H∞ Filtering with Inequality Constraints for Aircraft Turbofan Engine Health Estimation

H∞ filters (also called minimax filters) can estimate the state variables of a dynamic system. However, in the application of state estimators, some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of state estimators. The contribution of this paper is three-fold: first, this paper extends previous work on equality-constrained H∞ filtering and derives some new theoretical results; second, this paper shows how the inequalityconstrained H∞ filtering problem can be reduced to a standard quadratic programming problem; third, this paper shows how inequality-constrained H∞ filtering can be applied to aircraft engine health estimation to obtain improved performance. The incorporation of state constraints significantly increases the computational effort of the filter but also improves its estimation accuracy. The improved estimation accuracy is shown in this paper both theoretically and experimentally. We also show that the Kalman filter performs better for aircraft engine health estimation under nominal conditions, but the H∞ filter performs better in the presence of unmodeled errors with respect to worst case estimation error.