  To reduce the chattering and overestimation phenomena existing in classical
adaptive sliding mode control, this paper presents a new class K_infinity
function-based adaptive sliding mode control scheme. Two controllers are
proposed in terms of concave and convex barrier functions to implement this
kind of control methodology. To avoid large initial control magnitudes, two
modified control schemes are provided, which extend the proposed methodology to
different scenarios. It is proven that the proposed controllers yield
finite-time convergence to a real sliding mode. Finally, simulations and
discussions are presented to show the advantages and effectiveness of the
proposed control methodology.
