Threshold computation for fault detection in a class of discrete‐time nonlinear systems

In this paper, we address the problem of designing robust thresholds for fault detection in discrete‐time nonlinear uncertain systems in the presence of process disturbances. Both constant and dynamic thresholds are proposed. For the computation of constant thresholds, a generalized framework based on signal norms is developed. Different kinds of constant thresholds are studied in the framework proposed. Using linear matrix inequalities (LMI) techniques, algorithms are derived for the computation of these thresholds. Similarly, the dynamic threshold is designed by deriving an inequality on the upper bound of the modulus of the residual signal. This inequality is based on the solution of discrete‐time nonlinear uncertain systems. The simulation examples illustrate that false alarms are successfully eliminated using the proposed thresholds. Copyright © 2010 John Wiley & Sons, Ltd.     

Fault detection for a class of Markov jump systems with unknown disturbances

An optimized fault detection observer is designed for a class of Markov jump systems with unknown disturbances. By reconstructing the system, the residual error dynamic characteristics of unknown input and fault signals, including unknown disturbances and modeling error are obtained. The energy norm indexes of disturbance and fault signals of the residual error are selected separately to reflect the restraint of disturbance and the sensitivity of faults, and the design of the fault detection observer is described as an optimization problem. By using the constructed Lyapunov function and linear matrix inequalities, a sufficient condition that the solution to the fault detection observer exists is given and proved, and an optimized design approach is presented. The designed observer makes the systems have stochastic stability and better capability of restraining disturbances, and the given norm index is satisfied. Simulation results demonstrate that the proposed observer can detect the faults sensitively, and the influence of unknown disturbance on residual error can be restrained to a given range. __________ Translated from Journal of Xi’an Jiaotong University, 2007, 41(4): 458–462 [译自 : 西安交通大学学报]     

Integrated design of fault detection,isolation, and control for continuous‐time Markovian jump systems

In this paper, the problem of integrated fault detection, isolation, and control design of continuous‐time Markovian jump linear systems with uncertain transition probabilities is introduced and addressed for the first time in the literature. A single Markovian jump module designated as the integrated fault detection, isolation, and control under a mixed robust framework is considered to simultaneously achieve the desired detection, isolation, and control objectives. Conventional mixed robust approaches to the fault detection and isolation problem lead to conservative results due to the selection of identical Lyapunov matrices. Consequently, the extended linear matrix inequality methodology is utilized in this work to reduce the conservativeness of standard approaches by introducing additional matrix variables so that the coupling of Lyapunov matrices with the system matrices is eliminated. Simulation results for an application to the GE F‐404 aircraft engine system illustrate the effectiveness and capabilities of our proposed design methodologies. Comparisons with relevant work in the literature are also provided to demonstrate the advantages of our proposed solutions.     

and filter design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates

This paper addresses the problems of and full‐order filter design for continuous‐time Markov jump linear systems subject to uncertainties. Different from the available methods in the literature, the main novelty of the proposed approach is the possibility of computing bounds to the and norms of the augmented system composed by the uncertain Markov jump linear system plus the robust filter through Lyapunov matrices depending polynomially on the uncertainties affecting independently the matrices of each operation mode and the transition rate matrix. By means of a suitable representation of the uncertainties, the proposed filter design conditions are expressed in terms of linear matrix inequality relaxations associated with searches on scalar parameters. As an additional flexibility, the conditions can be used to synthesize filters with partial, complete, or null Markov mode availability. Numerical experiments illustrate that the proposed approach is more general and can be less conservative than the available methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Fault detection filter design for discrete‐time switched linear systems with mode‐dependent average dwell‐time

This paper is concerned with the problem of the fault detection (FD) filter design for discrete‐time switched linear systems with mode‐dependent average dwell‐time. The switching law is mode‐dependent and each subsystem has its own average dwell‐time. The FD filters are designed such that the augmented switched systems are asymptotically stable, and the residual signal generated by the filters achieves a weighted l₂‐gain for some disturbances and guarantees an H _? performance for the fault. By the aid of multiple Lyapunov functions combined with projection lemma, sufficient conditions for the design of the FD filters are formulated by linear matrix inequalities, furthermore, the filters gains are characterized in terms of the solution of a convex optimization problem. Finally, an application to boost convertor is given to illustrate the effectiveness and the applicability of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.     

马尔可夫跳跃系统的鲁棒故障检测

对时滞依赖于模态的离散马尔可夫跳跃系统的鲁槔故障检测问题进行了研究.利用多面体系统表征系统时变参数的不确定性,在其顶点求解可以显著减少计算量.基于依赖于系统模态的滤波器构造残差产生系统,所设计的故障检测滤波器,其参数矩阵不是常值,而是以同一概率随着系统模态的变化而变化.设置H∞性能指标并利用线性矩阵不等式推导出故障检测滤波器存在的充分条件,求解出滤波器的参数矩阵.仿真结果表明:设计得到的鲁棒故障检测滤波器能够保证对故障信号的敏感性,并对外界扰动信号和系统时变参数的不确定性具有鲁棒性.     

Mode‐independent H∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements

This paper is concerned with the problem of H_∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements, when the jumping mode information is not accessible. By converting the quantized errors into a sector‐bounded nonlinearity, the parametric uncertainties and measurements quantization are dealt with in a unified framework. The mode‐independent H_∞ filter is designed, and sufficient conditions are established via Lyapunov function approach, such that for all possible uncertain parameters and quantization errors, the resulting filtering error system is robustly stochastically stable and achieves a guaranteed H_∞ filtering error performance index. A numerical example is provided to demonstrate the feasibility and effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Network‐based fault detection for discrete‐time state‐delay systems: A new measurement model

In this paper, the fault detection problem is studied for a class of discrete‐time networked systems with multiple state delays and unknown input. A new measurement model is proposed to account for both the random measurement delays and the stochastic data missing (package dropout) phenomenon, which are typically resulted from the limited capacity of the communication networks. At any time point, one of the following cases (random events) occurs: measurement missing case, no time‐delay case, one‐step delay case, two‐step delay case, …, q‐step delay case. The probabilistic switching between different cases is assumed to obey a homogeneous Markovian chain. We aim to design a fault detection filter such that, for all unknown input and incomplete measurements, the error between the residual and weighted faults is made as small as possible. The addressed fault detection problem is first converted into an auxiliary H_∞ filtering problem for a certain Markovian jumping system (MJS). Then, with the help of the bounded real lemma of MJSs, a sufficient condition for the existence of the desired fault detection filter is established in terms of a set of linear matrix inequalities (LMIs). A simulation example is provided to illustrate the effectiveness and applicability of the proposed techniques. Copyright © 2007 John Wiley & Sons, Ltd.     

Constructive approximation of non‐linear discrete‐time systems

It is known that large classes of approximately‐finite‐memory maps can be uniformly approximated arbitrarily well by the maps of certain non‐linear structures. As an application, it was proved that time‐delay networks can be used to uniformly approximate arbitrarily well the members of a large class of causal nonlinear dynamic discrete‐time input–output maps. However, the proof is non‐constructive and provides no information concerning the determination of a structure that corresponds to a prescribed bound on the approximation error. Here we give some general results concerning the problem of finding the structure. Our setting is as follows. There is a large family 𝒢 of causal time‐invariant approximately‐finite‐memory input‐output maps G from a set S of real d‐vector‐valued discrete‐time inputs (with d⩾1) to the set of ℝ‐valued discrete‐time outputs, with both the inputs and outputs defined on the non‐negative integers 𝒵₊. We show that for each ϵ>0, any Gϵ𝒢 can be uniformly approximated by a structure map H(G, ·) to within tolerance ϵ, and we give analytical results and an example to illustrate how such a H(G, ·) can be determined in principle. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimal filtering,fault detection and isolation for linear discrete‐time systems in a noisy environment

In this paper the state observer design and the fault detection and isolation problems are investigated in the context of linear discrete‐time state‐space models whose state equations are affected by (actuator) faults and disturbances. Model as well as measurement errors, described as zero‐mean white Gaussian noise, are also assumed to act additively on the state and on the output equations, respectively. Upon introducing several deterministic and stochastic goals, that constitute the mathematical formalization of very natural and practical requirements, necessary and sufficient conditions for the existence of an asymptotic state observer and an observer‐based fault detector and isolator, that achieve the above goals, are finally derived and a constructive procedure is described. Copyright © 2003 John Wiley & Sons, Ltd.     

Neural‐network‐based finite‐time H∞ control for extended Markov jump nonlinear systems

This paper presents a neural‐network‐based finite‐time H_∞ control design technique for a class of extended Markov jump nonlinear systems. The considered stochastic character is described by a Markov process, but with only partially known transition jump rates. The sufficient conditions for the existence of the desired controller are derived in terms of linear matrix inequalities such that the closed‐loop system trajectory stays within a prescribed bound in a fixed time interval and has a guaranteed H_∞ noise attenuation performance for all admissible uncertainties and approximation errors of the neural networks. A numerical example is used to illustrate the effectiveness of the developed theoretic results. Copyright © 2009 John Wiley & Sons, Ltd.     

Risk‐sensitive filtering for nonlinear Markov jump systems on the basis of particle approximation

In this paper, the risk‐sensitive filtering method that relaxes the dependence on model accuracy is extended to nonlinear Markov jump systems (MJSs). In the method, the so‐called reference probability technique together with particle approximation is utilized to derive the risk‐sensitive filter in nonlinear non‐Gaussian framework. The novelty of the proposed approach is that a ‘risky’ interacting resampling step is performed to both moderate the modeling uncertainties and to solve the problem of particle explosion. A designer‐chosen parameter named risk‐sensitive parameter allows us to make a trade‐off between the filtering accuracy for the nominal model and the robustness to uncertainties. With a meaningful example, it shows that the developed method can outperform the widely used method‐particle filter and interacting multiple model‐particle filter in nonlinear MJSs with uncertainties. Copyright © 2011 John Wiley & Sons, Ltd.     

State smoothing in Markov jump systems with lagged mode observation

Estimation involving Markov jump systems (MJSs) is widely used in target tracking, speech recognition and communication. It is assumed in MJSs that state measurement and mode observation are synchronous. In applications such as image‐based target tracking, the target orientation, as one of the mode observations, needs additional computation time for pattern recognition and thus can be delayed. This motivates us to explore the smoothing problem of MJSs with mode observation lagged to state measurement. This brief paper presents a recursive estimator by deriving the conditional state mean and the conditional model probability from both delayed mode observation and state measurement. Simulations on maneuvering target tracking are carried out to validate the performance of the proposed smoother in comparison with existing methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust H∞ filtering for switched linear discrete‐time systems with polytopic uncertainties

In this paper, the problem of robust H_∞ filtering for switched linear discrete‐time systems with polytopic uncertainties is investigated. Based on the mode‐switching idea and parameter‐dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H_∞ performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H_∞ noise‐attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

Filter‐based fault detection and diagnosis using output PDFs for stochastic systems with time delays

In this paper, a fault detection and diagnosis (FDD) scheme is studied for general stochastic dynamic systems subjected to state time delays. Different from the formulation of classical FDD problems, it is supposed that the measured information for the FDD is the probability density function (PDF) of the system output rather than its actual value. A B‐spline expansion technique is applied so that the output PDF can be formulated in terms of the dynamic weights of the B‐spline expansion, by which a time delay model can be established between the input and the weights with non‐linearities and modelling errors. As a result, the concerned FDD problem can be transformed into a classic FDD problem subject to an uncertain non‐linear system with time delays. Feasible criteria to detect the system fault are obtained and a fault diagnosis method is further presented to estimate the fault. Simple simulations are given to demonstrate the efficiency of the proposed approach. Copyright © 2006 John Wiley & Sons, Ltd.     

Fault‐tolerant saturated control for switching discrete‐time systems with delays

In this paper, fault‐tolerant control problem for discrete‐time switching systems with delay and saturated input is studied. Sufficient conditions of building an observer are obtained by using multiple Lyapunov function. These conditions are worked out using cone complementarity technique, to obtain LMIs with slack variables and multiple weighted residual matrices. The obtained results are applied on a numerical example showing fault detection, localization of fault, and reconfiguration of the control to maintain asymptotic stability even in the presence of a permanent sensor fault and saturation on the control. Copyright © 2014 John Wiley & Sons, Ltd.     

Fault detection for discrete‐time switched singular time‐delay systems: an average dwell time approach

In this paper, the fault detection problem is investigated for a class of discrete‐time switched singular systems with time‐varying state delays. The residual generator is firstly constructed based on a switched filter, and the design of fault detection filter is formulated as an H _∞ filtering problem, that is, minimizing the error between residual and fault in the H _∞ sense. Then, by constructing an appropriate decay‐rate‐dependent piecewise Lyapunov function and using the average dwell time scheme, a sufficient condition for the residual system to be regular, causal, and exponential stable while satisfying a prescribed H _∞ performance is derived in terms of linear matrix inequalities (LMIs). The corresponding solvability condition for the desired fault detection filters is also established via LMI approach. Finally, a numerical example is presented to show the effectiveness of the developed theoretical results.Copyright © 2012 John Wiley & Sons, Ltd.     

LMI solutions to the mixed ℋ︁−/ℋ︁∞ fault detection observer design for linear parameter‐varying systems

This paper addresses the mixed ??_?/??_∞ fault detection observer design issue for a class of linear parameter‐varying (LPV) systems. Analogous to the definition of the quadratic ??_∞ performance for LPV systems and the ??_? index for linear time invariant (LTI) systems, the quadratic ??_? index and the affine quadratic ??_? index for LPV systems are defined in terms of linear matrix inequalities (LMIs). The first algorithm for designing the mixed ??_?/H_∞ observer is proposed, which aims at minimizing the quadratic ??_∞ performance and maximizing the quadratic ??_? index of the observer error dynamic systems. To reduce the conservativeness of this algorithm, the affine quadratic ??_∞ performance and the affine ??_? index for LPV systems are utilized. The robustness conditions and affine ??_? index conditions for the underlying observer optimization issue are formulated as parameter‐dependent LMIs. The Gridding technique and multi‐convexity concept are applied, respectively, for reducing the parameter‐dependent LMIs to finite LMI constraints. Correspondingly, two iterative algorithms are proposed. Furthermore, the threshold design and the estimation of the worst undetectable fault size are investigated. An example is studied to demonstrate the effectiveness of the proposed algorithms. Copyright © 2010 John Wiley & Sons, Ltd.