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A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems

Author

Listed:
  • Majid Roohi

    (School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China
    Department of Mathematics, Aarhus University, 8000 Aarhus, Denmark)

  • Saeed Mirzajani

    (Department of Mathematics, Payame Noor University, Tehran 19395-3697, Iran)

  • Andreas Basse-O’Connor

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

Abstract

Over the past decade, fractional-order laser chaotic systems have attracted a lot of attention from a variety of fields, including theoretical research as well as practical applications, which has resulted in the development of a number of different system classes. This paper introduces a novel single-input finite-time PID sliding mode control (SMC) technique to stabilize a specific group of unknown 4-dimensional chaotic fractional-order (FO) laser systems. By combining the PID concept with the FO-version of the Lyapunov stability theory, a novel finite-time PID SMC strategy has been developed, which effectively mitigates chaotic behavior in the mentioned unknown 4-dimensional chaotic FO laser system. This method makes use of a characteristic of FO chaotic systems known as boundedness, which is used here. Notably, the control input’s sign function, which is responsible for undesirable chattering, is transformed into the fractional derivative of the control input. This transformation results in a smooth and chattering-free control input, further enhancing the method’s performance. To demonstrate the efficacy of the proposed chattering-free–finite-time PID SMC technique, two numerical scenarios are presented, showcasing its efficient performance in stabilizing the unknown 4-dimensional chaotic FO laser system. These scenarios serve as illustrations of the method’s potential for practical applications.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4463-:d:1269090
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    References listed on IDEAS

    as
    1. Hajid Alsubaie & Amin Yousefpour & Ahmed Alotaibi & Naif D. Alotaibi & Hadi Jahanshahi, 2023. "Stabilization of Nonlinear Vibration of a Fractional-Order Arch MEMS Resonator Using a New Disturbance-Observer-Based Finite-Time Sliding Mode Control," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    2. Mathiyalagan, Kalidass & Sangeetha, G., 2020. "Second-order sliding mode control for nonlinear fractional-order systems," Applied Mathematics and Computation, Elsevier, vol. 383(C).
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