Performance guaranteed prescribed-time control of nonlinear strict-feedback systems with non-vanishing uncertainties

This paper addresses the global finite-time tracking control problem for nonlinear strict-feedback systems with non-vanishing uncertainties and arbitrary initial conditions. The objective is to establish a control framework that guarantees system performance throughout the control process. To achieve finite-time convergence of tracking errors and guaranteed performance, a new performance function is proposed. To ensure global transient and steady-state performance, a time-varying scaling transformation method is employed. Under the proposed control method, the output tracking error is ensured to converge to a neighborhood of the origin of the preassigned size within a prescribed time at a pre-specified convergence rate. Additionally, global uniform ultimate boundedness is ensured for all signals in the closed-loop systems. Simulation examples validate the effectiveness and benefits of the proposed approach.