Adaptive Sliding Mode Observers for Time‐Varying Fault Estimation in Nonlinear One‐Sided Lipschitz Systems Under Disturbances

ABSTRACT

This article addresses the critical challenge of estimating time‐varying faults in nonlinear one‐sided Lipschitz systems under external disturbances. A novel disturbance‐decoupled adaptive sliding‐mode observer is proposed, integrating sliding‐mode robustness with gradient‐based adaptation laws to simultaneously track system states and dynamic fault parameters. By leveraging null‐space projection techniques, the observer decouples disturbances from fault signals, ensuring robust estimation performance. The design is underpinned by a Lyapunov‐based stability analysis, yielding linear matrix inequality (LMI) conditions that guarantee asymptotic state error convergence and ultimate boundedness of parameter estimation errors. Theoretical advancements are validated through a comprehensive quadrotor UAV case study, demonstrating efficiency in disturbance rejection and steady‐state fault estimation accuracy. Comparative analysis reveals 62% faster convergence than existing constant‐fault observers, while Monte Carlo simulations confirm robustness against 20% initialization errors and input noise. The framework bridges a significant gap in fault‐tolerant control by providing rigorous solutions for systems with evolving fault dynamics.