Adaptive Fixed-Time Sliding Mode Control for Trajectory Tracking of Uncertain Dynamical Systems

Abstract

This paper introduces an innovative adaptive fixed-time sliding mode control (SMC) method that eliminates chattering, enhancing trajectory tracking accuracy and robustness in nonlinear dynamical systems facing uncertainties and external disturbances. The proposed control scheme ensures fixed-time convergence of system states to a predefined neighborhood around the origin, independent of initial conditions. An innovative adaptive tuning law is proposed to estimate the unknown upper bounds of synthetic uncertainties and disturbances without requiring prior knowledge. This law forces system states to trend to the sliding surface within a fixed time, achieving stabilization of tracking errors at the origin without undesirable chattering and while avoiding singularities. Comprehensive simulations and comparisons among four control strategies (C1, C2, C3, and C4) demonstrate that the proposed C1 control strategy outperforms others in terms of faster convergence speed, higher tracking accuracy, less chattering, and stronger robustness.