具有衰减测量和随机时滞的离散非线性复杂网络的保概率集员滤波  

Probability-Guaranteed Set-Membership Filtering for Discrete Nonlinear Complex Networks with Fading Measurements and Random Delay

作　　者：颛美斐 陈东彦 胡军 ZHUAN Meifei;CHEN Dongyan;HU Jun(School of Science,Harbin University of Science and Technology,Harbin 150080;School of Automation,Harbin University of Science and Technology,Harbin 150080)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080 [2]哈尔滨理工大学自动化学院,哈尔滨150080

出　　处：《系统科学与数学》2022年第8期1960-1972,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(12071102,12171124)资助课题.

摘　　要：研究一类离散非线性复杂网络的保概率集员滤波问题.考虑网络节点受状态随机时滞、衰减测量等影响,为了更贴合实际,采用两类相互独立的随机变量分别描述状态时滞和测量衰减特征.引入Bernoulli随机变量将随机时滞刻画为随机发生时滞,引入在某区间上服从已知概率分布的随机变量刻画衰减测量.文章设计一个分布式集员滤波器,给出滤波误差系统所需满足的充分条件以保证滤波误差被限制在已知椭球集内的概率不小于已给定的概率值,且该充分条件由一个递推线性矩阵不等式表示;建立在矩阵迹最小意义下的凸优化问题以最小化每个时刻所获得的概率椭球集,并设计一个保概率集员滤波器增益矩阵的求解算法.最后,通过一个数值算例验证所设计的滤波设计方案的有效性.This paper deals with the probability-guaranteed set-membership filtering problem for a class of discrete nonlinear complex networks under the influence of unknown but bounded noise.Consider that network nodes are affected by random delay and fading measurements,two kinds of uncorrelated random variables are utilized to describe the state delay and the fading rates respectively.A Bernoulli random variable is introduced to characterize the phenomenon of randomly occurring delay.A random variable which obeys the known probability distribution on a certain interval is used to describe the attenuation coefficient of the fading measurements.The aim of the problem addressed is to design a distributed set-membership filtering such that:1)the probability of the filtering error restricted to a given ellipsoid is not less than a specified value;and 2)the ellipsoid is minimized in the sense of matrix norm at each time instant.To achieve this purpose,a recursive linear matrix inequality is utilized and the sufficient conditions are derived for the existence of the desired filter in terms of the solution to the matrix inequalities.By means of the probability-guaranteed set-membership approach,the convex optimization problem is formulated with the purpose of minimizing the set of the probability ellipsoids obtained in the sense of the minimal matrix trace at each moment.Moreover,a recursive optimization algorithm is designed to get the gain matrix of the probability-guaranteed set-membership filtering to guarantee the locally optimal performance.Finally,an illustrative numerical example is given to verify the effectiveness of the developed probability-guaranteed set-membership filtering scheme.

关 键 词：保概率集员滤波 复杂网络 随机时滞 衰减测量 递推线性矩阵不等式 

分 类 号：O157.5[理学—数学]