Neural network-based terminal sliding mode control for the uncertainty coupled chaotic system with two freedoms

A radial basis functions (RBF) neural network terminal sliding mode strategy is developed to control a uncertain coupled chaotic system with the two freedoms. Based on the designed adaptive update laws, the weights of RBF neural network are trained on-line so that the designed controllers can be updated adaptively. Based on the Lyapunov stability theorem, the stability and the robustness of the controlled system are proved theoretically. Experiments about resisting the uncertain external disturbance are proved to show the robustness of the controlled system. Moreover, the proposed method allows us to select parameters T₁ and T₂ respectively to adjust time when the variables of the controlled system make tracks for the targets.