Adaptive barrier function‐based fractional‐order chattering‐free finite‐time control for uncertain chaotic systems

• Published in: Mathematical methods in the applied sciences Vol. 46; no. 16; pp. 17345 - 17366
• Main Authors: Askari Sepestanaki, Mohammadreza, Soofi, Mohammad, Barhaghtalab, Mojtaba Hadi, Bahmani, Hamidreza, Mobayen, Saleh, Jalilvand, Abolfazl
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 15.11.2023
• Subjects: Adaptive control; Chaos theory; Continuity (mathematics); Control theory; Controllers; Disturbances; Perturbation; Sliding mode control; Uncertainty
• ISSN: 0170-4214; 1099-1476; 1099-1476
• DOI: 10.1002/mma.9503

This study proposes the adaptive continuous barrier function as the fractional‐order control system using the terminal sliding mode control technique with chattering‐free property to stabilize chaotic systems that have unknown uncertainties. The important reason for using the fractional‐order controller is its greater flexibility than the integer‐order controller. Using adaptive approach and Lyapunov's stability theory, an adaptive continuous barrier fractional‐order chattering‐free finite‐time controller for a category of chaotic systems with the unknown uncertainties and external disturbances is presented. The suggested controller can stabilize the chaotic system excellently with a continuous and smooth control law even without knowing the boundaries and in the presence of unknown disturbances due to the model uncertainties. According to MATLAB simulation results, the high efficiency of the suggested control technique to control the chaotic systems in the attendance of unknown perturbations is obviously confirmed.