Robust fault detection of singular Markov jump systems with partially unknown information

Event-Based Asynchronous H∞ Control for Nonhomogeneous Markov Jump Systems With Imperfect Transition Probabilities

The event-based H∞ control problem is investigated for a class of nonhomogeneous Markov jump systems (MJSs) with partially unknown transition probabilities (TPs). The MJS is characterized by a piecewise nonhomogeneous Markovian chain, where the switching of the system TP matrix is governed by a higher-level chain. A hidden Markov model (HMM) is employed to observe the system mode, which cannot always be correctly detected in practice. Under this framework, the partially unknown TPs existing in both higher-level TPs (HTPs) and conditional TPs (CTPs) are taken into account for practical consideration. Additionally, an observed-mode-dependent event-triggered mechanism (ETM) is employed to design an asynchronous controller, which is expected to alleviate the burden of the communication network. Evidently, the considered scenario is fairly general and covers some special cases. With the above consideration, sufficient conditions are established to guarantee stochastic stability of the resulting closed-loop system with a prescribed H∞ performance. Finally, two examples are presented to demonstrate the effectiveness and applicability of the proposed method.

Asynchronous fault detection filter of positive Markov jump systems by dynamic event-triggered mechanism

This paper explores the design of a positive l₁-gain asynchronous non-fragile fault detection filter (FDF) for discrete-time positive Markov jump systems (PMJSs) based on the dynamic event-triggered method (DETM). Due to the effect of positivity on event-triggered mechanisms and non-triviality on stability of discrete-time PMJSs, a new more powerful and generic DETM that can avoid non-triviality is developed. The asynchronous situation between the non-fragile FDF modes and the system modes is effectively managed by employing a hidden Markov model. Then, the solvability criteria for issues of concern are presented by building the copositive Lyapunov function (CLF) with internal dynamic variables (IDV). An alternative sufficient condition is derived based on the obtained results. Subsequently, a co-design project of the expected dynamic event-triggered positive l₁-gain asynchronous non-fragile fault detection filter (DETPGAN-FFDF) and the designed DETM is proposed in this paper. Finally, the effectiveness and superiority of the approach are verified by numerical arithmetic examples and practical applications based on pest management.

Asynchronous Frequency-Dependent Fault Detection for Nonlinear Markov Jump Systems Under Wireless Fading Channels

In this article, the asynchronous fault detection (FD) strategy is investigated in frequency domain for nonlinear Markov jump systems under fading channels. In order to estimate the system dynamics and meet the fact that not all the running modes can be observed exactly, a set of asynchronous FD filters is proposed. By using statistical methods and the Lynapunov stability theory, the augmented system is shown to be stochastic stable with a prescribed l₂ gain even under fading transmissions. Then, a novel lemma is developed to capture the finite frequency performance. Some solvable conditions with less conservatism are subsequently deduced by exploiting novel decoupling techniques and additional slack variables. Besides, the FD filter gains could be calculated with the aid of the derived conditions. Finally, the effectiveness of the proposed method is shown by an illustrative example.

Robust Detection of Minute Faults in Uncertain Systems Using Energy Activity

Fault detection is one of the key steps in Fault Detection and Isolation (FDI) and, therefore, critical for subsequent prognosis or implementation of Fault Tolerant Control (FTC). It is, therefore, advisable to utilize detection algorithms which are quick and can detect the smallest faults. Model-based detection methods satisfy both these criteria and should be preferred. However, a big limitation for model-based methods is that they require the accurate value of the component parameters, which is difficult to obtain in real situations. This limits the accuracy of model-based methods. This paper proposes a new method for fault detection using Energy Activity (EA) which can detect minute levels of fault in systems with high component uncertainty. Different forms of EA are developed for use as an FDI metric. The proposed forms are simulated using a two-tank system under various types of faults. The results are compared with each other and with the traditional model-based FDI method using Analytical Redundancy Relations (ARRs). The simulations are performed considering model uncertainties to check the inherent performance of the methods. From initial simulations, it is established that the integral form of EA is most suited for fault detection. The integral for if EA is then tested using a real two-tank system considering both the model and measurement uncertainties.