Constant‐Rate Convergence for an Adaptive Sliding Mode Controller Using a Fixed‐Time Disturbance Observer

ABSTRACT

This paper presents an adaptive nonsingular terminal sliding mode controller designed to converge with a constant rate, which restrains the control input to avoid peaks at the initial time. Thus, during the convergence time, the control law is based on a fixed‐time extended state observer that provides a perturbation and uncertainty estimation, which is used to constrain such convergence. The sliding variable converges to a small region around the equilibrium at a desired time. On the other hand, a nonsingular terminal sliding mode is designed, guaranteeing practical finite‐time state convergence and robustness for the control method. The stability analysis of the adaptive controller and the sliding surface is proven by means of Lyapunov and practical finite‐time stability theories. Finally, a case study involving an unmanned surface vehicle subject to external disturbances and uncertainties is addressed, with an additional comparative analysis against alternative prescribed‐time controllers. Numerical simulations and real‐time experimental trials demonstrate the advantages and effectiveness of the proposed approach in a trajectory tracking scenario.