Command-filtered-based technique for a class of nonlinear systems with finite-time observer in the presence of mismatched disturbances

This paper considers the stabilization problem for a class of nonlinear systems in the presence of mismatched disturbances. To achieve this, a differentiator is defined using virtual controls and modified error compensation signals, and the output of the system is asymptotically stabilized by a command-filtered backstepping control scheme combined with a mismatched finite-time disturbance observer. In the employed disturbance observer, the imposed external disturbances are identified precisely within the finite-time period. This produces a better transient performance compared to the Lyapunov parameter estimation method. In addition, a wider range of disturbances can be included as the common restrictive condition is no longer applied to the first derivatives of disturbances. Apart from the functionalities of the employed disturbance observer, the proposed control scheme addresses the problem of the explosion of complexity caused by higher-order differentiation. As a result, when applied to a more complicated system, this method can significantly reduce the complexity of calculation. In the final step, by means of the common Lyapunov function, the finite-time estimation process of the disturbance observer and the asymptotic stability of the given control scheme is shown. Finally, a simulation example is provided to show the effectiveness of the theoretical developments.