Observer-Based Sliding Mode Control for Noncommensurate Fractional-order System with Mismatched Disturbances

This paper proposes a hierarchical sliding mode control strategy for a class of noncommensurate fractional-order systems with mismatched disturbances. Firstly, we design a control law based on a hierarchical terminal sliding surface. Then, based on fractional-order super-twisting algorithm, a sliding mode observer is designed to estimate the whole unknown term in control law. The proposed control method does not require information of the internal system states, but deal with mismatched disturbances effectively. Finally, numerical simulation results are shown to illustrate the effectiveness of the proposed method.