Fixed-Time Dynamic Surface Tracking of Nonlinear Systems with Unknown Control Directions

This paper presents an analysis of fixed-time stabilization with dynamic surfaces in strict-feedback nonlinear systems affected by multiple unknown control directions. To address the issue of unknown control directions within the system, the Nussbaum-type approach is introduced. A complete analysis of fixed-time stabilization is conducted to ensure that the signals converge within the fixed settling time. Additionally, the stability of the system in the presence of multiple unknown control directions is demonstrated through the recursive analysis of each subsystem based on the backstepping framework. Furthermore, a modified dynamic surface filter is introduced to guarantee the convergence of the filter errors within a fixed settling time. In this paper, radial basis neural networks are utilized to estimate unknown functions. Finally, the feasibility and effectiveness of the proposed design are validated through a simulation example.