Guaranteed active fault diagnosis for uncertain nonlinear systems

An input design method is presented to actively isolate faults for polynomial or rational systems in the presence of unknown-but-bounded uncertainties. For active fault isolation, the input is required to lead to outputs consistent with at most one fault model despite disturbances, measurement noise, and parametric uncertainty. This task is posed in terms of a bilevel optimization problem where the inner program verifies, for a given input, that the outputs are consistent with at most one model, while the outer program determines the minimally harmful input. Because of the nonlinear dynamics, we propose to replace the inner program with a convex relaxation that can be efficiently solved while still guaranteeing fault detection and isolation. The approach is numerically demonstrated on a two-tank system with three fault models.