Adaptive Fault-Tolerant Control for Nonlinear Singularly Perturbed Systems with Input Delay and State Uncertainties

This paper presents an advanced adaptive fault-tolerant control (FTC) strategy tailored for nonlinear singularly perturbed systems (SSPs) subject to time-delay in the control input, state uncertainties, and actuator faults. Extending the Lyapunov redesign framework proposed [11], this approach incorporates the Razumikhin stability criterion to address input delays and introduces a robust adaptive term to mitigate uncertainties and faults. By decomposing the system into slow and fast subsystems via the singular perturbation method, a composite controller is designed to ensure asymptotic stability under challenging conditions. The theoretical stability is rigorously proven using a Lyapunov function, and the approach is validated through detailed numerical simulations of a two-link robotic manipulator arm, a critical system in industrial automation. The fault rejection capabilities of the proposed FTC make it a robust solution for real-world applications, such as robotic welding and material handling.