Auxiliary Variable based Adaptive Sliding-Mode Control for Systems with Mismatched Disturbances

In this paper, a novel adaptive sliding-mode control strategy is proposed for nonlinear systems in the presence of mismatched and matched disturbances with the prior knowledge about the upper bound of these disturbances being unknown. In order to eliminate mismatched disturbances, a new auxiliary adaptive variable with first-order derivable is first designed, by constructing a new sliding mode surface. Then by coordinating transformation with the auxiliary variable, the original system can be transformed into a new one. An adaptive sliding mode controller is designed to ensure the states of the new system converge to zero in finite time. The designed adaptive laws can greatly alleviate the problem of gain over-estimation compared with the conventional adaptive method and accordingly the control chattering phenomenon can be attenuated significantly. The efficacy of the proposed algorithm is confirmed through numerical examples.