IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v153y2021ip1s0960077921007876.html
   My bibliography  Save this article

Chaos synchronization using differential equations as extended state observer

Author

Listed:
  • Izadbakhsh, Alireza
  • Nikdel, Nazila

Abstract

In this paper, an extended state observer (ESO) is presented for synchronizing a chaotic master-slave system based on linear differential equations. The universal approximation property enables linear differential equations to estimate uncertainties, consisting of disturbances and unmodeled dynamics. The main contribution of this study is developing a control scheme based on ESO, which is designed using differential equations. In other words, an Nth-order linear differential equation is utilized to model the lumped uncertainty. The controller is proposed based on a model-free approach to eliminate the need for accurate information from the system model and assure a robust tracking performance. Furthermore, a thorough mathematical analysis is given based on the Lyapunov stability theorem to confirm the uniform ultimate boundedness of the observation/tracking approximation errors. To analyze the performance of the ESO-controller scheme in terms of transient response behavior and robustness, the Duffing-Holmes oscillator is considered as the simulation testbed. A set of five different experiments are conducted to evaluate the efficiency of the introduced control approach. The results of ESO are also compared with two powerful approximation methods.

Suggested Citation

  • Izadbakhsh, Alireza & Nikdel, Nazila, 2021. "Chaos synchronization using differential equations as extended state observer," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
  • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s0960077921007876
    DOI: 10.1016/j.chaos.2021.111433
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921007876
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2021.111433?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. Asiain, Erick & Garrido, Rubén, 2021. "Anti-Chaos control of a servo system using nonlinear model reference adaptive control," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. 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).
    3. Xiong, Pei-Ying & Jahanshahi, Hadi & Alcaraz, Raúl & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alsaadi, Fawaz E., 2021. "Spectral Entropy Analysis and Synchronization of a Multi-Stable Fractional-Order Chaotic System using a Novel Neural Network-Based Chattering-Free Sliding Mode Technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Akinlar, Mehmet Ali & Tchier, Fairouz & Inc, Mustafa, 2020. "Chaos control and solutions of fractional-order Malkus waterwheel model," Chaos, Solitons & Fractals, Elsevier, vol. 135(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. Muhammad Marwan & Vagner Dos Santos & Muhammad Zainul Abidin & Anda Xiong, 2022. "Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems," Mathematics, MDPI, vol. 10(11), pages 1-15, June.

    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. Alsaade, Fawaz W. & Yao, Qijia & Bekiros, Stelios & Al-zahrani, Mohammed S. & Alzahrani, Ali S. & Jahanshahi, Hadi, 2022. "Chaotic attitude synchronization and anti-synchronization of master-slave satellites using a robust fixed-time adaptive controller," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Kavuran, Gürkan, 2022. "When machine learning meets fractional-order chaotic signals: detecting dynamical variations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Ávalos-Ruíz, L.F. & Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Cortes-Campos, H.M. & Lavín-Delgado, J.E., 2023. "A RGB image encryption technique using chaotic maps of fractional variable-order based on DNA encoding," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    4. Bekiros, Stelios & Yao, Qijia & Mou, Jun & Alkhateeb, Abdulhameed F. & Jahanshahi, Hadi, 2023. "Adaptive fixed-time robust control for function projective synchronization of hyperchaotic economic systems with external perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    5. Ouannas, Adel & Batiha, Iqbal M. & Bekiros, Stelios & Liu, Jinping & Jahanshahi, Hadi & Aly, Ayman A. & Alghtani, Abdulaziz H., 2021. "Synchronization of the glycolysis reaction-diffusion model via linear control law," LSE Research Online Documents on Economics 112776, London School of Economics and Political Science, LSE Library.
    6. Yan, Fang & Hou, Xiaorong & Tian, Tingting & Chen, Xiaojie, 2023. "Nonlinear model reference adaptive control approach for governance of the commons in a feedback-evolving game," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    7. Chu, Xiaoyan & Xu, Liguang & Hu, Hongxiao, 2020. "Exponential quasi-synchronization of conformable fractional-order complex dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. Liu, Chongyang & Zhou, Tuo & Gong, Zhaohua & Yi, Xiaopeng & Teo, Kok Lay & Wang, Song, 2023. "Robust optimal control of nonlinear fractional systems," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    9. Bekiros, Stelios & Jahanshahi, Hadi & Bezzina, Frank & Aly, Ayman A., 2021. "A novel fuzzy mixed H2/H∞ optimal controller for hyperchaotic financial systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Guo, Pengteng & Shi, Qiqing & Jian, Zeng & Zhang, Jing & Ding, Qun & Yan, Wenhao, 2024. "An intelligent controller of homo-structured chaotic systems under noisy conditions and applications in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    11. Khalid A. Alattas & Mai The Vu & Omid Mofid & Fayez F. M. El-Sousy & Abdullah K. Alanazi & Jan Awrejcewicz & Saleh Mobayen, 2022. "Adaptive Nonsingular Terminal Sliding Mode Control for Performance Improvement of Perturbed Nonlinear Systems," Mathematics, MDPI, vol. 10(7), pages 1-18, March.
    12. Yan, Shaohui & Wang, Ertong & Gu, Binxian & Wang, Qiyu & Ren, Yu & Wang, Jianjian, 2022. "Analysis and finite-time synchronization of a novel double-wing chaotic system with transient chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    13. Hu, Chenyang & Wang, Qiao & Zhang, Xiefu & Tian, Zean & Wu, Xianming, 2022. "A new chaotic system with novel multiple shapes of two-channel attractors," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    14. Deepika, S. & Veeresha, P., 2023. "Dynamics of chaotic waterwheel model with the asymmetric flow within the frame of Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    15. Qijia Yao & Hadi Jahanshahi & Stelios Bekiros & Jinping Liu & Abdullah A. Al-Barakati, 2023. "Fixed-Time Adaptive Chaotic Control for Permanent Magnet Synchronous Motor Subject to Unknown Parameters and Perturbations," Mathematics, MDPI, vol. 11(14), pages 1-14, July.
    16. Wu, Qianqian & Yang, Dan & Li, Xiaodi, 2023. "Output tracking control for state-dependent switched systems with input delay," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    17. Wang, Yong-Long & Jahanshahi, Hadi & Bekiros, Stelios & Bezzina, Frank & Chu, Yu-Ming & Aly, Ayman A., 2021. "Deep recurrent neural networks with finite-time terminal sliding mode control for a chaotic fractional-order financial system with market confidence," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    18. Ahmad, Israr, 2021. "A Lyapunov-based direct adaptive controller for the suppression and synchronization of a perturbed nuclear spin generator chaotic system," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    19. Xin, Baogui & Peng, Wei & Kwon, Yekyung, 2020. "A discrete fractional-order Cournot duopoly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    20. Ostrovskii, Valerii Yu. & Rybin, Vyacheslav G. & Karimov, Artur I. & Butusov, Denis N., 2022. "Inducing multistability in discrete chaotic systems using numerical integration with variable symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

    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:153:y:2021:i:p1:s0960077921007876. 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.