Huang, Xia & Chen, Xiangyong & Wang, Jing, 2020. "Sampled-data H∞ exponential synchronization for delayed semi-Markov jump CDNs: A looped-functional approach," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    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. Wang, Yuxiao & Cao, Yuting & Guo, Zhenyuan & Wen, Shiping, 2020. "Passivity and passification of memristive recurrent neural networks with multi-proportional delays and impulse," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    8. Houssem Jerbi & Mourad Kchaou & Attia Boudjemline & Mohamed Amin Regaieg & Sondes Ben Aoun & Ahmed Lakhdar Kouzou, 2021. "H ∞ and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults," Mathematics, MDPI, vol. 9(18), pages 1-25, September.
    9. Wang, Le & Sun, Wei & Su, Shun-Feng, 2022. "Adaptive asymptotic tracking control for nonlinear systems with state constraints and input saturation," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    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. Suriguga, & Kao, Yonggui & Shao, Chuntao & Chen, Xiangyong, 2021. "Stability of high-order delayed Markovian jumping reaction-diffusion HNNs with uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    12. Zhou, Wenjia & Hu, Yuanfa & Liu, Xiaoyang & Cao, Jinde, 2022. "Finite-time adaptive synchronization of coupled uncertain neural networks via intermittent control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    13. Liu, Shanlin & Niu, Ben & Zong, Guangdeng & Zhao, Xudong & Xu, Ning, 2022. "Adaptive fixed-time hierarchical sliding mode control for switched under-actuated systems with dead-zone constraints via event-triggered strategy," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    14. Zhang, Huasheng & Zhuang, Guangming & Sun, Wei & Li, Yongmin & Lu, Junwei, 2020. "pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized H-representation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    15. Harshavarthini, S. & Sakthivel, R. & Kong, F., 2020. "Finite-time synchronization of chaotic coronary artery system with input time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    16. Rajchakit, G. & Sriraman, R. & Vignesh, P. & Lim, C.P., 2021. "Impulsive effects on Clifford-valued neural networks with time-varying delays: An asymptotic stability analysis," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    17. Hu, Yifan & Liu, Wenhui & Liu, Guobao, 2022. "Adaptive finite‐time event‐triggered control for uncertain nonlinearly parameterized systems with unknown control direction and actuator failures," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    18. Yoo, Sung Jin, 2021. "Decentralized event-triggered adaptive control of a class of uncertain interconnected nonlinear systems using local state feedback corrupted by unknown injection data," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    19. Hu, Yue & Cai, Chenxiao & Lee, SeungHoon & Lee, YongGwon & Kwon, Oh-Min, 2023. "New results on H∞ control for interval type-2 fuzzy singularly perturbed systems with fading channel: The weighted try-once-discard protocol case," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    20. Yan, Yan & Wu, Libing & Yan, Weijun & Hu, Yuhan & Zhao, Nannan & Chen, Ming, 2022. "Finite-time event-triggered fault-tolerant control for a family of pure-feedback systems," Applied Mathematics and Computation, Elsevier, vol. 426(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:eee:apmaco:v:410:y:2021:i:c:s0096300321005567. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.