Robust state and fault estimation for non-linear stochastic systems with unknown disturbances: a multi-step delayed solution

A study on the simultaneous state and fault estimation for non-linear discrete-time stochastic systems subjected to unknown disturbances is presented. The augmented system approach, system reformation using the state-dependent coefficient (SDC) factorisation, and unknown input filtering method are integrated to simultaneously estimate the state of the system and actuator and/or sensor faults. To achieve this aim, the non-linear system with faults and unknown disturbances is first transformed into an equivalent augmented system by using delayed measurements and the SDC factorisation. Next, within the SDC factorised linear-like augmented system and inspired by the robust two-stage Kalman filter, a novel multi-step estimator named as the robust simultaneous state and fault estimator is proposed to yield a robust state and fault estimation with a multi-step delay. Moreover, a novel real-time state estimator is designed based on the proposed hybrid fault reconstruction model in order to address the inherent time-delay problem. A comparison of the performance of the proposed filters with those of existing methods from the literature is demonstrated using a non-linear two-link manipulator system with friction forces acting simultaneously at each joint.