Neural adaptive learning synchronization of second-order uncertain chaotic systems with prescribed performance guarantees

This paper focuses on the neural adaptive learning synchronization of second-order chaotic systems with guaranteed prescribed performance subject to model uncertainties, external disturbances, and input saturation. First, a neural adaptive state feedback controller is designed. The barrier Lyapunov function (BLF) is utilized to guarantee the output synchronization tracking error always stays within the prescribed performance bounds. The neural network (NN) is adopted to approximate the uncertain lumped nonlinear term in the synchronization tracking error dynamic system. Then, a neural adaptive output feedback controller is exploited based on the state feedback controller. A high gain observer is introduced to estimate the synchronization tracking error of the immeasurable states. The remarkable features of the proposed neural adaptive controllers are as follows. (1) Owing to the use of NN, the proposed controllers are model-independent. In this way, the proposed controllers are still applicable even when the dynamics of the second-order chaotic systems are completely unknown. (2) Benefiting from the BLF, the transient and steady-state performance of the proposed controllers can be assured during the whole synchronization process. (3) Both the state feedback and output feedback are addressed. The output feedback controller only requires the output information for feedback. Finally, the effectiveness and advantages of the proposed controllers are illustrated through simulations and comparisons.