Adaptive sliding mode controller with monotonically nonincreasing gain for nonlinear uncertain systems

In this paper, the adaptive sliding mode controller (ASMC) is proposed for a class of nonlinear uncertain systems. Conventional adaptive robust control system and/or adaptive sliding mode control system could not give when the system shows invariance property against parameter uncertainties and external disturbances. Thus, although the initial system state is on the sliding surface, one can not ensure the occurrence of the sliding mode for the conventional adaptive sliding mode control systems; that is, the system state may leave the sliding surface even if the state hits the sliding surface. For the proposed ASMC, no a priori knowledge of the exact bounds for parameter uncertainties and external disturbances is needed because the proposed control scheme uses adaptive algorithm for bounds of the uncertainty. The overall system is shown to be globally asymptotically stable