IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v141y2020ics0960077920307268.html
   My bibliography  Save this article

Simplified synchronizability scheme for a class of nonlinear systems connected in chain configuration using contraction

Author

Listed:
  • Anand, Pallov
  • Sharma, Bharat Bhushan

Abstract

This paper derives results for the stabilizing and synchronizing controller for a generalized class of nonlinear systems connected in chain configuration. The proposed procedure utilizes contraction based backstepping approach blended with Gershgorin theorem instead of Lyapunov stability based backstepping technique for designing controllers for such systems. A systematic step by step strategy is adopted to obtain a single controller to achieve stabilization of states of systems. Further, results are extended to synchronize the systems belonging to the given generalized class of nonlinear systems. The proposed procedure leads to quite a simple controller for targeted synchronization task in comparison to existing controllers in literature for such class of systems. The systems among which the synchronization has to be done are assumed to be connected in chain formation through one-way coupling. To verify the efficacy of the proposed approach, chaotic systems such as Lorenz-Stenflo, Chen, Lu¨ and Lorenz systems have been considered and detailed numerical validations are presented appropriately.

Suggested Citation

  • Anand, Pallov & Sharma, Bharat Bhushan, 2020. "Simplified synchronizability scheme for a class of nonlinear systems connected in chain configuration using contraction," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307268
    DOI: 10.1016/j.chaos.2020.110331
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920307268
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110331?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. Shukla, Manoj Kumar & Sharma, B.B., 2017. "Stabilization of a class of fractional order chaotic systems via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 56-62.
    2. Park, Ju H., 2005. "Stability criterion for synchronization of linearly coupled unified chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1319-1325.
    3. Chen, Hsien-Keng, 2005. "Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lü," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1049-1056.
    4. Kocamaz, Uğur Erkin & Cevher, Barış & Uyaroğlu, Yılmaz, 2017. "Control and synchronization of chaos with sliding mode control based on cubic reaching rule," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 92-98.
    5. Sharma, B.B. & Kar, I.N., 2009. "Parametric convergence and control of chaotic system using adaptive feedback linearization," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1475-1483.
    6. Singh, Piyush Pratap & Singh, Jay Prakash & Roy, B.K., 2014. "Synchronization and anti-synchronization of Lu and Bhalekar–Gejji chaotic systems using nonlinear active control," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 31-39.
    7. Shukla, Manoj Kumar & Sharma, B.B., 2017. "Backstepping based stabilization and synchronization of a class of fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 274-284.
    8. Li, Xian-Feng & Chu, Yan-Dong & Leung, Andrew Y.T. & Zhang, Hui, 2017. "Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 24-30.
    9. Ghamati, Mina & Balochian, Saeed, 2015. "Design of adaptive sliding mode control for synchronization Genesio–Tesi chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 111-117.
    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. Luo, Shaohua & Yang, Guanci & Li, Junyang & Ouakad, Hassen M., 2022. "Dynamic analysis, circuit realization and accelerated adaptive backstepping control of the FO MEMS gyroscope," Chaos, Solitons & Fractals, Elsevier, vol. 155(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. Cai, Xinshan & Liu, Ling & Wang, Yaoyu & Liu, Chongxin, 2021. "A 3D chaotic system with piece-wise lines shape non-hyperbolic equilibria and its predefined-time control," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Deepika, Deepika & Kaur, Sandeep & Narayan, Shiv, 2018. "Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 196-203.
    3. Weiqiu Pan & Tianzeng Li & Muhammad Sajid & Safdar Ali & Lingping Pu, 2022. "Parameter Identification and the Finite-Time Combination–Combination Synchronization of Fractional-Order Chaotic Systems with Different Structures under Multiple Stochastic Disturbances," Mathematics, MDPI, vol. 10(5), pages 1-26, February.
    4. Cai, Rui-Yang & Zhou, Hua-Cheng & Kou, Chun-Hai, 2021. "Boundary control strategy for three kinds of fractional heat equations with control-matched disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Runzi Luo & Meichun Huang & Haipeng Su, 2019. "Robust Control and Synchronization of 3-D Uncertain Fractional-Order Chaotic Systems with External Disturbances via Adding One Power Integrator Control," Complexity, Hindawi, vol. 2019, pages 1-11, May.
    6. Yu, Yongguang, 2008. "Adaptive synchronization of a unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 329-333.
    7. Tam, Lap Mou & Si Tou, Wai Meng, 2008. "Parametric study of the fractional-order Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 817-826.
    8. J. Humberto Pérez-Cruz & Pedro A. Tamayo-Meza & Maricela Figueroa & Ramón Silva-Ortigoza & Mario Ponce-Silva & R. Rivera-Blas & Mario Aldape-Pérez, 2019. "Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control," Complexity, Hindawi, vol. 2019, pages 1-10, July.
    9. Park, Ju H., 2005. "Chaos synchronization of a chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 579-584.
    10. Zhang, Huamin, 2018. "The eigenvalues range of a class of matrices and some applications in Cauchy–Schwarz inequality and iterative methods," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 37-48.
    11. 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).
    12. Singh, Jay Prakash & Roy, Binoy Krishna, 2018. "Five new 4-D autonomous conservative chaotic systems with various type of non-hyperbolic and lines of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 81-91.
    13. Hamid, Syeda Rabiya & Nazir, Muhammad Shahid & Rehan, Muhammad & ur Rashid, Haroon, 2019. "New results on regional observer-based stabilization for locally Lipchitz nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 173-184.
    14. Park, Ju H., 2006. "Synchronization of a class of chaotic dynamic systems with controller gain variations," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1279-1284.
    15. Min, Fuhong & Luo, Albert C.J., 2012. "Periodic and chaotic synchronizations of two distinct dynamical systems under sinusoidal constraints," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 998-1011.
    16. Park, Ju H., 2006. "Synchronization of Genesio chaotic system via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1369-1375.
    17. Chen, Heng-Hui, 2009. "Chaos control and global synchronization of Liu chaotic systems using linear balanced feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 466-473.
    18. Jahanshahi, Hadi & Yousefpour, Amin & Wei, Zhouchao & Alcaraz, Raúl & Bekiros, Stelios, 2019. "A financial hyperchaotic system with coexisting attractors: Dynamic investigation, entropy analysis, control and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 66-77.
    19. Yu, Yongguang & Li, Han-Xiong & Duan, Jian, 2009. "Chaos synchronization of a unified chaotic system via partial linearization," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 457-463.
    20. Tarai (Poria), Anindita & Poria, Swarup & Chatterjee, Prasanta, 2009. "Synchronization of generalised linearly bidirectionally coupled unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 885-892.

    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:141:y:2020:i:c:s0960077920307268. 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.