Observer-based asymptotic active fault diagnosis: A two-layer optimization framework

Abstract

This paper proposes a novel asymptotic online robust active fault diagnosis (AFD) framework for discrete linear time-invariant (LTI) systems using a bank of set-valued observers (SVO), each SVO designed to match a healthy/faulty actuator mode. Different from the existing set-based AFD methods, the proposed AFD method designs an input at each time instant by solving a two-layer optimization problem. At each time instant, an input is designed such that the output sets estimated by the SVOs at the next time instant keep away from each other as far as possible. With this idea, faults can be diagnosed after a sufficiently long period by designing and injecting inputs into the system online. The key point of the proposed AFD method is to establish a logic describing the process keeping a group of output estimation sets asymptotically away from each other as far as possible, which is done by formulating a two-layer optimization problem to simultaneously optimize the center distances and sizes of output estimation sets. At the end, a case study is used to illustrate the effectiveness of the proposed method.