Observer-based residual generator for fault detection and isolation of convex sets

In this paper, we formulate and solve a novel residual generation problem that incorporates elements from both set-based estimation and unknown input observers. The objective is to determine whether the unknown input variables (e.g., possible faults) lie in a generic convex set of the input (fault) space, without needing to estimate the exact value of these variables. The output residual states if the unknown variables belong to a predefined region or not. Sufficient existence conditions are proven and discussed from a geometric point of view. An extension to non-convex, or even non-connected sets is also provided. The need to detect whether an unknown variable lies inside a region of the input space is motivated by fault detection and isolation purposes. Hence, simulation results showcase how the solution can deal with actuator fault isolation in autonomous systems, namely a quadrotor.