Global Asymptotic Tracking Under Prescribed Performance for a Class of Uncertain Nonlinear Strict-Feedback Systems With Actuator Faults

This paper investigates global adaptive asymptotic tracking with prescribed performance control (PPC) for nonlinear systems subject to unknown nonparametric uncertainties, mismatched external disturbances, and potential actuator faults. The challenge lies in driving the tracking error to a prescribed region within a given time globally, achieving independent performance criteria for all errors under unknown nonlinear functions and any initial condition, while maintaining arbitrary settling time and accuracy specifications. Hence, we propose a robust global fault-tolerant control scheme using a barrier Lyapunov function and bound estimation. Key features of our approach include: 1) the use of heterogeneous tuning functions for independent error adjustment; 2) the ability to preassign global transient performance criteria off-line, independent of initial conditions, and high-order derivatives of the reference trajectory; 3) a constraint analysis scheme on account of proof by contradiction is introduced to demonstrate the inherent robustness to unknown system functions, disturbances and actuator faults. The theoretical results are demonstrated through a comparative experiment on a linear motor platform. Note to Practitioners—The escalating demands for product quality and production efficiency have necessitated stringent requirements for the performance of motion systems in contemporary industrial production equipment. PPC has demonstrated its effectiveness as a highly successful strategy for addressing this problem. However, achieving the objective of driving the tracking error to a prescribed region within a given time globally, satisfying independent performance criteria for all errors under unknown nonlinear functions, actuator faults, and any initial conditions, while simultaneously maintaining arbitrary settling time and accuracy specifications in the design of PPC, is a complex and challenging task. To tackle these challenges, this paper introduces a global asymptotic fault-tolerant tracking control method with prescribed performance. In contrast to existing approaches, this method ensures asymptotic output tracking with predefined settling time and accuracy for any initial states, despite actuator faults, unknown system nonlinearities, and external disturbances. Comparative experimental results validate the applicability of this method to practical gantry platform systems, illustrating its effectiveness and superiority over existing methods.