Adaptive tracking control of high-order nonlinear systems with unknown time-varying input delay and unmodeled dynamics

In this paper, an adaptive dynamic surface control (DSC) strategy is studied for high-order nonlinear systems with unknown time-varying input delay and unmodelled dynamics. An error transform for a high-order nonlinear system is established by introducing an integral term and utilizing an upper bound of the input delay. On this basis, a new Lyapunov functional applicable to higher order systems is constructed, and with the help of integral mean value theorem, the unknown input delay is effectively handled. By using inequality transformation technique and selecting appropriate virtual controllers, the control error term caused by power disturbances in high-order nonlinear systems is eliminated, overcoming the difficulties in designing controllers for high-order systems with unknown input delays. The uncertainty of the system is processed by using dynamic signals and radial basis function neural networks. An adaptive tracking control scheme is designed to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB). The effectiveness of the scheme is verified through simulation examples.