广义系统H_∞多步预报器设计

Design of H-infinity multi-step predictor for descriptor systems

基于格林空间中的新息分析方法和卡尔曼滤波理论,首次给出了广义系统H∞多步预报器存在的充要条件和一种简单的计算方法.本文将广义系统的H∞多步预报问题转化为带有当前观测和时滞观测的格林空间中广义系统最小方差估计问题,然后引入新息重组序列解决该最小方差估计问题.通过求解维数与变换后的系统相同的两个黎卡提方程得到了H∞预报器,避免了处理带观测时滞系统时常采用的系统增广方法.数值例子表明利用本文的新息重组方法计算广义系统H∞多步预报器比用系统增广方法计算量小.

Based on the method of innovation re-organization and the theory of Kalman filtering in Krein space, a sufficient and necessary condition for the existence of an H-infinity multi-step prediction for descriptor systems is given for the first time and a simple computation method is derived in this paper. Firstly, the H-infinity multi-step prediction problem for descriptor system is converted into a Krein space H2 estimation problem with current and delayed measurements. Then, the latter one is solved by introducing a re-organization innovation sequence. The H-infinity predictor is thus computed by performing two Riccati equations that are with the same dimensions as a transformed system, and the usually used augmentation method for systems with delayed measurements is avoided. Finally, numerical example shows that the calculation burden of the descriptor systems H-infinity multi-step predictor based on re-organization innovation method is lighter than the one based on the method of system augmentation.