Adaptive Control for a Second-order Chaotic System with Unknown Nonsymmetric Actuator Dead-Zone

In this paper, an adaptive controller design method is proposed for chaotic systems with unknown actuator dead-zone. First, the terminal sliding mode (TSM) manifold is proposed to ensure exponential stability as well as faster finite-time stability. In addition, a neural network (NN) is introduced to estimate the partially unknown nonlinear dynamic behavior of the object, and according to the implicit function theorem, the unknown asymmetric dead zone of the actuator is overcome by another static neural network. Furthermore, a robust terminology updated online deals with refactoring errors and external interferences of neural networks. Finally, the system can stably track any smooth target trajectory online is rigidly proved via Lyapunov analysis, and numerical simulation shows its effectiveness and feasibility.