Fault detection for discrete-time networked nonlinear systems with incomplete measurements

This article addresses the problem of fault detection (FD) for discrete-time networked systems with global Lipschitz nonlinearities and incomplete measurements, including time delays, packet dropouts and signal quantisation. By utilising a discrete-time homogeneous Markov chain, an improved model which considers packet dropout compensation has been proposed to describe the above network-induced phenomena. We aim to design a mode-dependent fault detection filter (FDF) such that the FD system is asymptotically mean-square stable and satisfies a prescribed attenuation level. The addressed FD problem is then converted into an auxiliary H _∞ filtering problem of Markov jump system with time-varying delay. A sufficient condition for the existence of the FDF is derived in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired FDF can also be characterised. A numerical example is exploited to show the effectiveness of the results obtained.     

Fault detection for a class of discrete‐time nonlinear systems subject to network‐induced uncertainties

This paper addresses the problem of fault detection (FD) for discrete‐time systems with global Lipschitz conditions and network‐induced uncertainties. By utilizing Bernoulli stochastic variables and a switching signal, a unified measurement model is proposed to describe three kinds of network‐induced uncertainties, that is, access constraints, time delays, and packet dropouts. We aim to design a mode‐dependent fault detection filter (FDF) such that, for all external disturbances and the above uncertainties, the error between the residual and fault is made as small as possible. The addressed FD problem is then converted into an auxiliary H_∞ filtering problem for discrete‐time stochastic system with multiple time‐varying delays. By applying the Lyapunov‐Krasovskii approach, a sufficient condition for the existence of the FDF is derived in terms of certain linear matrix inequalities (LMI). When these LMIs are feasible, the explicit expression of the desired FDF can also be characterized. A numerical example is exploited to show the effectiveness of the results obtained. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Input–output method to fault detection for discrete-time fuzzy networked systems with time-varying delay and multiple packet losses

The fault detection (FD) problem for discrete-time fuzzy networked systems with time-varying delay and multiple packet losses is investigated in this paper. The communication links between the plant and the FD filter (FDF) are assumed to be imperfect, and the missing probability is governed by an individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time delayed fuzzy networked system is first transformed into the form of interconnect ion of two subsystems by applying an input–output method and a two-term approximation approach, which are employed to approximate the time-varying delay. Our attention is focused on the design of fuzzy FDF (FFDF) such that, for all data missing conditions, the overall FD dynamics are input–output stable in mean square and preserves a guaranteed performance. Sufficient conditions are first established via H_∞ performance analysis for the existence of the desired FFDF; meanwhile, the corresponding solvability conditions for the desired FFDF gains are characterised in terms of the feasibility of a convex optimisation problem. Moreover, we show that the obtained criteria based on the input–output approach can also be established by applying the direct Lyapunov method to the original time-delay systems. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed approaches.     

Fault detection filter design for stochastic time-delay systems with sensor faults

This article considers the fault detection (FD) problem for a class of Itô-type stochastic time-delay systems subject to external disturbances and sensor faults. The main objective is to design a fault detection filter (FDF) such that it has prescribed levels of disturbance attenuation and fault sensitivity. Sufficient conditions for guaranteeing these levels are formulated in terms of linear matrix inequalities (LMIs), and the corresponding fault detection filter design is cast into a convex optimisation problem which can be efficiently handled by using standard numerical algorithms. In order to reduce the conservatism of filter design with mixed objectives, multi-Lyapunov functions approach is used via Projection Lemma. In addition, it is shown that our results not only include some previous conditions characterising H _∞ performance and H _? performance defined for linear time-invariant (LTI) systems as special cases but also improve these conditions. Finally, two examples are employed to illustrate the effectiveness of the proposed design scheme.     

Robust fault detection for networked control systems with nonlinear disturbances and imperfect measurements

In this article, the robust fault detection (FD) problem is investigated for networked control systems with nonlinear disturbances and imperfect measurements. Under the consideration of packet-dropout compensation, a new measurement model is proposed to take the time-varying delay, random packet dropout and quantisation effect into account simultaneously. After properly augmenting the states of the original system and the FD filter, the robust FD problem is formulated as an auxiliary H _∞ filtering problem for a stochastic parameter system with time-varying delays and uncertainties. A sufficient condition for the existence of the robust FD filter is derived in terms of linear matrix inequalities, which depends on both the network status and the quantisation density. A numerical example is provided to illustrate the effectiveness of the proposed method.     

线性离散马尔科夫跳跃系统最优故障检测

本文研究线性离散马尔科夫跳跃系统的最优故障检测问题。通过设计基于观测器的故障检测滤波器作为残差产生器,将滤波器的设计问题归结为随机意义下H_/H或H/H性能指标优化问题。基于算子优化方法,通过解耦合Riccati方程得到上述问题的统一解。算例验证所提方法的有效性。     

Robust fault detection for networked systems with communication delay and data missing

In this paper, the robust fault detection problem is investigated for a class of discrete-time networked systems with unknown input and multiple state delays. A novel measurement model is utilized to represent both the random measurement delays and the stochastic data missing phenomenon, which typically result from the limited capacity of the communication networks. The network status is assumed to vary in a Markovian fashion and its transition probability matrix is uncertain but resides in a known convex set of a polytopic type. The main purpose of this paper is to design a robust fault detection filter such that, for all unknown inputs, possible parameter uncertainties and incomplete measurements, the error between the residual signal and the fault signal is made as small as possible. By casting the addressed robust fault detection problem into an auxiliary robust H_∞ filtering problem of a certain Markovian jumping system, a sufficient condition for the existence of the desired robust fault detection filter is established in terms of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and applicability of the proposed technique.     

H∞ fault detection with randomly occurring nonlinearities and channel fadings

In this paper, the H_∞ fault detection problem is investigated for a class of discrete-time stochastic systems with both channel fadings and randomly occurring nonlinearities. Due to Doppler effect and multi-path delays, channel fadings are inevitable and also cause unpredictable dynamic behaviour. The Lth Rice fadings model, which is accounted for both channel fadings and time delays, can be employed to describe this phenomenon. Meanwhile, by using a Bernoulli distributed white sequence, a kind of non-linear disturbance appearing in a random way is also considered in the H_∞ fault detection issue. The purpose of the addressed problem is to design a fault detection filter such that, in the presence of channel fadings, the overall fault detection dynamics is stochastically stable and, at the same time, the error between the residual (generated by the fault detection filter) and the fault signal is made as small as possible. By utilising the Lyapunov stability theory associated with the intensive stochastic analysis techniques, sufficient conditions are established under which the addressed H_∞ fault detection problem is recast as solving a convex optimisation problem via the semi-definite programme method. Finally, a simulation example is exploited to show the effectiveness of the method proposed in this paper.     

Fault detection for discrete-time switched systems with interval time-varying delays

This paper investigates the problem of fault detection filter design for discrete-time switched systems with interval time-varying delays. The residual generator is constructed based on a mode-dependent fault detection filter, i.e., the designed fault detection filter is also a switched system as well. By constructing a novel switched Lyapunov functional, a new criterion is obtained for the residual system. Based on this, a sufficient condition for the existence of the above filter is established in terms of linear matrix inequalities (LMIs). The designed fault detection filter can guarantee the difference between the generated residual signal and the fault signal as small as possible. An example is provided to illustrate the effectiveness of the proposed method.     

Fault detection filter design for stochastic networked control systems

This paper is concerned with the fault detection filter (FDF) design for networked control systems subject to time‐varying transmission intervals and delays, packet dropouts, and communication constraints. The considered communication constraint is that only one network node is allowed to gain access to the shared communication channel. Also, the accessing of each node is scheduled by a specified stochastic protocol, and the remote FDFs perform the FD task only with these partially available measurements. By focus on the network‐induced phenomena, the whole FD system are first modeled in the framework of switched stochastic systems with multiple stochastic parameters. Subsequently, by using the multi‐Lyapunov functional approach and novel analysis approach, less conservative conditions including some previous existing results are derived to construct such FDFs. Finally, an example is given to illustrate the effectiveness of the proposed method.Copyright © 2013 John Wiley & Sons, Ltd.     

Fuzzy-model-based robust fault detection with stochastic mixed time delays and successive packet dropouts

This paper is concerned with the network-based robust fault detection problem for a class of uncertain discrete-time Takagi-Sugeno fuzzy systems with stochastic mixed time delays and successive packet dropouts. The mixed time delays comprise both the multiple discrete time delays and the infinite distributed delays. A sequence of stochastic variables is introduced to govern the random occurrences of the discrete time delays, distributed time delays, and successive packet dropouts, where all the stochastic variables are mutually independent but obey the Bernoulli distribution. The main purpose of this paper is to design a fuzzy fault detection filter such that the overall fault detection dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Sufficient conditions are first established via intensive stochastic analysis for the existence of the desired fuzzy fault detection filters, and then, the corresponding solvability conditions for the desired filter gains are established. In addition, the optimal performance index for the addressed robust fuzzy fault detection problem is obtained by solving an auxiliary convex optimization problem. An illustrative example is provided to show the usefulness and effectiveness of the proposed design method.     

Robust H∞ performance for discrete time T-S fuzzy switched memristive stochasticneural networks with mixed time-varying delays

ABSTRACT

In this paper, we study the robust H _∞ performance for discrete-time T-S fuzzy switched memristive stochastic neural networks with mixed time-varying delays and switching signal design. The neural network under consideration is subject to time-varying and norm bounded parameter uncertainties. Decomposing of the delay interval approach is employed in both the discrete delays and distributed delays. By constructing a proper Lyapunov-Krasovskii functional (LKF) with triple summation terms and using an improved summation inequality techniques. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to guarantee the considered discrete-time neural networks to be exponentially stable. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the developed theoretical results.     

Optimal fault detection for linear discrete time-varying systems

This paper deals with the problem of observer-based fault detection for linear discrete time-varying (LDTV) systems. A problem formulation is first proposed to address the optimization of the fault detection filter (FDF) design, which is expressed in terms of maximizing a finite horizon H_∞/H_∞ or H₋/H_∞ performance index. This formulation can be applied to FDF design of LDTV systems subject to l₂-norm bounded unknown inputs or stochastic noise sequences. It is shown that a unified optimal solution to the FDF can be obtained by solving the discrete time Riccati equation and the optimal FDF is not unique. A numerical example is given to illustrate the proposed method.     

Fault Estimation for Nonlinear Networked Systems with Time‐Varying Delay and Random Packet Dropout

In this paper, the fault estimation problem is studied for a class of nonlinear networked control systems with imperfect measurements. A novel measurement model is proposed to take time‐varying delays, random packet dropouts, and the packet‐dropout compensation into consideration simultaneously. After properly augmenting the states of the original system and the fault estimation filter, the addressed fault estimation problem is converted into an auxiliary H_∞ filtering problem for a stochastic parameter system. In terms of matrix inequalities, a sufficient condition for the existence of the fault estimation filter is derived that depends on the packet dropout rate, the upper and lower bounds of time delays, and the size of the consecutive packet dropouts. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.     

Fault detection for nonlinear networked control systems with stochastic interval delay characterisation

In this article, we are concerned with the fault detection (FD) problem for nonlinear networked control systems (NCSs) with network-induced stochastic interval delay. By employing the information of probabilistic distribution of networked-induced time-varying delay, nonlinear constraint and the FD filter, nonlinear stochastic delay system model is established. Based on the obtained nonlinear model, utilising FD filter as residual generator, FD of nonlinear NCSs is formulated as nonlinear H _∞-filtering problem. Especially, the stochastic stability and prescribed H _∞ attenuation level are achieved using the Lyapunov functional approach, the desired FD filter is constructed in terms of certain linear matrix inequalities, which depends on not only nonlinear level but also on delay-interval and delay-interval-occurrence-rate. Numerical examples are provided to illustrate the effectiveness and applicability of proposed technique.     

存在多步测量数据包丢失的线性离散时变系统鲁棒H∞故障检测滤波器设计

研究了一类存在多步测量数据包丢失的线性离散时变系统故障检测滤波器(Fault detection filter, FDF)设计问题. 采用基于观测器的鲁棒H∞故障检测滤波器作为残差产生器,将故障检测滤波器的设计问题转化为一类随机时变系统的H∞滤波问题, 基于Riccati方程推导并证明了其存在的充分必要条件. 将滤波器参数矩阵求取转化为二次型优化问题, 通过求解Riccati方程, 得到滤波器参数矩阵的显式解. 算例验证了所提算法的有效性.     

A finite frequency domain approach to fault detection for linear discrete-time systems

This paper deals with the fault detection (FD) problem in the finite frequency domain for linear time-invariant discrete-time systems with bounded disturbances. A fault detection observer is designed by employing two performance indesxes which are used to increase the fault sensitivity in finite frequency domain and attenuate the effects of disturbances in full frequency domain. With the aid of the generalized Kalman–Yakubovich–Popov (GKYP) Lemma, the design methods are presented in terms of solutions to a set of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed method.     

Fault detection for discrete-time LPV systems using interval observers

This paper is concerned with the fault detection (FD) problem for discrete-time linear parameter-varying systems subject to bounded disturbances. A parameter-dependent FD interval observer is designed based on parameter-dependent Lyapunov and slack matrices. The design method is presented by translating the parameter-dependent linear matrix inequalities (LMIs) into finite ones. In contrast to the existing results based on parameter-independent and diagonal Lyapunov matrices, the derived disturbance attenuation, fault sensitivity and nonnegative conditions lead to less conservative LMI characterisations. Furthermore, without the need to design the residual evaluation functions and thresholds, the residual intervals generated by the interval observers are used directly for FD decision. Finally, simulation results are presented for showing the effectiveness and superiority of the proposed method.     

Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays

In this paper, the problem of stochastic synchronization analysis is investigated for a new array of coupled discrete-time stochastic complex networks with randomly occurred nonlinearities (RONs) and time delays. The discrete-time complex networks under consideration are subject to: 1) stochastic nonlinearities that occur according to the Bernoulli distributed white noise sequences; 2) stochastic disturbances that enter the coupling term, the delayed coupling term as well as the overall network; and 3) time delays that include both the discrete and distributed ones. Note that the newly introduced RONs and the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmission process is affected by a noisy environment (e.g., internet-based control systems). By constructing a novel Lyapunov-like matrix functional, the idea of delay fractioning is applied to deal with the addressed synchronization analysis problem. By employing a combination of the linear matrix inequality (LMI) techniques, the free-weighting matrix method and stochastic analysis theories, several delay-dependent sufficient conditions are obtained which ensure the asymptotic synchronization in the mean square sense for the discrete-time stochastic complex networks with time delays. The criteria derived are characterized in terms of LMIs whose solution can be solved by utilizing the standard numerical software. A simulation example is presented to show the effectiveness and applicability of the proposed results.