CN112911530A - Method for establishing small and micro intelligent sensor network congestion identification model - Google Patents
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Abstract
Translated fromChinese
Description
Translated fromChinese技术领域technical field
本发明涉及网络拥塞辨识模型，具体涉及一种小微智能传感器网络拥塞辨识模型的建立方法。The invention relates to a network congestion identification model, in particular to a method for establishing a congestion identification model of a small and micro intelligent sensor network.
背景技术Background technique
在透明电网，由小微智能传感器组成的无线传感器网络中大规模的数据流输入到传感器节点可能引起网络拥塞，网络拥塞严重影响网络的性能。小微智能传感器网络系统具有很强的非线性，这为进一步分析和设计网络拥塞控制器增加了困难，因此，建立小微智能传感器网络拥塞系统线性化模型是小微智能传感器的重点研究方向之一。In the transparent grid, the large-scale data flow input to the sensor nodes in the wireless sensor network composed of small and micro smart sensors may cause network congestion, which seriously affects the performance of the network. The small and micro smart sensor network system has strong nonlinearity, which makes it difficult to further analyze and design the network congestion controller. Therefore, establishing a linear model of the small and micro smart sensor network congestion system is one of the key research directions of the small and micro smart sensor. one.
拥塞控制直接影响网络的服务质量，针对网络拥塞模型具有很强的非线性问题，大多数学者着重在平衡点进行局部线性化，之后进行后续网络拥塞控制器的设计。Congestion control directly affects the service quality of the network. Aiming at the strong nonlinear problem of the network congestion model, most scholars focus on local linearization at the equilibrium point, and then design the subsequent network congestion controller.
国内外的研究人员进行了大量研究，鲁东大学学者采用拥塞度门限值作为拥塞调节的依据，提出了一种基于RED的拥塞避免策略。(期刊：计算机仿真，著者：李路伟，杨洪勇；出版年月：2012；文章题目：基于 RED的无线传感器网络的拥塞控制；页码：168-172)Researchers at home and abroad have carried out a lot of research. Scholars from Ludong University use the congestion degree threshold as the basis for congestion adjustment, and propose a congestion avoidance strategy based on RED. (Journal: Computer Simulation, Authors: Li Luwei, Yang Hongyong; Publication Year: 2012; Article Title: Congestion Control for Wireless Sensor Networks Based on RED; Pages: 168-172)
北京科技大学学者提出一种基于PID型神经网络控制队列的控制器，利用RBF神经网络的自学习能力解决网络实时变化时算法参数的在线整定问题，使路由器缓存中的队列长度稳定在设定值。(期刊：小型微型计算机系统；著者：唐懿芳，穆志纯，赵仕俊，钟达夫；出版年月：2010；文章题目：基于RBF预估神经网络控制器的无线传感器网络拥塞算法；页码：32-35)Scholars from the University of Science and Technology Beijing proposed a controller based on a PID neural network to control queues. The self-learning ability of the RBF neural network is used to solve the problem of online tuning of algorithm parameters when the network changes in real time, so that the queue length in the router cache is stable at the set value. . (Journal: Small Microcomputer System; Authors: Tang Yifang, Mu Zhichun, Zhao Shijun, Zhong Dafu; Publication Year: 2010; Article Title: Congestion Algorithm for Wireless Sensor Networks Based on RBF Prediction Neural Network Controller; Page: 32- 35)
学者提出一种基于非线性干扰观测器的鲁棒拥塞控制器，其重点是抑制队列振荡，并对时滞进行补偿。(期刊：IFAC Proceedings Volumes；著者：Hsu P,Lin C；出版年月：2014；文章题目：Active queue management in wireless networks by using nonlinearextended network disturbance；页码：1613-1618)Scholars propose a robust congestion controller based on nonlinear disturbance observer, which focuses on suppressing queue oscillation and compensating for time delay. (Journal: IFAC Proceedings Volumes; Authors: Hsu P, Lin C; Publication Year: 2014; Article Title: Active queue management in wireless networks by using nonlinearextended network disturbance; Pages: 1613-1618)
合肥工业大学学者采用一种滑模学习控制方法，其可以减轻拥塞，降低包丢失和保持队列长度。(会议：2014International Conference on Wireless Communication andSensor Network；著者：Jiang K W,Wang J P,Sun W,Qi yue Li；出版年月：2015；文章题目：Sliding mode learning control for congestion control of wireless sensornetworks；页码：291-296)Scholars at Hefei University of Technology adopted a sliding mode learning control method, which can alleviate congestion, reduce packet loss and maintain queue length. (Conference: 2014 International Conference on Wireless Communication and Sensor Network; Authors: Jiang K W, Wang J P, Sun W, Qi yue Li; Publication Year: 2015; Article Title: Sliding mode learning control for congestion control of wireless sensornetworks; Page: 291- 296)
伊斯兰阿扎德大学学者提出一种模糊PID的控制方法，控制缓冲区队列长度。(期刊：Wireless Personal Communications；著者：Rezaee A A,Pasandideh F；出版年月：2017；文章题目：A fuzzy congestion control protocol based on active queuemanagement in wireless sensor networks with medical applications；页码：816-842)Scholars from Islamic Azad University proposed a fuzzy PID control method to control the buffer queue length. (Journal: Wireless Personal Communications; Authors: Rezaee A A, Pasandideh F; Publication Year: 2017; Article Title: A fuzzy congestion control protocol based on active queuemanagement in wireless sensor networks with medical applications; Pages: 816-842)
现有方法大多着重将网络拥塞系统进行局部线性化，然后进行控制律设计。由于这些方法考虑的数学模型存在不完整性，结论难以推广至一般情况。Most of the existing methods focus on the local linearization of the network congestion system, and then design the control law. Due to the incompleteness of the mathematical models considered by these methods, the conclusions are difficult to generalize to the general case.
发明内容SUMMARY OF THE INVENTION
(一)解决的技术问题(1) Technical problems solved
针对现有技术所存在的上述缺点，本发明提供了一种小微智能传感器网络拥塞辨识模型的建立方法，能够有效克服现有技术所存在的无法建立具有普适性的全局线性化模型的缺陷。Aiming at the above shortcomings of the prior art, the present invention provides a method for establishing a congestion identification model for a small and micro intelligent sensor network, which can effectively overcome the defect of the prior art that a universal global linearization model cannot be established. .
(二)技术方案(2) Technical solutions
为实现以上目的，本发明通过以下技术方案予以实现：To achieve the above purpose, the present invention is achieved through the following technical solutions:
一种小微智能传感器网络拥塞辨识模型的建立方法，包括以下步骤：A method for establishing a congestion identification model for a small and micro smart sensor network, comprising the following steps:
S1、利用Koopman算子理论分析建立小微智能传感器网络系统数据集；S1. Use the theoretical analysis of Koopman operator to establish a data set of small and micro intelligent sensor network system;
S2、选取基函数对数据集进行升维，将原系统升维到一个高维的可观测函数空间；S2. Select the basis function to upgrade the dimension of the data set, and upgrade the original system to a high-dimensional observable function space;
S3、建立小微智能传感器网络Koopman高维线性模型；S3. Establish a Koopman high-dimensional linear model of a small and micro intelligent sensor network;
S4、利用得到的升维数据集求取Koopman算子有限维逼近，并利用神经网络进行训练，得到最终高维线性模型。S4. Obtain the finite-dimensional approximation of the Koopman operator by using the obtained increased-dimensional data set, and use the neural network for training to obtain a final high-dimensional linear model.
优选地，所述利用Koopman算子理论分析建立小微智能传感器网络系统数据集，包括：Preferably, the use of Koopman operator theoretical analysis to establish a small and micro intelligent sensor network system data set, including:
利用能够激发小微智能传感器网络特性的控制输入进行输入输出数据的采集，利用产生的输出数据与控制输入数据建立数据集：Use the control input that can stimulate the characteristics of the small and micro intelligent sensor network to collect input and output data, and use the generated output data and control input data to establish a data set:
其中，U为输入序列，X为当前状态序列，Y为下一状态序列，n表示每次控制的总采样次数，k表示收集k组数据，即以k种不同的初始状态在k个不同随意输入序列下进行开环控制，p为分组丢弃概率，
优选地，所述选取基函数对数据集进行升维，包括以下步骤：Preferably, the selection of basis functions to increase the dimension of the data set includes the following steps:
S21、定义一组基函数Ψ(x)＝[Ψ1(x),Ψ2(x),...Ψm(x)]T；S21, define a group of basis functions Ψ(x )=[Ψ1(x),Ψ2( x),...Ψm (x)]T ;
S22、选取一个简单的神经网络作为基函数的逼近器，形式设置为：S22, select a simple neural network as the approximator of the basis function, and the form is set as:
Ψ(x)＝Wouth+boutΨ(x)=Wout h+bout
h＝tanh(Wx+b) (1)h=tanh(Wx+b) (1)
其中，W∈R16×2，Wout∈R40×16，b∈R16×1，bout∈R40×1，需要训练的参数集为θ＝{W，b，Wout，bout}；Among them, W∈R16×2, Wout∈R40×16, b∈R16×1, bout∈R40×1, the parameter set to be trained is θ={W, b, Wout, bout};
S23、将数据集带入神经网络进行升维，得到升维后的数据集Xlift、Ylift。S23. Bring the data set into the neural network to increase the dimension, and obtain the data sets Xlift and Ylift after the dimension increase.
优选地，所述建立小微智能传感器网络Koopman高维线性模型，包括：Preferably, the establishment of a Koopman high-dimensional linear model for the small and micro intelligent sensor network includes:
基于Koopman算子理论和扩展动力学模态分解算法结合，将小微智能传感器网络表示为高维线性模型：Based on the combination of Koopman operator theory and extended dynamic mode decomposition algorithm, the small and micro smart sensor network is represented as a high-dimensional linear model:
z(k+1)＝Az(k)+Bu(k)z(k+1)=Az(k)+Bu(k)
其中，z为升维后的状态，
优选地，所述利用得到的升维数据集求取Koopman算子有限维逼近，并利用神经网络进行训练，得到最终高维线性模型，包括：Preferably, the finite-dimensional approximation of the Koopman operator is obtained by using the obtained increased-dimensional data set, and a neural network is used for training to obtain a final high-dimensional linear model, including:
利用得到的升维数据集Xlift、Ylift，通过扩展动力学模态分解算法求取Koopman算子有限维逼近，即求解如下最小化问题得到高维线性模型中的矩阵A、B、C：Using the obtained ascending-dimensional data sets Xlift and Ylift, the finite-dimensional approximation of the Koopman operator is obtained through the extended dynamic mode decomposition algorithm, that is, the following minimization problems are solved to obtain the matrices A, B, and C in the high-dimensional linear model:
求解最小值的解析式为：The analytical formula for finding the minimum value is:
通过式(1)和式(4)得到高维线性模型(2)的初步解析，为得到与真实模型更加接近的模型，利用神经网络自动训练的能力，将得到的矩阵A、B、C和神经网络参数集进行训练，定义的损失函数表示为：The preliminary analysis of the high-dimensional linear model (2) is obtained by formulas (1) and (4). In order to obtain a model that is closer to the real model, the automatic training ability of the neural network is used to convert the obtained matrices A, B, C and The neural network parameter set is trained, and the defined loss function is expressed as:
将式(1)、(4)和损失函数(5)通过神经网络不断训练，直到
(三)有益效果(3) Beneficial effects
与现有技术相比，本发明所提供的一种小微智能传感器网络拥塞辨识模型的建立方法，利用Koopman算子理论得到小微智能传感器网络系统全局线性化模型，利用神经网络形式作为基函数，并通过自动训练提高全局线性化模型的精度，有效解决了现有技术只在平衡点处进行局部线性化，考虑的数学模型存在不完整性，从而难以推广至一般情况的问题，并且全局线性化模型设计简单，为后续分析和设计小微智能传感器网络拥塞控制提供便利。Compared with the prior art, the method for establishing a congestion identification model of a small and micro intelligent sensor network provided by the present invention uses the Koopman operator theory to obtain a global linearization model of the small and micro intelligent sensor network system, and uses the neural network form as the basis function. , and improve the accuracy of the global linearization model through automatic training, which effectively solves the problem that the existing technology only performs local linearization at the equilibrium point, and the mathematical model considered is incomplete, so it is difficult to generalize to the general situation, and the global linearity The design of the model is simple, which facilitates the subsequent analysis and design of congestion control for small and micro smart sensor networks.
附图说明Description of drawings
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍。显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to illustrate the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that are required in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can also be obtained from these drawings without creative effort.
图1为本发明小微智能传感器网络拥塞辨识模型建立的流程示意图；1 is a schematic flow chart of the establishment of a congestion identification model for a small and micro intelligent sensor network according to the present invention;
图2为本发明所设计正弦输入下Koopman高维线性模型准确度验证图；Fig. 2 is the Koopman high-dimensional linear model accuracy verification diagram under the sinusoidal input designed by the present invention;
图3为本发明所设计方波输入下Koopman高维线性模型准确度验证图。FIG. 3 is an accuracy verification diagram of the Koopman high-dimensional linear model under the square wave input designed by the present invention.
具体实施方式Detailed ways
为使本发明实施例的目的、技术方案和优点更加清楚，下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述。显然，所描述的实施例是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.
Koopman算子是一种无限维线性算子，把系统从原始状态空间变换到另一个空间以达到近似的目的，是非线性动力系统分析和分解的有力工具。Koopman算子K的作用如下：The Koopman operator is an infinite-dimensional linear operator, which transforms the system from the original state space to another space for the purpose of approximation. It is a powerful tool for nonlinear dynamic system analysis and decomposition. The role of the Koopman operator K is as follows:
Kg(xk)＝gof(xk)Kg(xk )=gof(xk )
其中，o为函数符合操作符，xk为系统的状态，f为状态空间下状态演化的函数，g为实值观测函数，为无穷维Hilbert空间的一个元素。 Koopman算子K是作用在观测函数上的无穷维线性运算符，换言之，原系统可以被升维到一个无穷维的可观测函数空间，Koopman算子将状态的观测g(xk)推进到下一时间步：Among them, o is the function coincidence operator, xk is the state of the system, f is the function of state evolution in the state space, and g is the real-valued observation function, which is an element of the infinite-dimensional Hilbert space. The Koopman operator K is an infinite-dimensional linear operator acting on the observation function. In other words, the original system can be upgraded to an infinite-dimensional observable function space, and the Koopman operator pushes the state observation g(xk) to the next time step:
Kg(xk)＝g(xk+1)Kg(xk )=g(xk+1 )
Koopman算子在可观测空间上捕获底层系统的动态，并且原系统在新的坐标系下进行线性演化。理论上无限维空间能完全还原非线性系统，但在实际应用中是对无限维模型的有限维逼近，通常的方法是采用扩展动力学模态分解算法求解出Koopman算子的有限维逼近。要得到Koopamn算子有限维逼近，首先定义一组基函数：Ψ(x)＝[Ψ1(x),Ψ2(x),...Ψm(x)]T，并得到由基函数线性组合的观测函数：The Koopman operator captures the dynamics of the underlying system in the observable space, and the original system evolves linearly in the new coordinate system. In theory, infinite-dimensional space can completely restore nonlinear systems, but in practical applications, it is a finite-dimensional approximation of infinite-dimensional models. The usual method is to use the extended dynamic mode decomposition algorithm to solve the finite-dimensional approximation of the Koopman operator. To obtain the finite-dimensional approximation of the Koopamn operator, first define a set of basis functions: Ψ(x)=[Ψ1 (x),Ψ2 (x),...Ψm (x)]T , and get the basis functions Linearly combined observation functions:
其中，a为权值矩阵，则有下式成立：Among them, a is the weight matrix, then the following formula holds:
Kfg(x)＝gof(x)＝Ψof(x)a＝KfΨ(x)a+r(x)Kf g(x)=gof(x)=Ψof(x)a=Kf Ψ(x)a+r(x)
其中，r(x)为残差项。则可通过最小二乘法计算近似Koopamn算子 Kf：where r(x) is the residual term. Then the approximate Koopamn operator Kf can be calculated by the least square method:
其中，
一种小微智能传感器网络拥塞辨识模型的建立方法，如图1所示，包括以下步骤：A method for establishing a congestion identification model for a small and micro smart sensor network, as shown in Figure 1, includes the following steps:
S1、利用Koopman算子理论分析建立小微智能传感器网络系统数据集；S1. Use the theoretical analysis of Koopman operator to establish a data set of small and micro intelligent sensor network system;
S2、选取基函数对数据集进行升维，将原系统升维到一个高维的可观测函数空间；S2. Select the basis function to upgrade the dimension of the data set, and upgrade the original system to a high-dimensional observable function space;
S3、建立小微智能传感器网络Koopman高维线性模型；S3. Establish a Koopman high-dimensional linear model of a small and micro intelligent sensor network;
S4、利用得到的升维数据集求取Koopman算子有限维逼近，并利用神经网络进行训练，得到最终高维线性模型。S4. Obtain the finite-dimensional approximation of the Koopman operator by using the obtained increased-dimensional data set, and use the neural network for training to obtain a final high-dimensional linear model.
利用Koopman算子理论分析建立小微智能传感器网络系统数据集，为便于后续网络拥塞控制分析和设计，现将窗口大小和队列长度(w,q)作为状态，分组丢弃概率p作为输入，队列长度q作为输出。The Koopman operator theory is used to establish the data set of the small and micro intelligent sensor network system. In order to facilitate the subsequent analysis and design of network congestion control, the window size and queue length (w, q) are now used as the state, the packet drop probability p is used as the input, and the queue length is used as the input. q as output.
利用能够激发小微智能传感器网络特性的控制输入进行输入输出数据的采集，利用产生的输出数据与控制输入数据建立数据集：Use the control input that can stimulate the characteristics of the small and micro intelligent sensor network to collect input and output data, and use the generated output data and control input data to establish a data set:
其中，U为输入序列，X为当前状态序列，Y为下一状态序列，n表示每次控制的总采样次数，k表示收集k组数据，即以k种不同的初始状态在k个不同随意输入序列下进行开环控制，p为分组丢弃概率，Among them, U is the input sequence, X is the current state sequence, Y is the next state sequence, n is the total sampling times of each control, k is the collection of k groups of data, that is, k different initial states are randomly selected in k different Open-loop control is performed under the input sequence, p is the probability of packet discarding,
选取基函数对数据集进行升维，包括以下步骤：Select the basis function to increase the dimension of the dataset, including the following steps:
S21、定义一组基函数Ψ(x)＝[Ψ1(x),Ψ2(x),...Ψm(x)]T；S21, define a group of basis functions Ψ(x )=[Ψ1(x),Ψ2( x),...Ψm (x)]T ;
S22、选取一个简单的神经网络作为基函数的逼近器，形式设置为：S22, select a simple neural network as the approximator of the basis function, and the form is set as:
Ψ(x)＝Wouth+boutΨ(x)=Wout h+bout
h＝tanh(Wx+b) (1)h=tanh(Wx+b) (1)
其中，W∈R16×2，Wout∈R40×16，b∈R16×1，bout∈R40×1，需要训练的参数集为θ＝{W，b，Wout，bout}；Among them, W∈R16×2, Wout∈R40×16, b∈R16×1, bout∈R40×1, the parameter set to be trained is θ={W, b, Wout, bout};
S23、将数据集带入神经网络进行升维，得到升维后的数据集 Xlift、Ylift。S23. Bring the data set into the neural network to increase the dimension, and obtain the data sets Xlift and Ylift after the dimension increase.
建立小微智能传感器网络Koopman高维线性模型，包括：Build a Koopman high-dimensional linear model for small and micro smart sensor networks, including:
基于Koopman算子理论和扩展动力学模态分解算法结合，将小微智能传感器网络表示为高维线性模型：Based on the combination of Koopman operator theory and extended dynamic mode decomposition algorithm, the small and micro smart sensor network is represented as a high-dimensional linear model:
z(k+1)＝Az(k)+Bu(k)z(k+1)=Az(k)+Bu(k)
其中，z为升维后的状态，
利用得到的升维数据集求取Koopman算子有限维逼近，并利用神经网络进行训练，得到最终高维线性模型，包括：The finite-dimensional approximation of the Koopman operator is obtained by using the obtained ascending-dimensional data set, and the neural network is used for training to obtain the final high-dimensional linear model, including:
利用得到的升维数据集Xlift、Ylift，通过扩展动力学模态分解算法求取Koopman算子有限维逼近，即求解如下最小化问题得到高维线性模型中的矩阵A、B、C：Using the obtained ascending-dimensional data sets Xlift and Ylift, the finite-dimensional approximation of the Koopman operator is obtained through the extended dynamic mode decomposition algorithm, that is, the following minimization problems are solved to obtain the matrices A, B, and C in the high-dimensional linear model:
求解最小值的解析式为：The analytical formula for finding the minimum value is:
通过式(1)和式(4)得到高维线性模型(2)的初步解析，为得到与真实模型更加接近的模型，利用神经网络自动训练的能力，将得到的矩阵A、B、C和神经网络参数集进行训练，定义的损失函数表示为：The preliminary analysis of the high-dimensional linear model (2) is obtained by formulas (1) and (4). In order to obtain a model that is closer to the real model, the automatic training ability of the neural network is used to convert the obtained matrices A, B, C and The neural network parameter set is trained, and the defined loss function is expressed as:
将式(1)、(4)和损失函数(5)通过神经网络不断训练，直到
图2中，(a)是系统给定正弦控制输入变化曲线；(b)是正弦输入下Koopman高维模型队列长度与真实模型队列长度对比曲线；(c)是正弦输入下Koopman高维模型窗口大小与真实模型窗口大小对比曲线。In Figure 2, (a) is the change curve of the given sinusoidal control input of the system; (b) is the comparison curve of the queue length of the Koopman high-dimensional model and the real model under the sinusoidal input; (c) is the Koopman high-dimensional model window under the sinusoidal input Size and real model window size comparison curve.
图3中，(a)是系统给定方波控制输入变化曲线；(b)是正弦输入下Koopman高维模型队列长度与真实模型队列长度对比曲线；(c)是正弦输入下Koopman高维模型窗口大小与真实模型窗口大小对比曲线。In Figure 3, (a) is the change curve of the given square wave control input of the system; (b) is the comparison curve of the queue length of the Koopman high-dimensional model and the real model under the sinusoidal input; (c) is the Koopman high-dimensional model under the sinusoidal input Comparison curve between the window size and the real model window size.
为了验证本发明设计的辨识模型性能，将传统小微智能传感器网络拥塞数学模型作为真实模型对本发明设计辨识模型进行验证。其中，小微智能传感器网络环境仿真参数设定为：激活的TCP链接数为60，链路容量为300包，往返时延为3.2秒，固定的广播时延为0.2秒。In order to verify the performance of the identification model designed by the present invention, the traditional small and micro intelligent sensor network congestion mathematical model is used as a real model to verify the design identification model of the present invention. Among them, the small and micro smart sensor network environment simulation parameters are set as: the number of activated TCP links is 60, the link capacity is 300 packets, the round-trip delay is 3.2 seconds, and the fixed broadcast delay is 0.2 seconds.
本发明方法中数据收集时状态初值和开环输入取值范围：分组丢弃概率p在0到1内随机取值，队列长度q在100到300内随机取值，窗口大小w在0到10内随机取值，仿真设定期望的队列长度为200包。仿真时间为100秒，采样频率为200赫兹。In the method of the present invention, the initial value of the state and the value range of the open-loop input during data collection: the packet discard probability p is randomly selected within 0 to 1, the queue length q is randomly selected within the range of 100 to 300, and the window size w is within 0 to 10. The value is randomly selected within the simulation, and the expected queue length is set to 200 packets. The simulation time is 100 seconds and the sampling frequency is 200 Hz.
从图2可以看出，在给定正弦开环输入下，本发明所设计Koopman模型下队列长度和窗口大小两个状态能很好地拟合真实情况。为避免偶然性，给定系统不同的输入验证模型拟合效果图如图3所示。从图3可以看出，在方波输入下，Koopman模型仍可以很好地拟合队列长度和窗口大小的变化情况。It can be seen from FIG. 2 that, under a given sinusoidal open-loop input, the two states of queue length and window size under the Koopman model designed by the present invention can well fit the real situation. In order to avoid chance, the fitting effect diagram of different input validation models for a given system is shown in Figure 3. As can be seen from Figure 3, under the square wave input, the Koopman model can still fit the changes of queue length and window size well.
从而可以表明Koopman算子可以还原非线性小微智能传感器网络系统，对原系统能够进行很好地预测，并对原来系统模型实现全局线性化，为后续分析和设计小微智能传感器网络拥塞控制器提供方便。总之，本发明所采用的方法能够对原来非线性系统进行全局线性化，解决了现有技术将网络拥塞系统只在平衡点处进行局部线性化的缺点，可以将结论推广至一般情况，为分析小微智能传感器网络系统提供便利。Therefore, it can be shown that the Koopman operator can restore the nonlinear small and micro intelligent sensor network system, can predict the original system well, and realize the global linearization of the original system model, which is used for the subsequent analysis and design of the small and micro intelligent sensor network congestion controller. to offer comfort. In a word, the method adopted in the present invention can perform global linearization on the original nonlinear system, solves the shortcomings of the prior art that the network congestion system is only partially linearized at the equilibrium point, and can generalize the conclusion to the general situation. Small and micro intelligent sensor network system provides convenience.
经过上述分析，证明了本发明算法的有效性。After the above analysis, the effectiveness of the algorithm of the present invention is proved.
以上实施例仅用以说明本发明的技术方案，而非对其限制；尽管参照前述实施例对本发明进行了详细的说明，本领域的普通技术人员应当理解：其依然可以对前述各实施例所记载的技术方案进行修改，或者对其中部分技术特征进行等同替换；而这些修改或者替换，并不会使相应技术方案的本质脱离本发明各实施例技术方案的精神和范围。The above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: The recorded technical solutions are modified, or some technical features thereof are equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
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