Adaptive finite reaching time control and continuous second order sliding modes

In this paper adaptive finite reaching time control is designed for first and second order dynamic systems with perturbation terms given in a regressive form. The adaptive finite reaching time controllers which are proposed do not contain any discontinuities while retaining robustness to bounded disturbances with unknown bounds. The proposed finite reaching time adaptive control algorithms are interpreted as continuous second order sliding mode controls. Simulation results demonstrate the efficacy of the proposed algorithms.