  This paper proposes a new adaptation methodology to find the control inputs
for a class of nonlinear systems with time-varying bounded uncertainties. The
proposed method does not require any prior knowledge of the uncertainties
including their bounds. The main idea is developed under the structure of
adaptive sliding mode control; an update law decreases the gain inside and
increases the gain outside a vicinity of the sliding surface. The semi-global
stability of the closed-loop system and the adaptation error are guaranteed by
Lyapunov theory. The simulation results show that the proposed adaptation
methodology can reduce the magnitude of the controller gain to the minimum
possible value and smooth out the chattering.
