IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v150y2021ics0960077921004963.html
   My bibliography  Save this article

Tracking control with disturbance rejection of nonlinear fractional order fuzzy systems: Modified repetitive control approach

Author

Listed:
  • Mahmoudabadi, Parvin
  • Tavakoli-Kakhki, Mahsan

Abstract

This paper addresses the problem of tracking control and disturbance rejection for nonlinear fractional order systems. To this end, based on Takagi-Sugeno (T-S) fuzzy modeling approach and a fractional order modified repetitive controller, an output feedback strategy is constructed for a class of nonlinear fractional order systems. T-S fuzzy model represents an accurate model of nonlinear fractional order systems and simplifies the procedure of control system design. By introducing a novel Fuzzy Lyapunov Function (FLF), sufficient conditions are established in the framework of Linear Matrix Inequalities (LMIs) to ensure the stability of the closed-loop system. Based on the achieved conditions, it is shown that the external disturbance is attenuated and the output of the system tracks the periodic reference input with an ignorable error. Lastly, three examples including fractional order Chua’s circuit, Lorenz-like and Chen systems are performed to show the efficiency of the method proposed in this paper.

Suggested Citation

  • Mahmoudabadi, Parvin & Tavakoli-Kakhki, Mahsan, 2021. "Tracking control with disturbance rejection of nonlinear fractional order fuzzy systems: Modified repetitive control approach," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004963
    DOI: 10.1016/j.chaos.2021.111142
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921004963
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111142?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. Fausto Cavallaro, 2015. "A Takagi-Sugeno Fuzzy Inference System for Developing a Sustainability Index of Biomass," Sustainability, MDPI, vol. 7(9), pages 1-13, September.
    2. Al-khedhairi, A. & Matouk, A.E. & Khan, I., 2019. "Chaotic dynamics and chaos control for the fractional-order geomagnetic field model," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 390-401.
    3. Pratap, A. & Raja, R. & Cao, J. & Rihan, Fathalla A. & Seadawy, Aly R., 2020. "Quasi-pinning synchronization and stabilization of fractional order BAM neural networks with delays and discontinuous neuron activations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Li, Hong-Li & Kao, Yonggui & Hu, Cheng & Jiang, Haijun & Jiang, Yao-Lin, 2021. "Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Baba, Bashir Abdullahi & Bilgehan, Bulent, 2021. "Optimal control of a fractional order model for the COVID – 19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    6. Gao, Richie, 2019. "A novel track control for Lorenz system with single state feedback," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 236-244.
    7. Sachin Bhalekar, 2012. "Chaos Control and Synchronization in Fractional-Order Lorenz-Like System," International Journal of Differential Equations, Hindawi, vol. 2012, pages 1-16, August.
    8. Nian, Fuzhong & Liu, Xinmeng & Zhang, Yaqiong, 2018. "Sliding mode synchronization of fractional-order complex chaotic system with parametric and external disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 22-28.
    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. Huan, Mingchen & Li, Chuandong, 2022. "Stability analysis of state-dependent impulsive systems via a new two-sided looped functional," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Abinandhitha, R. & Sakthivel, R. & Tatar, N. & Manikandan, R., 2022. "Anti-disturbance observer-based control for fuzzy chaotic semi-Markov jump systems with multiple disturbances and mixed actuator failures," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Shu, Jingsi & Zhang, Yongping, 2023. "Fractal control and synchronization of population competition model based on the T–S fuzzy model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. Pishro, Aboozar & Shahrokhi, Mohammad & Mohit, Mohammaderfan, 2023. "Adaptive neural quantized control for fractional-order full-state constrained non-strict feedback systems subject to input fault and nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Mohanapriya, S. & Crispin Sweety, C. Antony & Satheesh, T. & Sakthivel, R. & Kwon, O.M., 2024. "Modified equivalent input disturbance estimator-based active disturbance rejection for fractional-order T-S fuzzy stochastic systems," Chaos, Solitons & Fractals, Elsevier, vol. 182(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. Zhenyu Zhu & Zhanshan Zhao & Haoliang Cui & Fengdong Shi, 2019. "Improved T-S Fuzzy Control for Uncertain Time-Delay Coronary Artery System," Complexity, Hindawi, vol. 2019, pages 1-11, May.
    2. Alsaedi, Ahmed & Cao, Jinde & Ahmad, Bashir & Alshehri, Ahmed & Tan, Xuegang, 2022. "Synchronization of master-slave memristive neural networks via fuzzy output-based adaptive strategy," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    3. Zhang, Zhengqiu & Yang, Zhen, 2023. "Asymptotic stability for quaternion-valued fuzzy BAM neural networks via integral inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Chunli Zhang & Yangjie Gao & Junliang Yao & Fucai Qian, 2024. "Synchronization of Bidirectionally Coupled Fractional-Order Chaotic Systems with Unknown Time-Varying Parameter Disturbance in Different Dimensions," Mathematics, MDPI, vol. 12(17), pages 1-16, September.
    5. C. J. Luis Pérez, 2020. "Using a Fuzzy Inference System to Obtain Technological Tables for Electrical Discharge Machining Processes," Mathematics, MDPI, vol. 8(6), pages 1-26, June.
    6. Zhen Yang & Zhengqiu Zhang, 2022. "Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
    7. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Xu, Changjin & Liu, Zixin & Liao, Maoxin & Li, Peiluan & Xiao, Qimei & Yuan, Shuai, 2021. "Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 471-494.
    9. Mehrbakhsh Nilashi & Fausto Cavallaro & Abbas Mardani & Edmundas Kazimieras Zavadskas & Sarminah Samad & Othman Ibrahim, 2018. "Measuring Country Sustainability Performance Using Ensembles of Neuro-Fuzzy Technique," Sustainability, MDPI, vol. 10(8), pages 1-20, August.
    10. Yu, Nanxiang & Zhu, Wei, 2021. "Event-triggered impulsive chaotic synchronization of fractional-order differential systems," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    11. Fausto Cavallaro & Edmundas Kazimieras Zavadskas & Saulius Raslanas, 2016. "Evaluation of Combined Heat and Power (CHP) Systems Using Fuzzy Shannon Entropy and Fuzzy TOPSIS," Sustainability, MDPI, vol. 8(6), pages 1-21, June.
    12. Hongguang Fan & Yue Rao & Kaibo Shi & Hui Wen, 2023. "Global Synchronization of Fractional-Order Multi-Delay Coupled Neural Networks with Multi-Link Complicated Structures via Hybrid Impulsive Control," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    13. Kashkynbayev, Ardak & Cao, Jinde & Suragan, Durvudkhan, 2021. "Global Lagrange stability analysis of retarded SICNNs," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    14. Shafiya, M. & Nagamani, G., 2022. "New finite-time passivity criteria for delayed fractional-order neural networks based on Lyapunov function approach," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    15. Stamov, Gani & Stamova, Ivanka & Martynyuk, Anatoliy & Stamov, Trayan, 2021. "Almost periodic dynamics in a new class of impulsive reaction–diffusion neural networks with fractional-like derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    16. C. J. Luis Pérez, 2020. "A Proposal of an Adaptive Neuro-Fuzzy Inference System for Modeling Experimental Data in Manufacturing Engineering," Mathematics, MDPI, vol. 8(9), pages 1-38, August.
    17. Zheng, Bibo & Wang, Zhanshan, 2022. "Mittag-Leffler synchronization of fractional-order coupled neural networks with mixed delays," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    18. Wang, Shuzhan & Zhang, Ziye & Lin, Chong & Chen, Jian, 2021. "Fixed-time synchronization for complex-valued BAM neural networks with time-varying delays via pinning control and adaptive pinning control," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    19. Gani Stamov & Ivanka Stamova & Stanislav Simeonov & Ivan Torlakov, 2020. "On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    20. Ameen, Ismail Gad & Baleanu, Dumitru & Ali, Hegagi Mohamed, 2022. "Different strategies to confront maize streak disease based on fractional optimal control formulation," Chaos, Solitons & Fractals, Elsevier, vol. 164(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:chsofr:v:150:y:2021:i:c:s0960077921004963. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.