Smooth, Singularity-Free, Finite-Time Tracking Control for Euler-Lagrange Systems

This paper investigates the problem of constrained finite-time tracking control of Euler-Lagrange systems subject to system uncertainties and external disturbances. Firstly, we introduce a nonsingular, fast, constrained terminal sliding manifold (NFCTSM) that contains a time-varying gain to deal with the output tracking error constraint. Therefore, the desired performance in steady-state and transience such as ultimate-tracking-error bound, maximum overshoot, and convergence speed are provided. Then, based on the proposed NFCTSM, a smooth adaptive finite-time control is designed such that the tracking errors converge to an arbitrary small region around the origin during a finite period of time. Moreover, the square of the upper bound of the lumped uncertainty is estimated by the adaptive law in order not to use the discontinuous signum function. The efficacy and usefulness of the proposed control methodology are demonstrated via simulation results and comparison with relevant works.