Active Fault Diagnosis for Stochastic Systems: A Unified Design With Optimal Control

This article is concerned with the unified design problem of active fault diagnosis (AFD) and optimal control (OC) for a class of stochastic systems. In AFD, the input is designed to minimize the misdiagnosis probability, whereas the control performance is optimized by designing the input in OC. By exploiting a finite-horizon constrained optimization formulation, a novel unified design framework with normalization strategies is developed for AFD and OC to balance the diagnosis and control performances. The control task is treated as a constraint of the optimization problems to ensure that the task is fulfilled. The Holder divergence family is proposed to construct a new input design criterion for AFD with multifault modes, whose maximization is proven to minimize an upper bound on the misdiagnosis probability. The input design problem under the constructed design criterion for AFD and the input design problem for OC can be solved to global optimality. Based on this global optimality, normalization strategies are utilized to adjust the magnitudes of the objective functions for AFD and OC into the same scale. The quantitative balance between the diagnosis and control performances can be achieved within the developed unified design framework. The effectiveness and superiority of the proposed approach are demonstrated by simulation results on a four-tank system.