Continuous adaptive finite reaching time control and second-order sliding modes

This paper focuses on the design of adaptive finite reaching time control for first- and second-order dynamic systems with perturbation terms given in a regressive form. The uncertainties considered here are assumed to be bounded with unknown bounds. The proposed adaptive finite reaching time controllers not only retain robustness to these disturbances, but also are continuous. The proposed finite reaching time adaptive control algorithms are interpreted as continuous second-order sliding mode control laws. Simulation results demonstrate the efficacy of the proposed algorithms.