【作者】 石莹；

【导师】 段广仁；

【作者基本信息】 哈尔滨工业大学 ， 控制理论与控制工程， 2007， 博士

【摘要】 广义系统广泛出现在机器人、经济学、电路和化工等系统中,是比正常系统更具有普遍性的一种对实际系统的描述形式。而广义系统的状态估计问题是进行广义系统控制和设计的重要理论基础。随着多传感器系统的出现,关于多传感器广义系统的融合估计问题也得到了人们的关注,但还处于初步阶段。本文基于Kalman滤波理论和白噪声估值器,研究了单通道广义线性系统和多传感器广义线性系统的最优状态估计和稳态估计问题,主要以理论分析为主,辅以计算机仿真研究。主要内容和研究成果包括如下几个方面一、考虑了Y-可观条件下的单通道广义线性系统的降阶固定区间Kalman平滑器问题。通过受限等价变换将广义线性系统转化为等价的两个子系统,利用Kalman滤波理论和白噪声估值器得到子系统的状态估计,进而得到广义系统的固定区间平滑器。新平滑器避免了计算预报误差阵P (t |t?1)的逆;并且算法实现了平滑器的正向计算。二、考虑了完全可观条件下的单通道广义线性系统的降阶极点配置固定滞后Kalman平滑器问题。通过奇异值分解将广义线性系统转化为等价的两个子系统,利用配置极点得到一种渐近稳定的降阶稳态Kalman固定滞后平滑器。新算法不仅可以减少计算负担,而且通过配置平滑器的极点可快速消除任意选取的平滑器初始值对估值器的影响。三、考虑了单通道广义线性系统的降阶Wiener估值器问题。在广义线性系统完全可观的条件下,基于稳态Kalman滤波器,得到降阶的Wiener状态估值器,表示为以观测信号为输入的传递函数形式,可统一处理滤波、预报和平滑问题,估计具有渐近稳定性,不需要考虑初值的选取问题。最终给出数值仿真算例,证明了所提算法的有效性。四、考虑了在正则、因果的假设条件下多传感器广义线性系统的状态融合最优估计问题。一种方法是:通过受限等价变换将广义线性系统表示为过程噪声是有色噪声的正常系统。利用Kalman滤波理论推导出广义系统的状态超前一步预报器、N步预报器和滤波器。通过计算各子系统的误差互协方差阵,在线性最小方差信息融合准则下,提出了按矩阵、对角阵和标量加权的分布式最优Kalman融合预报器和滤波器。另一种方法是通过受限等价变换,将多传感器广义系统转化为观测噪声相关的正常多传感器系统。给出了降阶子系统递推形式的稳态Kalman滤波器,在此基础上推导出状态的滤波误差互协方差阵,按照线性最小方差信息融合准则提出了按矩阵、对角阵和标量加权的三种稳态融合Kalman滤波器。五、考虑了观测系数阵维数相同和不同两种情形下的带相关噪声的广义线性系统的观测融合状态估计问题,得到了集中式观测融合Kalman滤波器和加权观测融合Kalman滤波器。当各子系统观测噪声以及系统噪声之间均不相关,并且带有相同的观测系数阵时,两种滤波器是功能等价的。所有结果均用数值算例进行了MATLAB仿真,并结合图表的形式将真值和估计值进行了比较。六、考虑了多传感器广义线性系统的信息融合状态Wiener预报器问题。基于稳态Kalman预报器,推导出子系统的渐近稳定的Wiener状态预报器以及各子系统之间预报误差协方差阵,得到渐近稳定的Wiener预报器,可任意选取初值,并逐渐消除初值对估值器的影响。在线性最小方差融合准则下,给出了广义线性系统按矩阵、对角阵和标量加权的三种信息融合Wiener预报器。通过数值算例验证了理论结果的有效性。更多还原

【Abstract】 Descriptor systems occur naturally in robotics, economic, electronic and chemical systems, which are more common than conventional systems to describe the actual systems. The estimation problems for descriptor systems are fundamental to control and synthesis problems for them. With the advent of multi-sensor systems, fused estimation problems for multi-sensor descriptor systems have been received more and more attentions, but they are still in the preliminary stage.Based on Kalman filtering theory and white noise estimators, this dissertation mainly considers the problem of state estimation for single-channel descriptor linear systems and multi-sensor descriptor linear systems, respectively. The main research results in this dissertation can be given as the following.Firstly, reduced-order fixed-interval Kalman smoother for Y-observable single-chanel descriptor linear systems is proposed. By constrained equivalent transformation, the descriptor systems are changed into two conventional subsystems. Based on Kalman filtering theory and white noise estimators, state estimators for subsystems are obtained and therefore fixed-interval Kalman smoother for descriptor systems is proposed. The new smoother avoids the evaluation of the inverse of prediction error variance matrix P (t |t?1) and achieves positive direction calculation.Secondly,reduced-order fixed-lag Kalman smoother for completely observable single-chanel descriptor linear systems is proposed. By singular value decomposition, the descriptor systems are changed into two conventional subsystems. Hence, an asymptotically stable steady-state Kalman fixed-lag smoother is gained by pole assignments. The new algorithm can reduce the computational burden and quickly eliminate the influence of initial values by assigning poles. Thirdly,the reduced-order Wiener state estimation problem is considered for single-chanel descriptor linear systems. Based on steady-state Kalman filters, reduced-order Wiener state estimators are proposed under completely observable assumption. Reduced-order Wiener state estimators are expressed in transfer functions with measurements as inputs, which can handle the prediction, filtering and smoothing problems in an unified form and have asymptotical stability without considering the selection of initial values. A numerical example is given to demonstrate the effectiveness of the proposed algorithm.Fourthly, under the assumption that descriptor systems are regular and casual, the state information fusion optimal estimation problem is considered for multi-sensor descriptor linear systems. One method is that by constrained equivalent transformations a descriptor linear system is changed into a conventional system with color system noises. And the one-step forward Kalman predictor, N-step forward Kalman predictor and Kalman filter are derived based on Kalman filtering theory. Under linear least variance fusion rules, decentralized optimal Kalman fused predictors and fused filters weighted by matrices, diagonal matrices and scalars are proposed by calculating the cross-variance matrices between the th subsystem and the jth subsystem.Another method is to change the descriptor systems into conventional systems with correlated measurement noises by constrained equivalent transformations. A recursive steady-state Kalman filter is derived and therefore filter error cross-variance matrices are obtained. According to the linear least variance fusion rules, three kinds of steady-state Kalman fused filters weighted by matrices, diagonal matrices and scalars are proposed.Fifthly, two kinds of fused Kalman filters weighted by measurements are proposed for descriptor systems with same and different measurements matrices. When the descriptor systems have same dimensionality matrices and uncorrelated system noise and measurement noises , functional equivalence between fused measurement Kalman filters is verified. All results are illustrated by numerical examples and utilizing the forms of graphs and tables shows the comparison between true values and estimated values. w( t)vi(t)Finally, the information fusion state Wiener prediction problem is considered for multi-sensor descriptor linear systems. Based on steady-state Kalman predictors, asymptotically stable Wiener state predictors for subsystems and cross-variance matrices between them are derived. According to the linear least variance fusion rules, fused Wiener predictors weighted by matrices, diagonal matrices and scalars are proposed. The effectiveness of the proposed algorithms is demonstrated by a numerical example.更多还原