Adaptive prescribed-time control for uncertain nonlinear systems while maintaining the zeroed tracking error

The issue of accurate prescribed-time tracking control for uncertain nonlinear systems has been studied in past few years, however, it is still challenging to maintain the zeroed state tracking errors after the prescribed settling time. This paper solves this problem by proposing a parameter estimation-based adaptive prescribed-time control approach. A set of four-layer filters is established for the parameter estimation based on the dynamic regressor extension and mixing method. It not only increases the order of the available time derivatives of the regressors and outputs in linear parametric models, but also ensures that the parameters are estimated under initial excitation conditions. Then, the adaptive backstepping control algorithm is designed by applying a time-varying scaling function, regulating both state tracking errors and parameter estimation errors to zero within a prescribed settling time. Thereafter, since the uncertain parameters have been estimated exactly, the zeroed state tracking errors can be maintained by the backstepping control for a certain system. The boundedness of all closed-loop system signals and the continuity of the control input signal are proved. Two simulation examples illustrate the effectiveness of the proposed approach.