An iterative learning observer for fault detection and accommodation in nonlinear time‐delay systems

This article addresses fault detection, estimation, and compensation problem in a class of disturbance driven time delay nonlinear systems. The proposed approach relies on an iterative learning observer (ILO) for fault detection, estimation, and compensation. When there are no faults in the system, the ILO supplies accurate disturbance estimation to the control system where the effect of disturbances on estimation error dynamics is attenuated. At the same time, the proposed ILO can detect sudden changes in the nonlinear system due to faults. As a result upon the detection of a fault, the same ILO is used to excite an adaptive control law in order to offset the effect of faults on the system. Further, the proposed ILO‐based adaptive fault compensation strategy can handle multiple faults. The overall fault detection and compensation strategy proposed in the paper is finally demonstrated in simulation on an automotive engine example to illustrate the effectiveness of this approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Distributed moving horizon estimation for nonlinear constrained systems

In this paper we consider a nonlinear constrained system observed by a sensor network and propose a distributed state estimation scheme based on moving horizon estimation (MHE). In order to embrace the case where the whole system state cannot be reconstructed from data available to individual sensors, we resort to the notion of MHE detectability for nonlinear systems, and add to the MHE problems solved by each sensor a consensus term for propagating information about estimates through the network. We characterize the error dynamics and provide conditions on the local exchanges of information in order to guarantee convergence to zero and stability of the state estimation error provided by any sensor. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimization of fault detection performance for a class of nonlinear systems

The problem of observer design for fault detection in a class of nonlinear systems subject to parametric and signal uncertainties is studied. The design procedure includes formalized optimization of observer‐free parameters in terms of trade‐offs for fault detection performance and robustness to external disturbances and model uncertainties. The technique makes use of some monotonicity conditions imposed on the estimation error dynamics. Efficiency of the proposed approach is demonstrated through the oscillatory failure case in aircraft control surface servo‐loops. Copyright © 2011 John Wiley & Sons, Ltd.     

基于自适应观测器的四旋翼无人飞行器多传感器故障诊断方法

为了实现对四旋翼无人飞行器多传感器故障检测与诊断,提出一种基于自适应观测器的多传感器故障诊断方法。首先,在建立飞行器动力学模型和传感器模型的基础上,将传感器故障视为虚拟执行器故障,构建四旋翼无人飞行器多传感器故障检测与诊断系统;其次,设计非线性观测器实现多故障检测和与隔离,基于Laypunov方法设计非线性自适应观测器实现对多故障偏差值的估计;最后,在传感器测量噪声存在的情况下,证明自适应律的稳定性和参数收敛性。实验结果表明,该方法能有效进行多传感器的故障检测与隔离,实现对多传感器故障偏差的同时估计与跟踪。     

基于自适应观测器的四旋翼无人飞行器传感器故障诊断方法

针对四旋翼无人飞行器传感器故障诊断问题,提出一种用于四旋翼无人飞行器加速度计和陀螺仪故障同时发生的故障检测与隔离以及故障偏差值估计的非线性诊断方法.首先,在建立飞行器动力学模型和传感器模型的基础上,构建四旋翼无人飞行器传感器故障检测与诊断系统.其次,利用故障观测器完成传感器故障的检测与隔离,基于Laypunov方法设计非线性自适应观测器对未知故障偏差值进行估计.最后,在传感器测量噪声存在的情况下,证明自适应律的稳定性和参数收敛性.实验结果表明,该方法能有效进行传感器的故障检测与隔离,实现对传感器故障偏差的估计与跟踪.     

具有非线性扰动多时滞系统的鲁棒故障检测

基于状态观测器的方法研究了一类具有非线性扰动的多重状态时滞系统的鲁棒故障检测问题，应用RBF神经网络逼近系统的非线性扰动，采用线性矩阵不等式(LMI)给出了与时滞上界相关的增益阵设计方法，并利用Lyapunov函数和一致有界引理证明了故障检测残差信号的一致有界稳定条件和对非线性扰动的鲁棒性，仿真示例说明了该方法的有效性。     

Observer design for nonlinear discrete‐time systems: Immersion and dynamic observer error linearization techniques

This paper focuses on the observer design for nonlinear discrete‐time systems by means of nonlinear observer canonical form. At first, sufficient and necessary conditions are obtained for a class of autonomous nonlinear discrete‐time systems to be immersible into higher dimensional observer canonical form. Then a method called dynamic observer error linearization is developed. By introducing a dynamic auxiliary system, the augmented system is shown to be locally equivalent to the generalized observer form, whose nonlinear terms contain auxiliary states and output of the system. A constructive algorithm is also provided to obtain the state coordinate transformation. These results are an extension of their counterparts of nonlinear continuous‐time systems to nonlinear discrete‐time systems (Syst. Control Lett. 1986; 7 :133–142; SIAM. J. Control Optim. 2003; 41 :1756–1778; Int. J. Control 2004; 77 :723–734; Automatica 2006; 42 :321–328; IEEE Trans. Automat. Control 2007; 52 :83–88; IEEE Trans. Automat. Control 2004; 49 :1746–1750; Automatica 2006; 42 :2195–2200; IEEE Trans. Automat. Control 1996; 41 :598–603; Syst. Control Lett. 1997; 31 :115–128). Copyright © 2009 John Wiley & Sons, Ltd.     

Generalized set‐theoretic unknown input observer for LPV systems with application to state estimation and robust fault detection

This paper proposes to design an unknown input observer (UIO) for the linear‐parameter‐varying (LPV) system on the basis of the set theory, which is named as the set‐theoretic UIO (SUIO). The advantage of the SUIO consists in that it combines active and passive approaches to obtain robustness in state estimation (SE) and fault detection (FD). The active approach is based on the use of UIO to decouple unknown inputs, while the passive approach is based on the set theory to bound uncertain factors that cannot be actively decoupled. As a result, the effect of both unknown inputs (process disturbances, modeling errors, etc.) and measurement noises can be appropriately handled in the residual signals compared with the standard UIO‐based SE and FD approaches. The design of SUIO can overcome the limitations of the traditional UIO design conditions, which can significantly broaden the application of the UIO‐based SE and FD theory. Moreover, this paper proposes a generalized framework that can provide more flexibility in the design of SUIO guaranteeing their stability by means of a group of matrix inequalities. Because the LPV system uses a collection of online obtainable scheduling variables to embed nonlinearities, the design of SUIO for the LPV system can be used to address the SE and FD problems of nonlinear systems. At the end of this paper, two case studies are used to illustrate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

A robust fault detection approach for nonlinear systems

In this paper, we study the robust fault detection problem of nonlinear systems. Based on the Lyapunov method, a robust fault detection approach for a general class of nonlinear systems is proposed. A nonlinear observer is first provided, and a sufficient condition is given to make the observer locally stable. Then, a practical algorithm is presented to facilitate the realization of the proposed observer for robust fault detection. Finally, a numerical example is provided to show the effectiveness of the proposed approach.     

Recursive observer‐based fault detection for a class of nonlinear uncertain systems with output constraints

This paper investigates the fault detection (FD) problem for a class of nonlinear uncertain systems in strict feedback form with an output constraint. The key idea is to design an observer to generate the FD signals and the output estimate, which also satisfies the output constraint. To facilitate constraint handling, the constraints on the output and the output estimate are transformed into the output estimation error constraint. Then, the FD observer is designed in a recursive framework. By employing a barrier Lyapunov function, the output estimation error constraint is incorporated in the last step of the recursive observer design algorithm to prevent constraint violation. It is shown that the output estimation error is uniformly bounded and satisfies the constraint for the fault‐free case. Furthermore, the residual signal is constructed by the output estimation error, and its corresponding bound is used as threshold. Compared with the FD method without considering the constraints, the proposed FD scheme provides a smaller threshold and characterizes a larger set of faults, which can be detected. Finally, simulation results are presented to illustrate the benefits of the proposed FD scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Integrated observer based fault estimation for a class of Lipschitz nonlinear systems

The fault estimation for a class of nonlinear systems with Lipschitzian nonlinearities and faults is studied in this article. An integrated estimation observer that covers the robust estimation observer (REO) and adaptive estimation observer (AEO) is proposed to improve the accuracy of fault estimation. Compared with the traditional AEO, the designed observer does not involve the output derivatives and can be more suitable for practical applications. Furthermore, based on the designed observer, the coupling term emerging in the obtained error dynamics can be eliminated reasonably and less conservative stability conditions for the error dynamics can be obtained, whereas the case is hard to be achieved based on the existing intermediate estimator approach in the literature. Compared with the traditional REO and AEO, the fault can be estimated with a good accuracy by using the proposed integrated estimation observer. Numerical examples test the effectiveness and advantages of the proposed method.     

A real‐time algorithm for nonlinear receding horizon control using multiple shooting and continuation/Krylov method

In this paper, we propose a real‐time algorithm for nonlinear receding horizon control using multiple shooting and the continuation/GMRES method. Multiple shooting is expected to improve numerical accuracy in calculations for solving boundary value problems. The continuation method is combined with a Krylov subspace method, GMRES, to update unknown quantities by solving a linear equation. At the same time, we apply condensing, which reduces the size of the linear equation, to speed up numerical calculations. A numerical example shows that both numerical accuracy and computational speed improve using the proposed algorithm by combining multiple shooting with condensing. Copyright © 2008 John Wiley & Sons, Ltd.     

Interval estimation and fault detection for switched nonlinear systems based on zonotope method

This paper investigates the state interval estimation and fault detection (FD) problems for a Lipschitz nonlinear switched system based on the combination of the $H_{\infty }$ observer and the zonotope method. To begin with, an $H_{\infty }$ observer that is robust to the disturbance is designed, and the stability of the observer error dynamic system is analyzed under the average dwell time (ADT) concept. After this, the zonotope theory is applied on the $H_{\infty }$ observer error dynamic system such that the interval state estimation can be calculated iteratively when the system suffers from no fault. Furthermore, for FD purpose, a residual is constructed based on the $H_{\infty }$ observer. Because the constructed residual contains disturbance, it cannot be used for FD directly. To overcome this drawback, the interval estimation method of the residual is proposed by using the zonotope method, and a residual-based FD scheme is developed. Finally, a simulation example is given to verify the effectiveness of the proposed method.     

一类非线性系统故障诊断观测器设计

大多故障诊断算法集中在线性系统方面, 在非线性方面只考虑故障对状态起线性影响的那些系统. 本文根据系统的非线性本质特性, 提出了基于模型的一类非线性系统故障诊断观测器设计方法. 应用系统的(B;K; á)实现精确分解后的系统模型, 对它们的状态故障起非线性的影响. 采用干扰解耦技术,获得的残差对未知扰动有很好的鲁棒性. 在Lyapunov意义下, 验证了算法的稳定性. 仿真验证表明, 所提算法具有快速收敛性, 对一类非线性系统诊断效果较好.     

Robust periodically time‐varying horizon finite memory fault detection filter design for polytopic uncertain discrete‐time systems

In this paper, a robust periodically time‐varying horizon finite memory fault detection filter (PTVHFM‐FDF) is proposed to generate residual signal for the purpose of system monitoring. The major advantage of PTVHFM‐FDF is that finite historical data can be sufficiently utilized to enhance the robustness of fault detection against model uncertainty and external disturbance. The analysis, design, and application of PTVHFM‐FDF consist of several steps. Firstly, a periodic time‐varying residual error system is constructed on the basis of augmented method and time domain partition method. Secondly, in facilitating robust stability and performance analysis, the time‐varying residual error system is further transformed into a polyhedral time‐invariant system on the basis of time lifting technique. Thirdly, less conservative PTVHFM‐FDF analysis and design conditions are then obtained on the basis of Finsler relaxation lemma and slack variable structure definition. Fourthly, choices of memory window horizon parameters are properly suggested on the basis of a compromise between FDF robustness and its structural complexity. Finally, an integrated design and application algorithm of PTVHFM‐FDF is summarized. Effectiveness of PTVHFM‐FDF is verified through three examples. Copyright © 2017 John Wiley & Sons, Ltd.     

Fault estimation observer design for a class of nonlinear multiagent systems in finite‐frequency domain

This paper focuses on the fault estimation observer design problem in the finite‐frequency domain for a class of Lipschitz nonlinear multiagent systems subject to system components or actuator fault. First, the relative output estimation error is defined based on the directed communication topology of multiagent systems, and an observer error system is obtained by connecting adaptive fault estimation observer and the state equation of the original system. Then, sufficient conditions for the existence of the fault estimation observer are obtained by using a generalized Kalman‐Yakubovich‐Popov lemma and properties of the matrix trace, which guarantee that the observer error system satisfies robustness performance in the finite‐frequency domain. Meanwhile, the pole assignment method is used to configure the poles of the observer error system in a certain area. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.     

Experimental application of nonlinear minimum variance estimation for fault detection systems

The purpose of this paper is to present an experimental design and application of a novel model-based fault detection technique by using a nonlinear minimum variance (NMV) estimator. The NMV estimation technique is used to generate a residual signal which is then used to detect faults in the system. The main advantage of the approach is the simplicity of the nonlinear estimator theory and the straightforward structure of the resulting solution. The proposed method is implemented and validated experimentally on DC servo system. Experimental results demonstrate that the technique can produce acceptable performance in terms of fault detection and false alarm.     

Interval observer versus set‐membership approaches for fault detection in uncertain systems using zonotopes

This paper presents both analysis and comparison of the interval observer–based and set‐membership approaches for the state estimation and fault detection (FD) in uncertain linear systems. The considered approaches assume that both state disturbance and measurement noise are modeled in a deterministic context following the unknown but bounded approach. The propagation of uncertainty in the state estimation is bounded through a zonotopic set representation. Both approaches have been mathematically related and compared when used for state estimation and FD. A case study based on a two‐tanks system is employed for showing the relationship between both approaches while comparing their performance.     

马尔可夫跳变系统的鲁棒故障检测与时域优化

研究马尔可夫跳变系统(MJS) 鲁棒故障检测滤波器(FDF) 的设计与优化问题. 基于观测器构建残差发生器, 将相应的FDF 设计问题转化为H_∞ 滤波问题, 以LMI 的形式得到并证明了FDF 存在的充分条件及求解方法. 为进一步改善故障检测系统的性能, 采用一种时域优化方法对其进行优化, 并以矩阵Moore-Penrose 逆的形式给出了该优化问题的最优解. 数值仿真表明该方法具有较好的检测效果.