Design of bilinear observer for singular bilinear systems

A bilinear observer is proposed for a class of singular bilinear system subject to unknown input disturbance.Based on singular value decomposition technique, the existence of the solution to the decomposed system is presented.Then a bilinear observer is proposed for the decomposed system based on an algebraic Riccati equation, and the domain of attraction of the state estimation error is derived. Finally, a detailed design procedure is given to design a bilinear observer for a model of flexible joint robot, which demonstrates the effectiveness of the proposed method.     

Design of bilinear observer for singular bilinear systems

In this paper, by analyzing the worm’s propagation model, we propose a new worm warning system based on the method of system identification, and use recursive least squares algorithm to estimate the worm’s infection rate. The simulation result shows the method we adopted is an efficient way to conduct Internet worm warning.     

A simulation study on fault diagnosis of a high-temperature furnace using a bilinear observer method

A simulation study is undertaken on fault diagnosis for a gas-fired high-temperature furnace. A single-input multi-output bilinear model is found to be a suitable representation of the furnace. A recently proposed full-order bilinear state observer is used to generate the residual. Two actuator and two sensor faults are simulated and tested using this method.     

Residual generator design for singular bilinear systems subjected to unmeasurable disturbances: an LMI approach

In this paper, a method to design a bank of unknown input residual generator for fault detection and isolation is investigated. The plant model is assumed to be a bounded control inputs singular bilinear systems subjected to unknown disturbances. The measurements can be bilinear.     

A class of state observers for bilinear systems

By exploiting the fact that the output of the bilinear system is one-time differentiable whatever the input is, a new method of designing a state observer for bilinear system is proposed. The use of information on the derivative of y gives rise to a simple design procedure by which a wider class of bilinear systems has a state observer.     

Optimal bilinear observers for bilinear state-space models by interaction matrices

This paper formulates optimal bilinear observers for bilinear state-space models. Observers in bilinear form, as opposed to other nonlinear forms, are required to develop an extension of observer/Kalman filter identification for simultaneous identification of a bilinear state-space model and an associated bilinear observer from noisy input–output measurements. The paper establishes the relationship between the bilinear observer gains and the interaction matrices which are used to convert the original bilinear state-space model to a form that simplifies the identification of such a model. Techniques to find the interaction matrices are developed. In the absence of noises, these matrices produce the gains of the fastest converging observer. In the presence of noises, they minimise the state estimation error in the same manner as a standard steady-state Kalman filter. Numerical examples illustrate both the theoretical and computational aspects of the proposed algorithms.     

Output feedback fault-tolerant control for a class of discrete-time fuzzy bilinear systems

This paper studies the fault-tolerant control problem for a class of discrete-time fuzzy bilinear systems with unmeasurable states. A fuzzy detective observer is designed to detect the faults. Based on the fuzzy detective observer, a fuzzy controller is designed by solving a set of linear matrix inequalities (LMIs) to ensure that the closed-loop system without faults is asymptotically stable. For the discrete-time fuzzy bilinear system with faults, a fuzzy adaptive diagnostic observer is designed to estimate the faults by solving a set of LMIs. Then, a fuzzy faulttolerant controller is designed based on the fuzzy diagnostic observer to ensure that the closed-loop system with faults is asymptotically stable. At last, simulation results are presented to verify the effectiveness of the proposed output feedback fault-tolerant control method.     

A graph-theoretic approach to fault detection and isolation for structured bilinear systems

In this paper, using a graph-theoretic approach, we address some issues related to the fault detection and isolation for structured bilinear systems. Considering a structured bilinear system submitted to faults and disturbances, we give necessary and sufficient conditions to the solvability of the so-called bilinear fundamental problem of residual generation. We also treat the cases where the system is submitted to multiple failures occurring simultaneously or only one at a time. One of the main advantages of the proposed analysis tool is that all the given conditions are easy to check because they deal with finding paths in a digraph. This makes our approach well suited to studying large scale systems.     

Extension of the parity-space method to fault diagnosis of bilinear systems

In this paper, the parity-space method for linear fault diagnosis is extended to bilinear systems. By including bilinear terms into the system matrix, a linear time-varying model with known time-varying feature is obtained. The parity-space method can then be applied to generate residuals in each sampling interval. A recursive algorithm is developed for calculating the matrices in the parity equation, so that the computing time is greatly reduced. Fault isolation is achieved at the residual stage using one parity check instead looking at a bank of parity equations. Component, actuator and sensor faults are isolated by applying an elementary transformation and the singular value decomposition techniques. A numerical example is used to demonstrate the effectiveness of the method.     

一种故障检测滤波器的多目标优化设计方法

提出一种基于观测器的故障检测滤波器的非凸多目标优化设计方法.针对线性时不变动态系统,构建一个由输出观测器和后滤波器组成的故障检测滤波器,将其残差动态特性描述为非凸的双线性矩阵不等式形式.利用双线性矩阵不等式中可完全平方非正定项的上界替代原非正定项,将双线性矩阵不等式转化为一组线性矩阵不等式,进而获得多目标优化问题的可解条件以及观测器增益与后滤波器矩阵的求解方法.仿真算例说明了算法的有效性.     

不确定动态系统的执行器故障检测与重构

讨论不确定动态系统的执行器故障检测与重构问题.以滑模观测器为基础,利用状态和输出变换方法与奇异值分解方法相结合对系统进行降阶,提出一种鲁棒故障重构观测器.给出了优化滑模策略,并作了严格论证,保证对系统不确定性具有鲁棒性和跟踪系统状态的收敛性.应用等价输出控制的概念和设计的鲁棒故障重构观测器,获取故障信息并实现执行器故障的检测与重构.最后通过数值仿真验证了该方法的有效性和可靠性.     

双线性状态空间系统的状态观测器设计

针对受过程噪声和量测噪声干扰的双线性状态空间系统,研究其状态估计算法.借助双线性系统的特殊结构,将其等价表示为线性时变模型,推导基于Kalman滤波的状态估计算法.针对线性时变模型中存在的未知变量,基于辅助模型辨识思想,通过构造一个辅助模型,将未知变量用该模型的输出代替,提出基于辅助模型的双线性系统状态估计算法.构造双线性状态观测器,引入delta算子极小化状态估计误差协方差矩阵,从而得到最优状态估计增益,并提出基于delta算子的双线性系统状态估计算法.所提出的算法能够避免线性化过程带来的估计精度差的问题,提高双线性系统的状态估计精度.通过仿真实验验证了所提出算法的有效性,并对比分析了不同噪声情况下所提出算法的估计效果.     

不确定时滞双线性广义系统的鲁棒耗散控制

针对带有耗散不确定性的时滞双线性广义系统的鲁棒耗散控制问题,首先将耗散不确定性引入双线性广义系统,利用线性矩阵不等式方法给出系统鲁棒稳定且严格耗散的充分条件;然后利用线性矩阵不等式的解,构造出闭环系统鲁棒耗散的状态反馈控制器;最后通过数值算例验证了所得结论的可行性.     

带有不可测量扰动的广义双线性系统状态观测器设计及故障诊断

讨论了存在未知扰动情况下,广义双线性系统全阶状态观测器的存在条件及其设计方法。得到的观测器可直接用于解决广义双线性系统的故障诊断问题,最后的数值例子说明了设计步骤。仿真结果验证了设计的有效性。     

A robust fault diagnosis scheme based on signal modal estimation

A novel fault detection/diagnosis technique for linear dynamic systems is proposed. In comparison with existing schemes, the proposed method achieves fault detection/diagnosis using neither observer residuals nor parameter estimation errors; instead, it relies on the estimation of the underlying modal parameters of the system. The estimated modal parameters are compared with pre-calculated characteristic patterns of the system, which are represented as a set of root loci in terms of the physical system parameters. The modal parameter estimation is carried out using a numerically robust least-squares algorithm based on singular value decomposition. A pattern recognition technique employing linear multiprototype distance functions is used to classify the faults according to the variations of physical parameters. The proposed method has been applied to a simulated DC servo system where faults are introduced as abrupt changes in physical system parameters. It is shown that the proposed scheme is capable of diagnosing most of changes in physical system parameters.     

Design of switched controllers for discrete singular bilinear systems

In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems.The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.     

Design of switched controllers for discrete singular bilinear systems

In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems.The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.     

基于高增益鲁棒滑模观测器的故障检测和隔离

针对一类同时具有执行器和传感器故障的不确定线性系统,讨论了基于观测器的故障检测和隔离方法.首先,通过引入增维向量,使得在构造的增维系统中,故障向量包含了原系统的执行器故障和传感器故障.通过构造辅助输出使增维系统的观测器匹配条件得以满足,同时设计高增益滑模观测器对辅助输出进行估计.然后,对增维系统构造鲁棒滑模观测器并用作故障检测观测器,通过滑模控制项来抑制干扰,使观测器具有鲁棒性.在此基础上,结合多观测器故障隔离思想,提出了可以同时对执行器故障和传感器故障进行检测和隔离的方法. 最后,通过对一个五阶飞行器模型进行仿真,证明了所提方法的有效性.     

基于自适应观测器的时滞系统执行器故障诊断

该文研究了一类含有未知输人干扰和模型不确定性的线性时滞系统的故障诊断问题。通过设计自适应诊断观测器，得到了一种新型的鲁棒执行器故障诊断方法。首先针对确定性系统分别设计了检测观测器和自适应诊断观测器，前者能够检测出故障的发生，后者能够理想地估计出故障随时间变化的形状。然后考虑系统的外部干扰和模型不确定，改进了自适应诊断观测器的算法，证明了故障诊断系统的稳定性，提高了故障诊断系统的鲁棒性。最后给出了故障检测过程中阈值的选取原则。仿真结果表明算法具有良好的诊断性能。     

一种基于滑模—神经网络观测器的故障检测和诊断方法

本文针对一类非线性系统，提出了一种用于故障检测和诊断的滑模观测器方法．其 中，观测器中的滑模项保证了该系统在无故障情况时的鲁棒性，并且系统运行的滑动区域提供了故障检测的条件．当检测出故障之后，观测器中的故障估计部分被启动，利用RBF神经网络估计故障，从而能在线辨识故障的形态．仿真结果验证了该方法的有效性．