IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v105y2017icp92-98.html
   My bibliography  Save this article

Control and synchronization of chaos with sliding mode control based on cubic reaching rule

Author

Listed:
  • Kocamaz, Uğur Erkin
  • Cevher, Barış
  • Uyaroğlu, Yılmaz

Abstract

In this study, a new reaching rule in the Sliding Mode Control (SMC) is proposed for chaos control and synchronization. It is applied on the nonlinear Chua's circuit. The SMC signals are provided with the Lyapunov stability theory. Classical, cubic and partial cubic variants of SMC signals are constructed. Numerical simulations are performed to compare the effectiveness of the SMC signals and the results are discussed.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:chsofr:v:105:y:2017:i:c:p:92-98
    DOI: 10.1016/j.chaos.2017.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917304162
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2017.10.008?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. Peng, Chao-Chung & Chen, Chieh-Li, 2008. "Robust chaotic control of Lorenz system by backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 598-608.
    2. Zheng, Yongai & Ji, Zhilin, 2016. "Predictive control of fractional-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 307-313.
    3. Sun, Mei & Jia, Qiang & Tian, Lixin, 2009. "A new four-dimensional energy resources system and its linear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 101-108.
    4. Yan, Jun-Juh & Lin, Jui-Sheng & Liao, Teh-Lu, 2008. "Synchronization of a modified Chua’s circuit system via adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 45-52.
    5. Aguila-Camacho, Norelys & Duarte-Mermoud, Manuel A. & Delgado-Aguilera, Efredy, 2016. "Adaptive synchronization of fractional Lorenz systems using a reduced number of control signals and parameters," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 1-11.
    6. Agrawal, S.K. & Srivastava, M. & Das, S., 2012. "Synchronization of fractional order chaotic systems using active control method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 737-752.
    7. Nazzal, Jamal M. & Natsheh, Ammar N., 2007. "Chaos control using sliding-mode theory," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 695-702.
    8. Haeri, Mohammad & Khademian, Behzad, 2006. "Comparison between different synchronization methods of identical chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 1002-1022.
    9. Sun, Jitao & Zhang, Yinping, 2004. "Impulsive control and synchronization of Chua’s oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(6), pages 499-508.
    10. 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. 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. Borah, Manashita & Das, Debanita & Gayan, Antara & Fenton, Flavio & Cherry, Elizabeth, 2021. "Control and anticontrol of chaos in fractional-order models of Diabetes, HIV, Dengue, Migraine, Parkinson's and Ebola virus diseases," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    3. Fu, Shihui & Liu, Yuan & Ma, Huizhen & Du, Ying, 2020. "Control chaos to different stable states for a piecewise linear circuit system by a simple linear control," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Anguiano-Gijón, Carlos Alberto & Muñoz-Vázquez, Aldo Jonathan & Sánchez-Torres, Juan Diego & Romero-Galván, Gerardo & Martínez-Reyes, Fernando, 2019. "On predefined-time synchronisation of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 172-178.
    5. Sangpet, Teerawat & Kuntanapreeda, Suwat, 2020. "Finite-time synchronization of hyperchaotic systems based on feedback passivation," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    6. 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.
    7. Wang, Yang & Li, Huanyun & Guan, Yan & Chen, Mingshu, 2022. "Predefined-time chaos synchronization of memristor chaotic systems by using simplified control inputs," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    8. Parvizian, Majid & Khandani, Khosro, 2021. "Hyperbolic observer design for a class of nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    9. 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).
    10. Changjin Xu & Peiluan Li & Maoxin Liao & Zixin Liu & Qimei Xiao & Shuai Yuan, 2019. "Control Scheme for a Fractional-Order Chaotic Genesio-Tesi Model," Complexity, Hindawi, vol. 2019, pages 1-15, September.
    11. 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.

    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. Balootaki, Mohammad Ahmadi & Rahmani, Hossein & Moeinkhah, Hossein & Mohammadzadeh, Ardashir, 2020. "On the Synchronization and Stabilization of fractional-order chaotic systems: Recent advances and future perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    2. Zhu, Jianhua & Peng, Yan & Gong, Zhuping & Sun, Yanming & Lai, Chaoan & Wang, Qing & Zhu, Xiaojun & Gan, Zhongxue, 2019. "Dynamic analysis of SNG and PNG supply: The stability and robustness view #," Energy, Elsevier, vol. 185(C), pages 717-729.
    3. Falahpoor, M. & Ataei, M. & Kiyoumarsi, A., 2009. "A chattering-free sliding mode control design for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1755-1765.
    4. Wafaa S. Sayed & Moheb M. R. Henein & Salwa K. Abd-El-Hafiz & Ahmed G. Radwan, 2017. "Generalized Dynamic Switched Synchronization between Combinations of Fractional-Order Chaotic Systems," Complexity, Hindawi, vol. 2017, pages 1-17, February.
    5. Yifan Zhang & Tianzeng Li & Zhiming Zhang & Yu Wang, 2022. "Novel Methods for the Global Synchronization of the Complex Dynamical Networks with Fractional-Order Chaotic Nodes," Mathematics, MDPI, vol. 10(11), pages 1-22, June.
    6. Liu, Q.X. & Liu, J.K. & Chen, Y.M., 2017. "An analytical criterion for jump phenomena in fractional Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 216-219.
    7. Kingni, Sifeu Takougang & Pham, Viet-Thanh & Jafari, Sajad & Woafo, Paul, 2017. "A chaotic system with an infinite number of equilibrium points located on a line and on a hyperbola and its fractional-order form," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 209-218.
    8. Fiaz, Muhammad & Aqeel, Muhammad & Marwan, Muhammad & Sabir, Muhammad, 2022. "Integer and fractional order analysis of a 3D system and generalization of synchronization for a class of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    9. Michal Fečkan & T. Sathiyaraj & JinRong Wang, 2020. "Synchronization of Butterfly Fractional Order Chaotic System," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    10. Asemani, Mohammad Hassan & Majd, Vahid Johari, 2009. "Stability of output-feedback DPDC-based fuzzy synchronization of chaotic systems via LMI," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1126-1135.
    11. Gong, Xiao-Li & Liu, Xi-Hua & Xiong, Xiong, 2019. "Chaotic analysis and adaptive synchronization for a class of fractional order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 33-42.
    12. Chakraborty, Arkaprovo & Veeresha, P., 2024. "Investigating the dynamics, synchronization and control of chaos within a transformed fractional Samardzija–Greller framework," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    13. Hung, Yung-Ching & Yan, Jun-Juh & Liao, Teh-Lu, 2008. "Projective synchronization of Chua's chaotic systems with dead-zone in the control input," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 374-382.
    14. Khanzadeh, Alireza & Pourgholi, Mahdi, 2016. "Robust Synchronization of Fractional-Order Chaotic Systems at a Pre-Specified Time Using Sliding Mode Controller with Time-Varying Switching Surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 69-77.
    15. Yu Feng & Zhouchao Wei & Uğur Erkin Kocamaz & Akif Akgül & Irene Moroz, 2017. "Synchronization and Electronic Circuit Application of Hidden Hyperchaos in a Four-Dimensional Self-Exciting Homopolar Disc Dynamo without Equilibria," Complexity, Hindawi, vol. 2017, pages 1-11, May.
    16. Zhang, Jianxiong & Tang, Wansheng, 2009. "Analysis and control for a new chaotic system via piecewise linear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2181-2190.
    17. Salarieh, Hassan & Alasty, Aria, 2009. "Chaos control in uncertain dynamical systems using nonlinear delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 67-71.
    18. Yu, Hengguo & Zhong, Shouming & Ye, Mao, 2009. "Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 619-632.
    19. Jin, Maolin & Chang, Pyung Hun, 2009. "Simple robust technique using time delay estimation for the control and synchronization of Lorenz systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2672-2680.
    20. Zhang, Yan & Chen, Shihua & Zhou, Hong, 2009. "Synchronizing the noise-perturbed Lü chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2475-2482.

    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:105:y:2017:i:c:p:92-98. 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.