Adaptive Predefined-Time Control for Lü Chaotic Systems via Backstepping Approach

This brief focuses on the adaptive predefined-time backstepping control for Lü chaotic systems with an unknown parameter. Different from the existing research on convergence-time control for chaotic systems, based on the backstepping technique, an improved predefined-time stable lemma for strict-feedback systems is proposed, which can achieve precise control about convergence time. Moreover, a predefined-time control scheme is designed using the proposed lemma to suppress the chaotic phenomenon and stabilize the Lü chaotic systems with predefined time. And, a novel adaptive updating law is designed to make the derivative of Lyapunov function satisfy the predefined-time stable form. The stability analysis proves that the signals in the Lü chaotic system are predefined-time stable and the convergence time can be specified by the user. Finally, a simulation example is provided to prove the effectiveness of the presented predefined-time control scheme.