Robust control of nonlinear semi-strict feedback systems using finite-time disturbance observers

The output tracking controller design problem is dealt with for a class of nonlinear semi-strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances, and uncertain nonlinear virtual control coefficients of the subsystems. The controller is designed in a backstepping manner, and to avoid the shortcoming of 'explosion of terms', the dynamic surface control technique that employs a group of first-order low-pass filters is adopted. At each step of the virtual controller design, a robust feedback controller employing some effective nonlinear damping terms is designed to guarantee input-to-state practical stable property of the corresponding subsystem, so that the system states remain in the feasible domain. The virtual controller is enhanced by a finite-time disturbance observer that estimates the disturbance term in a finite-time. The properties of the composite control system are analyzed theoretically. Furthermore, by exploiting the cascaded structure of the control system, a simplified robust controller is proposed where only the first subsystem employs a disturbance observer. The performance of the proposed methods is confirmed by numerical examples. Copyright (C) 2017 John Wiley & Sons, Ltd.