带乘性噪声和延时观测广义系统的多步最优预测器

Optimal multi-step predictor for descriptor systems with multiplicative noise and delayed measurement

中文关键词  广义系统  多步预测器  延时观测  乘性噪声  新息重组

英文关键词  descriptor systems  multi-step predictor  delayed measurements  multiplicative noise  re-organized innovation

中文摘要

      本文研究了状态空间描述的离散广义系统最优预测器的设计问题, 该系统带有即时和延时观测, 所有观测中带有乘性噪声. 论文在两个基本假设条件下采用标准的奇异值分解方法给出了受限等价时滞系统, 对于此类系统没有采用状态增广方法, 而是采用新息重组分析理论给出了多步预测器. 因为延时观测的存在, 所给出的多步预测器包含了两套递推的广义系统黎卡提方程. 本文给出了一个数学算例验证了所提方法的正确性和有效性, 并给出了四幅图片, 根据算例可以看出一般情况下预测的步数越少, 预测的结果越好. 本文方法可以进一步来研究更复杂的一些问题, 如延时广义系统的${\rm H}_{\infty}$滤波和控制问题.

英文摘要

      Optimal multi-step predictor problem for the discrete-time descriptor systems is dealt with, where the descriptor systems is given in terms of state-space equations. The state-space equations involve instantaneous measurements and delayed measurements, and multiplicative noises in all measurements. Two standard assumptions are made for the descriptor system case, under which the restricted equivalent delayed system is derived by using standard singular value decomposition. Without resorting to state augmentation which is usually employed for dealing with estimation for delay system, we put forward a reorganized innovation lemma for presenting the result of multi-step predictor. The multi-step predictor involves two sets of recursive Riccati equations of descriptor systems since of the existence of the delayed measurements. The proposed approach is validated being efficient by a numerical example where four figures are presented, demonstrating that the proposed approach can give better predicting estimation when the number of steps is less. Furthermore, the proposed approach can be used to tackle more difficult problems, such as filtering and control for descriptor systems with multiplicative noises.