On designing an extended Hi/H∞-FDF for a class of nonlinear Systems

Abstract This paper investigates the problem of fault detection (FD) for a class of discrete-time nonlinear systems by using H i /H ∞ optimization. A finite horizon index H i and H ∞ norm are introduced to represent the sensitivity of residual to fault and robustness of residual against unknown input, respectively. Then the problem of residual evaluation is formulated as to a nonlinear H i /H ∞ optimization. It is shown that a local optimal H i /H ∞ FDF can be obtained by recursively computing of extended Kalman filter and a post-filter. Moreover, the local optimal solution is not unique and, for an arbitrary feasible filter gain matrix, a dynamic post-filter is also presented. A numerical example is given to demonstrate the effectiveness of the proposed method.