Trajectory Tracking Control for Disturbed Euler-Lagrange Systems: A Fixed-Time Adaptive Approach

This paper primarily focuses on addressing the challenging problem of trajectory tracking control for a specific class of Euler-Lagrange systems subjected to uncertainties and disturbances. A fixed-time tracking control strategy based on sliding mode is introduced, featuring a modified fixed-time surface that exhibits shorter convergence time compared to conventional fixed-time sliding surface. This surface has no singularity and can guarantee the settling-time to be independent of initial states. Furthermore, attaining the upper bound presents challenges given the uncertainty surrounding the disturbance. Consequently, an adaptation mechanism is incorporated into fixed-time nonsingular sliding mode (FTNSM) to devise a continuous adaptive FTNSM control law. This method entails estimating the disturbance upper bound using adaptive techniques, thus obviating the requirement for prior knowledge and efficiently alleviating the disturbance's influence on the system while also potentially mitigating the chattering phenomenon. Lyapunov theory shows that the closed-loop tracking system is stable and converges in a fixed amount of time. Theoretical analysis demonstrates that the proposed sliding mode surface, along with the errors, can converge within narrow vicinity within the specified time frame. Numerical simulations illustrate that despite uncertainties and disturbances, the proposed controller effectively achieves trajectory tracking with high accuracy and stability. DOI: 10.61416/ceai.v26i4.9118