Data-driven methods for dead-beat estimation of actuator faults

In this paper, we explore two data-driven methods to perform fault estimation on a linear time-invariant discrete-time state-space model, whose state equation is affected by both disturbances and actuator faults. We first investigate the design of a residual generator which is based on a dead-beat unknown-input observer. Necessary and sufficient conditions for the problem solvability, assuming that the system matrices are known, are first presented. Then we prove that, under suitable assumptions on the collected historical data, we can both check if the problem is solvable and identify the matrices of a possible dead-beat unknown-input observer-based residual generator by entirely relying on data. A simple algorithm that successfully performs both tasks is proposed. Secondly, starting from the dead-beat unknown-input observer-based residual generator, we derive a reduced-order residual generator that performs only partial state estimation and achieves exact fault estimation, after a transient period of finite duration. Also, this second solution is first investigated from a model-based perspective, and then via data-driven techniques. The two methods are illustrated through examples.