摘要
控制系统常处于各种内部和外部干扰影响的环境中,噪声污染源就可能来自传感器等信号检测仪表,也可能来自雷电、环境等随机因素。从受污染的信号中如何提取出真实的信号来,就是滤波技术要完成的任务,受到控制界的广泛关注。由于对象的大惯性特性、传输过程及复杂的在线分析仪器等因素,又不可避免引入观测滞后。时滞系统也广泛存在于许多工程领域,例如信号处理,通讯,网络传输与控制等,因为这类问题都很复杂,许多基础性理论问题尚未彻底得到解决。现有的方法,如状态扩维、偏微分方程、线性算子理论等,所得到的结果或者计算量大,或者需要求解复杂的偏微分方程,且难以对得到的滤波器进行性能分析。因此,就有必要围绕时滞系统的估计问题进行进一步加以研究与完善。
本文将研究并解决带有观测时滞系统的H_∞滤波、白噪声最优估计,及相关技术在控制系统故障诊断中的应用等问题。主要研究工作由以下部分组成:
●研究了最优白噪声估计问题,基于Kalman滤波理论及射影方法,通过求解Riccati方程得到最优白噪声估值器。该方法能同时对系统噪声和测量噪声做出估计,且这两种噪声可以是相关的。
●针对带有观测时滞的线性随机系统,研究了输入白噪声的最优估计问题。通过对观测序列进行重新组织,给出重组新息序列。根据在Hilbert空间上的正交投影定理,通过求解与原系统同维的两个Riccati方程实现递推计算。该方法避免了状态扩维,能有效地减轻计算负担。文中针对离散系统和连续系统两种情形分别进行讨论。
●针对带有多组观测时滞的线性离散系统,研究了H_∞滤波问题。首先将该问题转化为Krein空间的一个不定二次最优估计问题,然后利用Krein空间理论和新息重组方法,通过计算一组与原系统维数相同的Riccati方程,设计出H_∞滤波器,并且给出滤波器存在的条件。
●针对带有未知输入的线性系统,研究了当扰动能量有界时的H_∞故障估计问题。解决问题的关键是将问题转化为Krein空间的H_2故障问题。通过重组新息理论,并求解一组Riccati方程得到故障估计器。
Almost all control systems suffer from internal or external disturbance.The source of noise pollution may come from measuring instrument such as sensor,or come from stochastic factor such as thunder and environment,etc.The main task of filtering technique is to acquire real signals from noise pollution.Moreover,large inertia objects, transmission process and complicated on-line analyzer etc,are common in the industrial processes,which can cause measurement delays in the systems.Time-delay systems are of wide application background,and are available in many engineering fields such as signal processing,communication systems,transmission and control in networks, etc.until the present time,some problems upon fundamental theory remain unsettled as a great challenge,and the conventional approaches,covering state augmentation method,partial differential equation method and linear operator theory,etc, tend to consume enormous or complicated calculations and the results from them are hard to make further performance analysis.The filtering problems for the time-delay systems have been intriguing many researchers for decades,and remain to be perfected further.
The dissertation focuses on the H∞filtering for linear time-delay systems,white noise optimal filtering,and the main results are as follows.
●It considers the unified optimal white noise estimation problem in H_2 setting for linear systems.Based on the Kalman filtering method and projection theory,the optimal estimator is designed via solving Riccati equations.It can compute both system noise and measurement noise simultaneously,even when input noise and measurement noise is correlated.
●It studies the optimal input white noise estimator for linear stochastic systems with delayed measurements.To improve the computational efficiency,we propose a new approach without resorting to system state augmentation.The proposed approach is based on the re-organization innovation theory.The derived white noise smoother is given in terms of a series of Riccati difference equations(RDEs) with the same order as that of the original system.We discuss this problems in two cases:discrete-time systems and continuous-time systems.
●It discusses the H∞filtering problem for linear discrete system with multiple measurements time-delay,transforms the underlying problem into an indefinite quadratic optimal one in Krein space,makes use of the theory in Krein space and the reorganized innovation analysis,designs the optimal filter by solving a set of Riccati equation with the same dimension of the origin system.The sufficient condition for the present solvability of the problem is given.
●It investigates the H∞fault detection estimator for linear stochastic systems with unknown input and energy-bounded disturbance.The key technique is the measurements and the innovation re-organization in Krein space.The fault estimator can be designed by applying the reorganized innovation technique in Krein space and finally giving solutions by solving Riccati equations.
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