Design of adaptive sliding mode controllers for a class of perturbed fractional-order nonlinear systems

In this paper, a design methodology of the adaptive sliding mode controller was proposed for a class of multi-input fractional-order nonlinear systems with matched and unmatched perturbations to solve state regulation problems. The sliding surface is firstly introduced, and then the controller is designed with adaptive mechanisms and perturbation estimator embedded. Due to the employed adaptive and perturbation estimation mechanisms, the upper bounds of the perturbations and perturbation estimation errors do not need to be known in advance. The resultant control scheme is capable of driving the controlled states into the equilibrium point and stays thereafter within a finite time. Finally, a numerical example is given for demonstrating the feasibility of the proposed control scheme.