Neural Network-Based Adaptive Tracking Control for a Class of Nonlinear Singularly Perturbed Systems

In this paper, the neural network-based adaptive tracking control method is addressed for a class of multi-input affine unknown nonlinear singularly perturbed systems. Based on the Lyapunov stability theorem and by utilizing the neural networks to approximate the unknown nonlinear function, an adaptive neural network controller is constructed for the singularly perturbed nonlinear systems. Meanwhile, the proposed design method can avoid ill-conditioned numerical problems that often occur in the feedback design for singularly perturbed systems. It is proved that the proposed controller can ensure that semi-global ultimately uniformly boundedness of all the signals in the closed-loop systems while the target signals converge to a small neighborhood of the desired signal. Finally, two simulation examples are given to illustrate the theoretical results.