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.     

Design and analysis of robust residual generators for systems under feedback control

In this paper, a general approach is presented to design robust fault detection and isolation (FDI) filters for LTI uncertain systems under feedback control. A two-step design procedure is proposed to derive non-conservative robust FDI filters. The first step consists of designing an optimal FDI filter that maximizes fault sensitivity performance and simultaneously minimizes the influence of unknown inputs, for a large class of model perturbations. The design problem is formulated so that all free parameters are optimized via Linear Matrix Inequality techniques. The second step consists of a systematic post-design analysis procedure. A test is proposed to check if all FDI objectives are achieved for all specified model perturbations. The problem is formulated using an appropriate performance index over a specified frequency range. The solution is based on the generalized structured singular value. Finally, experimental results from a pilot laboratory system are presented to demonstrate the effectiveness of the proposed method.     

Robust fault detection filter design for uncertain LTI systems based on new bounded real lemma

This paper concerns the problem of robust fault detection filter design for uncertain linear time-invariant (LTI) systems with both model uncertainty and disturbances. Firstly, the fault detection filter design is formulated to H _∞ model-matching problem. Secondly, based on a new bounded real lemma, a sufficient condition for the existence of the robust fault detection filter is constructed in term of linear matrix inequalities (LMIs). Owing on the introduction of the tuning parameter and slack variables in obtained LMI condition, the proposed design method can provide higher fault detection sensitivity performance than the existing one. Finally, an illustrative example is employed to demonstrate the effectiveness of the proposed approach. Recommended by Editorial Board member Bin Jiang under the direction of Editor Jae Weon Choi. This work was supported by Postdoctoral Fundation of Jiangsu Province under grant 0901026c and Key Laboratory of Education Ministry for Image Processing and Intelligent Control under grant 200805. Tao Li received the Ph.D. degree in the Research Institute of Automation Southeast University, China. Now He is a postdoctoral researcher with the same university. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Lingyao Wu received the Ph.D. degree in the Research Institute of Automation Southeast University, China. Now He is an Assistant Professor in the Research Institute of Automation Southeast University. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Xinjiang Wei was born in Dongying, China, in 1977. He received the B.S. degrees from Yantai Normal University, China in 1999, M.S. degrees from Bohai University in 2002, and the Ph.D. degree in Department of Information from Northeastern University in 2005. From 2006 to Present, he was with Ludong University as an Associate Professor. From 2006 to 2009, he was a Postdoctoral Fellow at Southeast University. His research interests include robust control, nonlinear control, and fuzzy control.     

A time domain approach to robust fault detection of linear time-varying systems

This paper gives the optimal solutions to several robust fault detection problems such as ?₋/?_∞, ?₂/?_∞ and ?_∞/?_∞ problems for linear time-varying systems in a time domain, which extends the previous results on linear time-invariant systems in a frequency domain. It is shown that all three problems have the same optimal detection filter and the filter is a simple observer obtained by solving a standard differential Riccati equation. Finally, an example is given to illustrate our results.     

A risk adjusted approach to robust simultaneous fault detection and isolation

This paper addresses the problem of detecting and isolating faults in noisy MIMO uncertain-systems, subject to structured dynamic uncertainty. Its main result shows that this problem can be efficiently solved using a combination of sampling and LMI optimization tools. These results are illustrated with two examples and benchmarked against existing methods.     

An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.     

Off-line robust fault diagnosis using the generalized structured singular value

This paper presents a new approach to the problem of off-line model-based fault diagnosis for multivariable uncertain systems. The proposed method uses the generalized structured singular value and is based on frequency-domain model invalidation tools. A novel step-by-step methodology for off-line fault identification and symptom-aided diagnostic is developed. Fault detectability and isolability issues are discussed within the new framework. Experimental results obtained by using real data from a three-tank system are reported, showing the potential of the proposed techniques.     

LMI conditions for quadratic and robust D-stability of interval systems

Sufficient conditions for the quadratic D-stability and further robust D-stability of interval systems are presented in this paper. This robust D-stability condition is based on a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities （LMIs） defined at a series of partial-vertex-based interval matrices other than the total vertex matrices as in previous results. The results contain the usual quadratic and robust stability of continuous-time and discrete-time interval systems as particular cases. The illustrative example shows that this method is effective and less conservative for checking the quadratic and robust D-stability of interval systems.     

基于LMI的综合飞行/推进控制系统设计

飞机在飞行时,外界气流总存在不确定的扰动,对飞机的性能甚至稳定性会产生消极的影响。以某型飞机作为研究对象,在建立了综合飞行/推进系统（纵向）小偏离线性化数学模型后,根据H∞鲁棒控制理论所推导出的线性矩阵不等式,设计出干扰情况下的状态反馈控制器。仿真结果表明,所设计出的鲁棒控制器能够到达控制要求,在存在较大干扰时有一定的抑制作用。对于（LMI）线性矩阵不等式的H∞鲁棒控制方法在设计综合飞行/推进鲁棒控制系统时,是可行的,且能较好的解决飞行时存在的扰动问题。     

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.     

Optimal stochastic fault detection filter

A fault detection and identification algorithm, called optimal stochastic fault detection filter, is determined. The objective of the filter is to detect a single fault, called the target fault, and block other faults, called the nuisance faults, in the presence of the process and sensor noises. The filter is derived by maximizing the transmission from the target fault to the projected output error while minimizing the transmission from the nuisance faults. Therefore, the residual is affected primarily by the target fault and minimally by the nuisance faults. The transmission from the process and sensor noises is also minimized so that the filter is robust with respect to these disturbances. It is shown that the filter recovers the geometric structure of the unknown input observer in the limit where the weighting on the nuisance fault transmission goes to infinity. Further, the asymptotic behavior of the filter near the limit is determined by using a perturbation method. Filter designs can be obtained for both time-invariant and time-varying systems.     

LMI-based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.     

非线性系统观测器的设计:LMI方法

对满足Lipschitz条件的非线性系统给出了全维、降维观测器存在的充分条件并分别进行了证明,重点设计了新形式的降维状态观测器,观测器增益矩阵的获得完全取决于线性矩阵不等式(LMI)的解的情况,应用线性矩阵不等式工具箱使得设计更加方便,消除了增益矩阵选取的盲目性.通过对实际模型的仿真分析可知,两种观测器的状态估计误差均能渐近收敛到零,表明了该方法的有效性.     

Event-triggered simultaneous fault detection and tracking control for multi-agent systems

The main aim of this study is to design distributed simultaneous fault detection and control units for multi-agent systems subject to limited communication and energy resources. For this purpose, each agent is equipped with a single module that generates both the residual signal for the fault detection task, as well as the control input of each agent for the tracking objective. To reduce the communication among the agents, an event-triggered data transmission paradigm is considered by using a dynamic triggering rule which results in higher data transmission reduction in comparison with the static triggering condition. Moreover, the proposed dynamic observer-based structure for the detector-controller module provides more degrees of freedom compared to the static Luenberger observer. The design parameters are obtained by solving a multi-objective optimisation problem considering the fault detection, tracking, and communication objectives. Simulation results illustrate the effectiveness and capabilities of the proposed method.     

Robust fault detection for discrete-time Markovian jump systems with mode-dependent time-delays

This paper investigates a fault detection problem for a class of discrete-time Markovian jump systems with norm-bounded uncertainties and mode-dependent time-delays. Attention is focused on constructing the residual generator based on the filter of which its parameters matrices are dependent on the system mode, that is, the fault detection filter is a Markovian jump system as well. The design of fault detection filter is reduced to H-infinity filtering problem by using H-infinity control theory, which can guarantee the difference between the residual and the fault (or, more generally weighted fault) as small as possible in the context of enhancing the robustness of residual to modeling errors, control inputs and unknown inputs. Sufficient condition for the existence of the above filters is established by means of linear matrix inequalities, which can be readily solved by using standard numerical software. A numerical example is given to illustrate the feasibility of the proposed method.     

Observer-based robust fault detection of multirate linear system using a lift reformulation

This paper presents observer-based robust fault detection for multirate sampled-data linear system. It is assumed that all plant inputs are updated with a unique sampling period and that the plant outputs are sampled uniformly at integer multiples of the input sampling period. A state observer is constructed, as in the single-rate case, and a residual generator is derived. The paper shows that the residual signals can be decoupled from noise and disturbances. An illustrative numerical example is provided.     

Delay-dependent robust stabilisation of uncertain discrete-time switched systems with time-varying state delay

This paper considers the stabilisation problem for uncertain discrete-time switched systems with time-varying delay in the state. The uncertainty is assumed to be of structured linear fractional form, which includes the norm-bounded uncertainty as a special case. A stability condition is first proposed by using switched Lyapunov function, which is dependent on the minimum and maximum delay bounds. Based on the result, a switched state feedback controller is designed. Numerical examples are given to illustrate the effectiveness of the result.     

LMI Condition of Quadratic D-stability for a Class of Uncertain Linear Systems

A necessary and sufficient condition of the quadratic D-stability for a class of uncertain linear systems is presented in terms of linear matrix inequality (LMI) technology.Finally,the validity and less conservatism of the obtained results in this paper are illustrated by a benchmark example.