Nonsingular Terminal Sliding Mode Control Based on Adaptive Barrier Function for nth-Order Perturbed Nonlinear Systems

• Published in: Mathematics (Basel) Vol. 10; no. 1; p. 43
• Main Authors: Alattas, Khalid A., Mostafaee, Javad, Alanazi, Abdullah K., Mobayen, Saleh, Vu, Mai The, Zhilenkov, Anton, Abo-Dief, Hala M.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.01.2022
• Subjects: Adaptive control; adaptive function; Chaos theory; chaotic system; Control stability; Controllers; Convergence; Design; Dynamic stability; Dynamical systems; finite time synchronization; Mathematics; Nonlinear dynamics; nonlinear system; Nonlinear systems; Perturbation; Sliding mode control; Stability analysis; Synchronism; Systems design; Tracking control; Tracking errors; Upper bounds
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math10010043

In this study, an adaptive nonsingular finite time control technique based on a barrier function terminal sliding mode controller is proposed for the robust stability of nth-order nonlinear dynamic systems with external disturbances. The barrier function adaptive terminal sliding mode control makes the convergence of tracking errors to a region near zero in the finite time. Moreover, the suggested method does not need the information of upper bounds of perturbations which are commonly applied to the sliding mode control procedure. The Lyapunov stability analysis proves that the errors converge to the determined region. Last of all, simulations and experimental results on a complex new chaotic system with a high Kaplan–Yorke dimension are provided to confirm the efficacy of the planned method. The results demonstrate that the suggested controller has a stronger tracking than the adaptive controller and the results are satisfactory with the application of the controller based on chaotic synchronization on the chaotic system.