无线传感器网络中非线性随机系统的事件驱动分布式滤波

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"这篇研究论文探讨了一种针对无线传感器网络上非线性随机系统的基于事件的分布式滤波方法。文章作者包括Zhongrui Hu、Peng Shi、Ligang Wu和Choon Ki Ahn，发表在《国际控制、自动化与系统》期刊17卷4期，2019年，页码896-906。文章的doi是10.1007/s12555-018-0629-1，国际标准刊号（ISSN）为1598-6446（印刷版）和2005-4092（电子版）。" 本文的主要研究内容涉及了在传感器网络中处理非线性随机系统的分布式滤波问题。研究的核心是提出了一种基于事件触发的通信策略和分布式滤波方案，适用于离散时间的非线性随机系统。系统模型采用了Takagi-Sugeno（T-S）模糊模型，这是对非线性系统进行建模的一种常用方法，能够将复杂的非线性系统转化为一系列简单的线性子模型。在无线传感器网络的背景下，系统描述考虑了网络的特性，其中网络结构被设定为确定性的。基于事件触发的机制意味着只有当特定条件满足时，如传感器检测到的状态变化达到一定阈值，才会进行数据传输，这种方式可以显著减少不必要的通信开销，提高能效，并降低网络拥塞。论文中设计的分布式滤波器旨在通过网络中的各个节点协同工作，估计系统状态。每个节点根据接收到的局部信息和事件触发的更新规则，更新其滤波估计。这样的设计不仅降低了对中央处理器的需求，还允许在网络节点间分散计算负担，提高了整体系统的鲁棒性和可靠性。此外，由于传感器网络可能受到各种不确定性因素的影响，如通信干扰、节点故障或能量限制，因此，该方法还需要考虑如何在这些不确定环境下保持滤波性能的稳定性。作者可能通过分析滤波误差动态和设计适当的补偿策略，来确保滤波器的收敛性和稳定性。这项研究为无线传感器网络中的非线性随机系统提供了一种高效且节省资源的分布式滤波解决方案，对于优化网络资源利用，增强实时状态估计能力具有重要意义。这不仅有助于提升传感器网络的数据处理能力，还有可能应用于各种领域，如环境监测、工业自动化和智能交通系统等。

Event-based Distributed Filtering Approach to Nonlinear Stochastic Systems over Sensor Networks 897

ences therein. It is still worth emphasizing that, when a

system with distributed sensors becomes highly modular

and complex, various noises or disturbances are likely to

be observed in distributed sensors. Therefore, it remains

a practical concern to design appropriate distributed ﬁl-

tering approaches to maintain system stability and perfor-

mance.

Alongside the interest in desirable performance, it is the

concern for energy consumption of the individual sensor

node that has drawn more and more research attention.

Frequent signal transmissions can deplete sensor batter-

ies more easily and such is especially the case in net-

works with the periodic communication paradigm [15].

In contrast of sending information at time instants sepa-

rated by a constant interval, as is the essence of the de

facto strategy of time-triggering transmissions, the event-

based communication strategy is built with energy econ-

omy in mind and aims to reduce signal transmissions in

the network environment [16–18]. The general setting of

an event-triggering mechanism consists of an event detec-

tor unit and a sender unit. The detector unit monitors

a user-deﬁned event-triggering condition and, on viola-

tion of this condition, instructs the sender unit to trans-

mit new measurements. The issue of uncertainties in

the stream of measurements was investigated in [19, 20].

In [19], A modiﬁed Rice fading channel was used to

model the situations of missing measurements, whereas

in [20] the missing measurements are modeled as a se-

ries of Bernoulli random variables. Additionally in [20],

the norm-bounded uncertainties was interpreted as distur-

bances within a bounded set. Moreover, considering the

distributed sensors used to exchange those meausrements,

it deserves to be mentioned that Liu et al. in [ 12] inves-

tigated the distributed ﬁltering problem for linear time-

varying systems based on an event-triggered communica-

tion scheme over WSNs. Hu et al. [21] proposed an event-

triggered distributed state estimation scheme for linear

stochastic systems with randomly occurring uncertainties

and state-dependent noises over sensor networks. Ding et

al. [22] came up with a state estimation approach based on

event-triggered communication mechanism to the stochas-

tic systems with nonlinear stochastic process in a sensor

network. Another recent work in [23] investigated the

problem of designing event-driven distributed ﬁlters for

networked switched systems with network-induced trans-

mission delay to achieve ﬁnite-time boundedness. In view

of the stochastic nature of a wireless network, research on

stochastic system in relation to the networking arrange-

ment is still of great importance. And we feel that further

enrichment is possible for the above discussions on the

event-triggered ﬁltering problem of the nonlinear stochas-

tic systems over WSNs.

Moreover, to represent nonlinearities in the real systems

Takagi-Sugeno (T-S) fuzzy models [24–26] have been

widely utilized in stochastic process or jumping param-

eters [27–30]. In a T-S fuzzy model, a series of simple lin-

ear subsystems weighted with the so-called membership

functions are utilized to approximate a nonlinear plant. As

a result, the analysis and the synthesis of the systems be-

comes trainable based on the control and ﬁltering meth-

ods. Recently, Wu et al. designed an fuzzy ﬁlter approach

in [31] for the fault detection of fuzzy Itô stochastic sys-

tems. Wang et al. [32] discussed the event-triggered fuzzy

ﬁltering problem of nonlinear physical plant. But both

plants were considered as a deterministic system with a

single sensor. Su et al. dealt with the distributed fuzzy

ﬁlter problem of discrete-time fuzzy systems with time-

varying delays over sensor networks. Therefore it can be

suggested that an integrated view of the above-mentioned

features would be of much value and provide some inter-

esting research. In this respect however, there seems to be

few works addressing this topic. And we intend to offer

results of our investigation in this paper.

Hence, in this work we are ﬁrstly concerned with the

formulation problems of the distributed ﬁlters and the non-

linear stochastic systems over the WSN. Then the prob-

lems of event-triggering and the distributed ﬁltering are

considered. We intend to contribute the following results:

i) an event-driven distributed ﬁltering stochastic system is

formulated including the fuzzy-model-based WSN, ii) a

multiple-event-triggered mechanism is designed based on

the distributed WSN, and iii) an event-based ﬁltering ap-

proach with disk stability constraints is proposed for the

nonlinear stochastic systems. Subsequently, a simulation

example is provided to demonstrate the effectiveness of

the event-based distributed ﬁltering methods.

The rest of the paper is structured as follows: Section

2 introduces the models of the stochastic plant with the

WSN, and the event-based ﬁlters are presented. Section 3

details the main results on the distributed ﬁltering design

procedure. A simulation example is given in Section 4.

Section 5 concludes this paper.

Notation: N denotes the set of natural numbers.

ℓ

[0,∞) is the space of square-integrable vector func-

tions over [0, ∞). For a matrix X ∈ R

n×n

, “*” repre-

sents transposed elements in the symmetric positions;

“X

⊤

” the matrix transposition and “X

−1

” the inversion

of X. “I” and “0” are the identity and zero matrices re-

spectively with appropriate dimensions. X ◦ Y is used

here to denote element-wise multiplication for matri-

ces of suitable dimensions. X ⊗ Y stands for the Kro-

necker product of any dimensioned matrices X and Y .

∥e∥

= E{

∑

∞

k=0

∥e(k)∥

} =

∑

∞

k=0

E{∥e(k)∥

}. If not ex-

plicitly stated, all matrices are assumed to have compatible

dimensions for algebraic operations.

2. PROBLEM FORMULATION

We adopt the following a-rule T-S fuzzy model based

on b fuzzy sets to approximate the nonlinear stochastic

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