Nonlinear filtered prescribed-time control of uncertain nonlinear systems with mismatched uncertainties

In this article, a nonlinear filter based prescribed-time tracking control method is constructed for high-order nonlinear systems characterised by both matched and mismatched uncertainties. A time-varying function is incorporated into recursive back-stepping design, while a series of prescribed-time disturbance observers are developed as active compensation terms for uncertainties in each channel of the system. Moreover, to tackle the drawback of 'explosion of complexity', a nonlinear filter with time-varying gain is proposed and appropriately integrated into the back-stepping based prescribed-time controller design. The presented prescribed-time control method not only greatly simplifies the back-stepping design process for high-order system, but also theoretically attains exceptional prescribed-time tracking performance with zero steady-state error, and the prescribed time can be predetermined in a clear and explicit manner, irrespective of the initial conditions. Finally, the proposed controller is applied to an electro-hydraulic actuator for simulation to demonstrate its validity and superiority.