An LMI approach to design robust fault detection filter for uncertain LTI systems

In this paper, the robust fault detection filter design problem for uncertain linear time-invariant (LTI) systems with both unknown inputs and modelling errors is studied. The basic idea of our study is to use an optimal residual generator (assuming no modelling errors) as the reference residual model of the robust fault detection filter design for uncertain LTI systems with modelling errors and, based on it, to formulate the robust fault detection filter design as an H_∞ model-matching problem. By using some recent results of H_∞ optimization, a solution of the optimization problem is then presented via a linear matrix inequality (LMI) formulation. The main results include the development of an optimal reference residual model, the formulation of robust fault detection filter design problem, the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the LMI solution parameters, the determination of adaptive threshold for fault detection. An illustrative design example is employed to demonstrate the effectiveness of the proposed approach.     

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.     

Design and analysis of robust fault detection filter using LMI tools

In this paper, the robust fault detection filter design problem for linear time invariant (LTI) systems with unknown inputs and modeling uncertainties is studied. The basic idea of our study is to formulate the robust fault detection filter design as a H_∞ model-matching problem. A solution of the optimal problem is then presented via a linear matrix inequality (LMI) formulation. The main results include the formulation of robust fault detection filter design problems, the derivation of a sufficient condition for the existence of a robust fault detection filter and construction of a robust fault detection filter based on the iterative of LMI algorithm.     

Parameter-dependent robust H ∞ filter design for uncertain discrete-time systems with quantized measurements

This paper deals with the problem of parameter-dependent robust H _∞ filter design for uncertain discrete-time systems with output quantization. The uncertain parameters are supposed to reside in a polytope. The system outputs are quantized by a memoryless logarithmic quantizer before being transmitted to a filter. Attention is focused on the design of a robust H _∞ filter to mitigate quantization effects and ensure a prescribed H _∞ noise attenuation level. Via introducing some slack variables and using the parameter-dependent Lyapunov function, sufficient conditions for the existence of a robust H _∞ filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.     

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.     

A robust deconvolution scheme for fault detection and isolation of uncertain linear systems: an LMI approach

Optimal H_∞ deconvolution filter theory is exploited for the design of robust fault detection and isolation (FDI) units for uncertain polytopic linear systems. Such a filter is synthesized under frequency domain conditions which ensure guaranteed levels of disturbance attenuation, residual decoupling and deconvolution performance in prescribed frequency ranges. By means of the Projection Lemma, a quasi-convex formulation of the problem is obtained via LMIs. A FDI logic based on adaptive thresholds is also proposed for reducing the generation of false alarms. The effectiveness of the design technique is illustrated via a numerical example.     

Fault detection for a class of impulsive switched systems

The problem of fault detection for a class of nonlinear impulsive switched systems is investigated in this paper. Fault detection filters are designed such that the augmented systems are stable, and the residual error signal generated by the filters guarantees the H∞ performance for disturbances and faults. Sufficient conditions for the design of fault detection(FD) filters are presented by linear matrix inequalities. Moreover, the filter gains are characterized according to a solution of a convex optimization. Finally, an example derived from a pulse-width-modulation-driven boost converter is given to illustrate the effectiveness of the FD design approach.     

Robust H ∞ filter design for time-delay systems with saturation

This paper investigates the H∞ filtering problem for a class of linear continuous-time systems with both time delay and saturation. Such systems have time delay in their state equations and saturation in their output equations, and their process and measurement noises have unknown statistical characteristics and bounded energies. Based on the Lyapunov-Krasovskii stability theorem and the linear matrix inequalities (LMIs) technique, a generalized dynamic filter architecture is proposed, and a filter design method is developed. The linear H∞ filter designed by the method can guarantee the H∞ performance. The parameters of the designed filter can be obtained by solving a kind of LMI. An illustrative example shows that the design method proposed in this paper is very effective.     

不确定奇异时滞系统的鲁棒H∞故障诊断滤波器设计

研究一类受参数不确定性和干扰影响的奇异时滞系统鲁棒故障诊断滤波器设计问题. 把基于观测器的故障诊断滤波器作为残差产生器, 将故障诊断滤波器设计归结为H∞滤波问题, 使产生的残差信号即为故障的H∞估计, 给出了鲁棒H∞故障诊断滤波器存在的充分条件, 并利用锥面互补线性化迭代算法得到了故障诊断滤波器设计的线性矩阵不等式求解方法. 算例验证了算法的有效性.     

Finite-frequency fault detection for two-dimensional Fornasini–Marchesini dynamical systems

This paper is concerned with the fault detection problem for two-dimensional (2-D) discrete-time systems described by the Fornasini–Marchesini local state-space model. The goal of the paper is to design a fault detection filter to detect the occurrence of faults in finite-frequency domain. To this end, a finite-frequency H_? index is used to describe fault sensitivity performance, and a finite-frequency H_∞ index is used to describe disturbance attenuation performance. In light of the generalised Kalman–Yakubovich–Popov lemma for 2-D systems and matrix inequality techniques, convex conditions are derived for this fault detection problem. Based on these conditions, a numerical algorithm is put forward to construct a desired fault detection filter. Finally, a numerical example and an industrial example are given to illustrate the effectiveness of the proposed algorithm.     

Fault detection for a class of uncertain nonlinear Markovian jump stochastic systems with mode-dependent time delays and sensor saturation

This paper considers the problem of robust H_∞ fault detection for a class of uncertain nonlinear Markovian jump stochastic systems with mode-dependent time delays and sensor saturation. We aim to design a linear mode-dependent H_∞ fault detection filter that ensures, the fault detection system is not only stochastically asymptotically stable in the large, but also satisfies a prescribed H_∞-norm level for all admissible uncertainties. By using the Lyapunov stability theory and generalised Itô formula, some novel delay-dependent sufficient conditions in terms of linear matrix inequality are proposed to guarantee the existence of the desired fault detection filter. Explicit expression of the desired mode-dependent linear filter parameters is characterised by matrix decomposition, congruence transformation and convex optimisation technique. Sector condition method is utilised to deal with sensor saturation, a definite relation of sector condition parameters with fault detection system robustness against disturbances and sensitivity to faults is put forward, and weighting fault signal approach is employed to improve the performance of the fault detection system. A simulation example and an industrial nonisothermal continuous stirred tank reactor system are utilised to verify the effectiveness and usefulness of the proposed method.     

Robust switching-type H∞ filter design for linear uncertain systems with time-varying delay

This paper is concerned with the problem of robust H_∞ filter design for a class of linear uncertain systems with time-varying delay. The uncertainty parameters are supposed to be time-varying, unknown, but bounded, which appear affinely in the matrices of the considered system model. Based on linear matrix inequality (LMI) method and switching laws, a new switching-type filter is designed to guarantee the asymptotic stability and H_∞ performance level of the filtering error systems. The key feature is that the new proposed filter parameters are switching between certain fixed gains automatically via the designed switching law. It is shown that the new filter design method is less conservative than the traditional fixed gain filter design method. An example is given to illustrate the validity of the proposed design.     

An LMI approach to minimum sensitivity analysis with application to fault detection

This paper systematically studies the minimum input sensitivity analysis problem. The lowest level of sensitivity of system outputs to system inputs is defined as an H_- index. A full characterization of the H_- index is given, first, in terms of matrix equalities and inequalities, and then in terms of linear matrix inequalities (LMIs), as a dual of the Bounded Real Lemma. A related problem of input observability is also studied, with new necessary and sufficient conditions given, which are necessary for a fault detection system to have a nonzero worst-case fault sensitivity. The above results are applied to the problem of fault detection filter analysis, with numerical examples given to show the effectiveness of the proposed approaches.     

具有多通道数据传输的飞行器网络控制系统故障检测

研究具有多通道数据传输的飞行器网络控制系统故障检测滤波器(FDF)设计问题.考虑每个通道存在各自的网络时延,且丢包符合Markov随机过程.首先,将系统建模为转移概率部分已知的离散Markov跳变线性系统,并设计了基于观测器的故障检测滤波器,将故障检测问题转化为H∞滤波问题;然后,利用LMI工具给出了FDF的可解条件和求解方法;最后,通过某飞行器网络控制系统的数值仿真实验验证了所提出方法的有效性.     

Robust filtering for 2-D discrete-time linear systems with convex-bounded parameter uncertainty

This paper is concerned with the problems of robust H_∞ and H₂ filtering for 2-dimensional (2-D) discrete-time linear systems described by a Fornasini-Marchesini second model with matrices that depend affinely on convex-bounded uncertain parameters. By a suitable transformation, the system is represented by an equivalent difference-algebraic representation. A parameter-dependent Lyapunov function approach is then proposed for the design of 2-D stationary discrete-time linear filters that ensure either a prescribed H_∞ performance or H₂ performance for all admissible uncertain parameters. The filter designs are given in terms of linear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed filter design methods.     

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.     

Robust H2/H∞ global linearization filter design for nonlinear stochastic time-varying delay systems

One can design a robust H_∞ filter for a general nonlinear stochastic system with external disturbance by solving a second-order nonlinear stochastic partial Hamilton-Jacobi inequality (HJI), which is difficult to be solved. In this paper, the robust mixed H₂/H_∞ globally linearized filter design problem is investigated for a general nonlinear stochastic time-varying delay system with external disturbance, where the state is governed by a stochastic Itô-type equation. Based on a globally linearized model, a stochastic bounded real lemma is established by the Lyapunov–Krasovskii functional theory, and the robust H_∞ globally linearized filter is designed by solving the simultaneous linear matrix inequalities instead of solving an HJI. For a given attenuation level, the H₂ globally linearized filtering problem with the worst case disturbance in the H_∞ filter case is known as the mixed H₂/H_∞ globally linearized filtering problem, which can be formulated as a linear programming problem with simultaneous LMI constraints. Therefore, this method is applicable for state estimation in nonlinear stochastic time-varying delay systems with unknown exogenous disturbance when state variables are unavailable. A simulation 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。     

Improved robust H2 and H∞ filtering for uncertain discrete-time systems

This paper is concerned with the robust H₂ and H_∞ filtering problems for linear discrete-time systems with polytopic parameter uncertainty. We aim to derive a less-conservative design than existing linear matrix inequality (LMI) based sufficient conditions. It is shown that a more efficient evaluation of robust H₂ or H_∞ performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations. When applying this new matrix inequality condition to the robust filter design, these parameters provide extra degrees of freedom in optimizing the guaranteed H₂ or H_∞ performance and lead to a less-conservative design.