IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i13p2078-d1686015.html
   My bibliography  Save this article

Adaptive Dynamic Programming-Based Intelligent Finite-Time Flexible SMC for Stabilizing Fractional-Order Four-Wing Chaotic Systems

Author

Listed:
  • Mai The Vu

    (Department of Artificial Intelligence and Robotics, Sejong University, Seoul 05006, Republic of Korea)

  • Seong Han Kim

    (Department of Artificial Intelligence and Robotics, Sejong University, Seoul 05006, Republic of Korea)

  • Duc Hung Pham

    (Faculty of Electrical and Electronic Engineering, Hung Yen University of Technology and Education, Hung Yen 17000, Vietnam)

  • Ha Le Nhu Ngoc Thanh

    (Faculty of Mechanical Engineering, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City 71307, Vietnam)

  • Van Huy Pham

    (Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam)

  • Majid Roohi

    (Department of Mathematics, Aarhus University, 8000 Aarhus, Denmark)

Abstract

Fractional-order four-wing (FO 4-wing) systems are of significant importance due to their complex dynamics and wide-ranging applications in secure communications, encryption, and nonlinear circuit design, making their control and stabilization a critical area of study. In this research, a novel model-free finite-time flexible sliding mode control (FTF-SMC) strategy is developed for the stabilization of a particular category of hyperchaotic FO 4-wing systems, which are subject to unknown uncertainties and input saturation constraints. The proposed approach leverages fractional-order Lyapunov stability theory to design a flexible sliding mode controller capable of effectively addressing the chaotic dynamics of FO 4-wing systems and ensuring finite-time convergence. Initially, a dynamic sliding surface is formulated to accommodate system variations. Following this, a robust model-free control law is designed to counteract uncertainties and input saturation effects. The finite-time stability of both the sliding surface and the control scheme is rigorously proven. The control strategy eliminates the need for explicit system models by exploiting the norm-bounded characteristics of chaotic system states. To optimize the parameters of the model-free FTF-SMC, a deep reinforcement learning framework based on the adaptive dynamic programming (ADP) algorithm is employed. The ADP agent utilizes two neural networks (NNs)—action NN and critic NN—aiming to obtain the optimal policy by maximizing a predefined reward function. This ensures that the sliding motion satisfies the reachability condition within a finite time frame. The effectiveness of the proposed methodology is validated through comprehensive simulations, numerical case studies, and comparative analyses.

Suggested Citation

  • Mai The Vu & Seong Han Kim & Duc Hung Pham & Ha Le Nhu Ngoc Thanh & Van Huy Pham & Majid Roohi, 2025. "Adaptive Dynamic Programming-Based Intelligent Finite-Time Flexible SMC for Stabilizing Fractional-Order Four-Wing Chaotic Systems," Mathematics, MDPI, vol. 13(13), pages 1-25, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2078-:d:1686015
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/13/2078/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/13/2078/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Majid Roohi & Saeed Mirzajani & Andreas Basse-O’Connor, 2023. "A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems," Mathematics, MDPI, vol. 11(21), pages 1-22, October.
    2. 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.
    3. Mathiyalagan, Kalidass & Sangeetha, G., 2020. "Second-order sliding mode control for nonlinear fractional-order systems," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    4. Duc Hung Pham & Mai The Vu, 2025. "Takagi–Sugeno–Kang Fuzzy Neural Network for Nonlinear Chaotic Systems and Its Utilization in Secure Medical Image Encryption," Mathematics, MDPI, vol. 13(6), pages 1-26, March.
    5. Baishya, Chandrali & Premakumari, R.N. & Samei, Mohammad Esmael & Naik, Manisha Krishna, 2023. "Chaos control of fractional order nonlinear Bloch equation by utilizing sliding mode controller," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    Full references (including those not matched with items on IDEAS)

    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. Li, Hui & Kao, YongGui & Stamova, Ivanka & Shao, Chuntao, 2021. "Global asymptotic stability and S-asymptotic ω-periodicity of impulsive non-autonomous fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Mei-Qi, Wang & Wen-Li, Ma & En-Li, Chen & Yu-Jian, Chang & Cui-Yan, Wang, 2022. "Principal resonance analysis of piecewise nonlinear oscillator with fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    3. Wang, Haitao & Chen, Xiangyong & Wang, Jing, 2022. "H∞ sliding mode control for PDT-switched nonlinear systems under the dynamic event-triggered mechanism," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    4. Arthi, G. & Suganya, K., 2021. "Controllability of higher order stochastic fractional control delay systems involving damping behavior," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    5. Liu, Lu & Ding, Shihong, 2021. "A unified control approach to finite-time stabilization of SOSM dynamics subject to an output constraint," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    6. Ning, Jinghua & Hua, Changchun, 2022. "H∞ output feedback control for fractional-order T-S fuzzy model with time-delay," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    7. Majid Roohi & Saeed Mirzajani & Andreas Basse-O’Connor, 2023. "A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems," Mathematics, MDPI, vol. 11(21), pages 1-22, October.
    8. Haddouchi, Faouzi & Samei, Mohammad Esmael, 2024. "Solvability of a generalized ψ-Riemann–Liouville fractional BVP under nonlocal boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 355-377.
    9. Wang, Mei-Qi & Ma, Wen-Li & Li, Yuan & Chen, En-Li & Liu, Peng-Fei & Zhang, Ming-Zhi, 2022. "Dynamic analysis of piecewise nonlinear systems with fractional differential delay feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    10. Mousavi, Yashar & Bevan, Geraint & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Sliding mode control of wind energy conversion systems: Trends and applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 167(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:gam:jmathe:v:13:y:2025:i:13:p:2078-:d:1686015. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.