Intermittent Fault Detection for Polynomial Nonlinear Systems via Reduced-Order Predefined-Time Unknown Input Observer

This paper investigates the problem of intermittent fault detection for a class of polynomial nonlinear systems with unknown inputs. Traditional fault detection methods face challenges in simultaneously suppressing the effects of unknown inputs and the smearing effect, which refers to an uncertain detection delay after fault disappearance. To address this challenge, a reduced-order predefined-time unknown input observer (PTUIO) is proposed, serving as the core mechanism for achieving accurate intermittent fault detection. Specifically, the structure of the reduced-order PTUIO is first developed to decouple unknown inputs from the observation error and reduce computational complexity. Then, the observer gain is designed using the generalized homogeneity method. To solve the observer gain, some parameter-dependent linear matrix inequalities are deduced by the implicit Lyapunov function approach, so that the predefined-time stability of the observation error system is guaranteed. With the designed observer, the complete intermittent fault detection algorithm is derived following the common steps of fault detection. Finally, the effectiveness and feasibility of the proposed algorithm are verified through both simulation and experiment validation on the permanent magnet synchronous motor system.