Synchronizations of rotating pendulums via self-learning terminal sliding-mode control subject to input nonlinearity

In this study, under the presentations of system uncertainties, external disturbances, and input nonlinearity in control, a self-learning terminal sliding-mode control scheme is adopted to control the synchronization and anti-synchronization between two chaotic rotating pendulums with different periods of harmonic parametric excitation. Without known bounds of the unmatched nonlinear dynamics, system uncertainties, and external disturbances, the proposed controller, which is associated with time-varying feedback gains, can achieve the control goals. Meanwhile, the feedback gains are not determined beforehand but are self-learning according to the learning rules. Some sufficient conditions for stable synchronizations are performed in the sense of the Lyapunov stability theorem. Besides, numerical simulations are provided to demonstrate the effectiveness of the present scheme.