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This paper proposes a new adaptation methodology to find the control inputsfor a class of nonlinear systems with time-varying bounded uncertainties. Theproposed method does not require any prior knowledge of the uncertaintiesincluding their bounds. The main idea is developed under the structure ofadaptive sliding mode control; an update law decreases the gain inside andincreases the gain outside a vicinity of the sliding surface. The semi-globalstability of the closed-loop system and the adaptation error are guaranteed byLyapunov theory. The simulation results show that the proposed adaptationmethodology can reduce the magnitude of the controller gain to the minimumpossible value and smooth out the chattering.

Adaptive sliding mode control without knowledge of uncertainty bounds