Predefined-time tracking control for high-order nonlinear systems with control saturation

In this paper, an innovative predefined-time tracking control algorithm is proposed for high-order nonlinear systems with control saturation and disturbance, which can directly calculate the upper bound of settling-time by user-defined parameters. First, a predefined-time observer based on tracking differentiator is applied to handle the disturbance. Next, a new predefined-time tracking control algorithm is designed using the backstepping method, and a novel auxiliary dynamic system is designed to deal with the control saturation. The stability of the closed-loop system is analyzed applying Lyapunov function-like method. The derivative of the virtual controller is obtained by the first-order filter to reduce the computation burden. It is worth mentioning that, different from the exiting results, all parameters related to settling-time in each virtual controller can be selected differently, and it can improve the flexibility of the controller design. Finally, the robustness and effectiveness of the investigated algorithm have been demonstrated by two typical numerical simulations.