Interval state and sensor fault estimation based on unknown input observer and interval hull computation

This paper investigates the problem of interval estimation of state and sensor fault simultaneously based on the unknown input decoupling technique and interval hull computation approach. To facilitate sensor fault estimation conveniently, it is first regarded as an auxiliary state, and the faulty system is transformed into an augmented descriptor system. Next, an unknown input observer is designed based on the P-radius method for this augmented descriptor system to decouple some of the unknown system disturbance. Then, the bounds of the augmented state set effected by the undecoupled system uncertainties are calculated via an interval hull approximation technique. Finally, the effectiveness and practicality of this work are illustrated by a numerical example and a quadruple-tank process system. This work demonstrates that by decoupling some unknown disturbances from the estimation error system, the zonotope's size, corresponding to state and sensor fault estimation, can be further reduced.