网络控制系统中基于K-means的延迟量化与预测方法

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"本文主要探讨了在网络控制系统（NCS）中，利用K-means聚类算法对控制器到执行器（C-A）延迟进行量化，并基于离散时间隐藏马尔可夫模型（DTHMM）参数估计进行延迟预测的方法。通过这种量化方法和DTHMM的估计，可以实现当前随机C-A延迟的预测。进而，考虑当前预测的C-A延迟，设计状态反馈控制器以直接补偿当前实际C-A延迟对网络控制系统的影响。文中详细阐述了用于量化过去C-A延迟的K-means聚类过程，并通过对比模拟实验验证了所提量化和预测方法的优越性。关键词：网络控制系统；离散时间隐藏马尔可夫模型" 详细说明：在现代自动化系统中，网络控制系统的应用越来越广泛，但网络引入的延迟问题会对系统的性能产生显著影响。本研究聚焦于解决这一问题，提出了一种基于K-means聚类的延迟量化策略和基于DTHMM的延迟预测方法。 K-means聚类是一种无监督学习算法，常用于数据分组或分类。在此背景下，它被用来将连续的C-A延迟数据离散化，转化为可处理的类别。这样做的好处是可以将复杂的延迟现象简化为有限数量的延迟状态，从而更方便地进行建模和分析。通过优化聚类中心，K-means能够有效地将延迟数据分配到不同的簇中，形成延迟的离散观察，为DTHMM参数的估计提供基础。 DTHMM是一种概率模型，适用于描述具有隐藏状态和观测序列的时间序列数据。在NCS中，它可以用来捕获C-A延迟的随机性和动态变化。利用K-means聚类得到的离散观测，可以更准确地估计DTHMM的参数，进而预测未来的延迟状态。有了延迟预测，系统可以提前预知并适应可能的延迟影响。为此，文章中设计了一个状态反馈控制器，该控制器能够考虑到当前预测的C-A延迟，实时调整控制信号以抵消延迟对系统性能的负面影响。这种方法有助于提高网络控制系统的稳定性、鲁棒性和控制性能。为了验证提出的量化和预测方法的有效性，作者进行了对比模拟实验。实验结果证实，这种方法相比于传统方法能更有效地处理C-A延迟，提高了NCS的性能和响应速度。总结来说，本文提供的K-means延迟量化和DTHMM预测方法为网络控制系统的延迟管理提供了一种创新解决方案，通过精确的延迟预测和有效的控制补偿策略，增强了系统的控制性能和可靠性。这种方法对于应对网络环境中的不确定性延迟挑战具有重要的理论和实践意义。

K-means Based Delay Quantization and Prediction in Networked

Control Systems

Yuan Ge, Shuang Cong

, and Weiwei Shang

Department of Automation, University of Science and Technology of China, Hefei, 230027, P. R. China

E-mail:

ygetoby@mail.ustc.edu.cn

, scong@ustc.edu.cn, wwshang@ustc.edu.cn

Abstract: In the networked control system (NCS) with the discrete-time hidden Markov model (DTHMM), K-means clustering

is proposed in this paper to quantize the controller-to-actuator (C-A) delays and to obtain the discrete observations for estimating

the DTHMM parameters. The prediction of the current stochastic C-A delay is achieved based on the quantizing method and the

estimated DTHMM. Then, by taking the current predicted C-A delay into account, a state-feedback controller is designed to

directly compensate for the effect of the current real C-A delay on the NCS. The detailed procedure of the K-means clustering

used to quantize the past C-A delays is given. The contrastive simulation experiments are implemented, and the results

demonstrate the superiority of the quantizing and predictive methods proposed in this paper.

Key Words:

Networked control system; discrete-time hidden Markov model; K-means clustering; delay quantization; delay

prediction

1. Introduction



Hidden Markov model (HMM) was first introduced to

networked control systems (NCSs) by Nilsson in [1]. Then,

the further application of the HMM in NCSs has been

investigated in [2-6]. The HMM was mainly used to model

the relation that the distribution of the network-induced

delays is usually probabilistically governed by the network

states. In this model, the hidden Markov chain consists of the

network states and the observations are the quantized results

from the network-induced delays. The HMM used in [1-6] is

actually a discrete-time HMM (DTHMM), which is a kind of

HMM with discrete states and discrete observations [7]. The

parameters of the DTHMM in [1-3] were all assumed to be

known in advance. In order to relax this unrealistic

assumption, some maximum likelihood estimation algorithms

(e.g., Baum-Welch, Expectation Maximization) were used in

[4-6] to estimate the DTHMM parameters. The main purpose

of the DTHMM parameter estimation in [5] is to statistically

predict the controller-to-actuator (C-A) delay in the current

sampling period (denoted as the current C-A delay). Then, the

predicted C-A delay was taken into account in the

state-feedback controller design and the effect of the real C-A

delay on the NCS was directly compensated in [6].

Generally, the estimation of the DTHMM parameters is

based on the discrete observations which are the inputs of this

model. In order to obtain the observations, the delay interval

in [4-6] was uniformly divided into several equal subintervals,

and then the delays were quantized into a discrete-time

sequence which served as the observations. This is so-called

uniform quantization of delays. However, in practical NCSs,

the delays do not always uniformly distribute over a time

interval. For example, the delay distribution has a lower mean

if the network has low load, and a higher mean if the network



This work is partially supported by the National Science Foundation of

China (61074050, 60843003, 50905172), the Science Foundation of Anhui

Province (090412071, 090412040), and the University of Science and

Technology of China Initiative Foundation.

Corresponding author

has a high load [1]. This is the reason why the precision of the

current C-A delay prediction based on the uniform

quantization is relatively lower [5-6]. Therefore, more

effective delay quantizing methods for the actual network

situation is much needed to improve the predictive precision,

which motivates this paper.

In this paper, K-means clustering is introduced to quantize

the past C-A delays. In NCSs, the delays are one-dimensional

data that stochastically distribute over a bounded interval.

When quantizing these delays, some relatively centralized

delays should be quantized as the same observation value

while those relatively decentralized delays should be

quantized into different observation values. Obviously, the

delay quantizing process is a clustering problem. As is known,

K-means is one of the efficient and most widely used

clustering algorithms [8] since it was first introduced by

MacQueen in 1967 [9]. So, K-means clustering can be used to

quantize the delays in NCSs. Then, the current stochastic C-A

delay can be predicted based on the quantizing method.

Compared with the uniform quantization, the K-means

clustering quantization gets closer to the real distribution of

the stochastic delays. As a result, the predictive precision

based on the K-means clustering quantization is higher than

that based on the uniform quantization. Moreover, the

state-feedback controller designed based on the prediction in

this paper can render the NCS better performance than that in

[6].

The remainder of this paper is organized as follows. In

Section 2, K-means clustering is proposed to quantize the

past C-A delays to get an observation sequence. In section 3,

the observation sequence is used as the input to estimate the

DTHMM parameters and the statistical prediction of the

current C-A delay is obtained. Section 3 presents the

contrastive simulation experiments to demonstrate the

superiority of the proposed quantizing and predictive

methods. Finally, the conclusions are given in Section 4.

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