Adaptive Control Design for Higher Order Nonlinear Delay Systems Based on Neural Network

This paper focuses on the control of high-order nonlinear time-delay systems in block-triangular form. The RBF NN (radial basis function neural network) is chosen to approximate the unknown nonlinear functions in the system dynamics. Lyapunov-Krasovskii functionals are used to compensate the influence of delay terms. Then an adaptive neural network output tracking controller is designed by using the back-stepping recursive method. Based on Lyapunov stability theory and Theorem 1, the proposed controller can guarantee all closed-loop signals are globally, uniformly and ultimately bounded, which is proved, while the output tracking converges to a neighborhood of the origin. Finally, a simulation example is given to illustrate the correctness of the theoretical results.