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

Majid Roohi*, Saeed Mirzajani, Andreas Basse-O’Connor

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

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.

Original languageEnglish
Article number4463
JournalMathematics
Volume11
Issue21
DOIs
Publication statusPublished - Nov 2023

Keywords

  • chattering-free controller
  • dynamic-free scheme
  • finite-time PID sliding mode control
  • FO laser systems
  • stabilization

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