Command-Filter-Based Backstepping for a Class of Nonlinear Systems with Finite-Time Observer in the Presence of Mismatched Disturbances

Abstract

This paper considers the stabilization problem for a class of nonlinear systems in the presence of mismatched disturbances. For this purpose, a differentiator is employed such that by using newly defined virtual controls and the modified error compensation signals, the command-filter backstepping approach combined with a mismatched finite-time disturbance observer such that the proposed control guarantees the asymptotic stabilization of system states. In the introduced observer, the imposed external disturbance parameters are identified precisely within the finite-time period. This produces a better transient performance compared to the Lyapunov parameter estimation method. Moreover, the imposed restrictions over external disturbances are relaxed, i.e., the common restrictive condition over the disturbances’ first derivatives is removed. This approach also helps to solve the problem of the explosion of complexity, which is usually caused by higher-order system differentiation in backstepping technique. As a result of applying this method, especially to more complicated systems, the complexity of calculation is greatly reduced. Moreover, by means of the common Lyapunov function, the stability of the proposed observer and the control scheme is shown. Finally, a simulation example is provided to show the effectiveness of the theoretical developments.