Fast Practical Fixed-Time Prescribed Performance Control for Nonlinear Systems With Unmodeled Dynamics

In this article, the tracking control problem for nonlinear systems is investigated. For the first time, a fixed-time dynamic signal is constructed to handle unmodeled dynamics. A novel error-based function is first designed and applied to prescribed performance control, significantly enhancing the transient performance of the system. To mitigate the issue of extensive differential calculations, a modified fixed-time dynamic surface technique is incorporated into the backstepping design process. Combining the backstepping technique with fixed-time stability theory, a fast practical fixed-time controller is proposed to effectively address the control problem. Finally, the proposed scheme is validated for its effectiveness through the practical simulation example.