Prescribed-Time Tracking Control for Robotic Systems with Uncertain Dynamics

This paper presents a prescribed-time tracking control scheme for robotic systems with unknown dynamics. One salient feature is that the robotic systems can achieve prescribed-time stability with the prescribed transient performance, which is different with the traditional work that achieves uniformly ultimately bounded (UUB) and/or asymptotic stability. To realize this purpose, the prescribed performance dynamics (PPD) instead of the traditional prescribed performance function (PPF) is suggested, by which both the transient and steady-state tracking performance can be guaranteed within a specified region in-priori. To avoid using the function approximators (i.e., neural networks (NNs), fuzzy logic systems (FLSs)), an approximation-free-based prescribed-time controller is established with the inertial matrix of robotic systems and the finite-time function merely, which can not only address the system unknown uncertainties but also regulate the control error to zero in a prescribed-time. Furthermore, the Lyapunov-based theoretical analysis is conducted to prove the prescribed-time stability of the closed-loop system. Finally, comparative numerical simulation results are provided to demonstrate the effectiveness of the proposed method.