Design of adaptive terminal super-twisting controllers for nonlinear systems with mismatched perturbations

In this paper, a design methodology of adaptive super-twisting control is proposed for a class of multi-input nonlinear systems with matched and mismatched perturbations to solve state regulation problems. The sliding surface is designed first, then the super-twisting controller is designed accordingly. Adaptive and perturbation estimation mechanisms are also embedded in the proposed control scheme, so that there is no need to know the upper bounds of perturbations and the perturbation estimation error in advance. The proposed control strategy can indeed drive the controlled states into the sliding surface first, then into the equilibrium point and stay thereafter within a finite time. Finally, a numerical example and a practical application are given for demonstrating the feasibility of the proposed control strategy.