Adaptive sliding mode control for disturbances with unknown bounds

In this paper, we propose an adaptive sliding mode approach based on average control to deal with disturbances of unknown bounds in nonlinear plants. Some advantages with respect to earlier results in the literature are its simplicity and the possibility of including non smooth disturbances. Differently from other adaptive algorithms, no overestimation for the controller gain neither the loss of the sliding motion are observed. The developed method allows for ideal sliding modes and reduces the chattering phenomena. In theory, the sliding variable which drives the relay function becomes identically zero after some finite time. Global stabilization is demonstrated and numerical simulations illustrate the potential of the new adaptation scheme.