Fixed-time sliding mode control with disturbance observer and variable exponent coefficient for nonlinear systems

This article presents a novel control approach for robust fixed-time trajectory tracking in nonlinear dynamic systems affected by external disturbances and model uncertainties, utilizing a fixed-time disturbance observer. Initially, a new fast disturbance observer was designed to reliably estimate external disturbances and model uncertainties within a fixed timeframe, independent of initial conditions and without requiring strict assumptions about the nature of these disturbances and uncertainties. Based on the disturbance estimates, a new robust fixed-time trajectory tracking sliding mode control strategy was developed, incorporating a fixed-time sliding variable and a reaching law with a state-dependent exponent coefficient. Using Lyapunov-based analysis, it is proven that the tracking errors of the closed-loop system converge to a neighborhood of the origin within a fixed time, independent of the initial conditions. Finally, comprehensive simulations were conducted to validate the effectiveness of the proposed strategy, demonstrating its advantages in achieving fast convergence, avoiding singularities, reducing chattering, and compensating for model uncertainties and external disturbances.