Fault Detection for Discrete‐Time Uncertain Systems with Polytopic Uncertainties: A Markov Approach

Abstract

In this paper, the fault detection problem for a class of discrete-time polytopic uncertain systems is studied. Different from the traditional methods dealing with polytopic uncertainties, not only its values but also the probability distributions are considered. First of all, the above process about polytopic uncertainty is described by applying a Markov process. Then, the original system with polytopic uncertainties becomes to be a Markovian jump system (MJS) without any uncertainty. Accordingly, the fault detection problem is transformed to be a similar one but considered for an MJS. Particularly, the fault detection and isolation (FDI) filter is constructed to be mode-dependent and also said to be polytope-dependent. Since more information of uncertainty is considered, it is claimed that the obtained results are less conservative. Finally, a practical example is used to show the effectiveness and superiority of the proposed methods.

Fault diagnosis for semilinear distributed parameter systems with actuator/sensor based on iterative learning control

“…where k (k = 0,1,2,…) denotes the kth iteration of the repetitive operation of the fault estimator (8). q k ðx,tÞ and y k ðtÞ are the estimates of the system state and the system output, respectively.…”

“…The residual signal e k (t) is the error between the output of the actual system (1) and the output of fault estimator (8).…”

“…To guarantee the dependability and security of systems, the technologies of fault diagnosis are indispensable. The fault diagnosis has been extensively concerned for various systems which contain stochastic Takagi-Sugeno fuzzy systems [1], discrete event systems [2,3], power systems [4], linear parameter varying systems [5], and many methods which have been used in fault diagnoses, such as Kalman filter [6], deep learning [7], and Markov approach [8]. Han et al [9] investigated the fault diagnosis problem for discrete-time systems with simultaneous considering the faults and delays with a reduced-order observer.…”

Fuzzy‐HMM modeling for emotion detection using electrocardiogram signals

“…Furthermore, probability models are efficient for modeling a dynamic system [17]. The well-known Markov process or Markov chain has been found to be useful in many modeling and control problems [18][19][20].-]. Consequently, Hidden Markov Models (HMMs) are applied in this paper for emotion modeling.…”

Asynchronous Fault Detection H2 Filter For Markov Jump Linear Systems

“…Over the last decades, industrial processes have become more complex and the demands for precise, reliable, and secure procedures followed the same path. In order to fulfill those demands, different approaches have been proposed in the literature and, in particular, one of them is the socalled Fault Detection and Isolation (FDI) approach, which primarily detects faults and rearranges the system to minimize the possible losses and/or chances of accidents, see for example (Wang et al, 2019), (Zhou et al, 2017), and (Atitallah et al, 2018). The FDI framework is widely applied to different fields in engineering as presented in the review (Venkatasubramanian et al, 2003).…”