Fixed-time Disturbance Observer-based Fixed-time Prescribed Performance Control for Nonlinear Systems With Disturbances and Full-state Constraints

This paper discusses a fixed-time disturbance observer-based fixed-time prescribed performance control problem for nonlinear systems subject to disturbances and state constraints. Fixed-time disturbance observers are designed to estimate disturbances with unknown upper bounds and the estimation error converges to the origin in a fixed time. The finite-time prescribed performance function predetermines the time the tracking error reaches the steady-state boundary. The prescribed performance constraint for tracking error is converted into an asymmetric time-varying state constraint. The integral barrier Lyapunov function is employed to suppress the tracking error in the time-varying preset boundary while the states remain within constraints. The fixed-time differentiator is used to address the issue of the “explosion of complexity” in the backstepping control. Moreover, it is proved that the tracking error converges to the origin within a fixed time based on the Lyapunov stability theory. Simulation analysis demonstrates the effectiveness of the proposed controller.