含随机穿越特征指标的离散系统满意估计问题

当待估量的期望值是一个有界区域时, 对待估量穿越目的域边界问题进行了讨论. 通过对离散估计系统的区域极点、随机穿越特征量等指标的相容性进行分析, 给出了一种满足多指标要求的满意待机估计策略, 并设计了基于双线性矩阵不等式组(BMIs)的求解算法. 所给出的待机估计策略可保证待估量在目的域内平均滞留度满足一定的指标, 同时相对目的域边沿的平均穿越周期尽可能小, 从而达到了待估量在目的域内、外的时间分布更加均匀 的目的. 数值算例说明了所设计的估计策略满足多指标要求.

Satisfactory estimation problem for discrete systems with stochastic passage characteristics index constraint

When the expectation value of an estimate is a finite area, the problem of stochastic passage over the target area boundary is discussed. By analyzing the consistency between the indices of the area pole and the stochastic passage characteristics of the discrete estimation system, we propose a satisfactory estimation strategy for opportunity-awaiting, which satisfies the requirements of multi indices; and develop the solution algorithm based-on bi-linear matrix inequalities(BMIs). The presented estimation strategy for opportunity-awaiting ensures the estimate to satisfy the index of average residence degree in the target area, and keeps the average traversing period over the target area boundary to be as small as possible. Therefore, the time distributions of the estimate being inside and outside the target area can be uniform as desired. Finally, the results are illustrated by a numerical example.