Active fault diagnosis for stochastic systems subject to non-convex input constraints

Abstract

In this paper, the problem of active fault diagnosis (AFD) is investigated for a class of continuous-time stochastic systems subject to non-convex input constraints. The input is designed to minimize the probability of misdiagnosis. Since the misdiagnosis probability cannot be expressed in the closed form, its Chernoff upper bound likely tighter than its widely used Bhattacharyya upper bound is exploited as an alternative. The closed-form expression of the Chernoff distance under Gaussian distributions is correctly deduced. For calculation simplification and diagnosis performance enhancement purposes, a novel input design criterion is constructed for AFD based on the Chernoff distance. The optimization problem for AFD is formulated as a bilevel optimization, where the outer and inner layers optimize the Chernoff distance parameter and the input respectively. A convex relaxation is proposed to relax non-convex input constraints into convex ones, and the optimal solution to the relaxed inner input design problem is proven to be also optimal for the original inner problem whose objective function and input constraints are both non-convex under certain conditions, which is referred to as lossless relaxation. The relaxed inner input design problem under the constructed design criterion can be solved to global optimums, and the relaxed outer optimization is solved by a grid search method. Given the optimal input, faults are diagnosed based on the minimum misdiagnosis probability decision rule. The effectiveness of the proposed AFD approach is demonstrated by utilizing a planetary landing example.