Fault detection for non-linear system with unknown input and state constraints

This study extends the problem of fault detection (FD) for linear discrete-time systems with unknown input to non-linear systems. Moreover, based on physical consideration, the constraints of state are considered. A non-linear recursive filter is developed where the constrained state and the input are interconnected. Constraints which can improve the quality of estimation are imposed on individual updated sigma points as well as the updated state. The advantage of algorithm is that it is able to incorporate arbitrary constraints on the states during the estimation procedure. Unknown input which can be any signal is obtained by least-squares unbiased estimation and the state estimation problem is transformed into a standard unscented Kalman filter problem. By testing the mean of the innovation process, a real-time FD approach is proposed. Simulations are provided to demonstrate the effectiveness of the theoretical results.