多層異質(zhì)復雜網(wǎng)絡(luò )系統的能控性

曹連謙; 王立夫; 孔芝; 郭戈

doi:10.16383/j.aas.c210654

多層異質(zhì)復雜網(wǎng)絡(luò )系統的能控性

doi: 10.16383/j.aas.c210654 cstr: 32138.14.j.aas.c210654

曹連謙^1,,
王立夫^1,,
孔芝^1,,
郭戈^1,

1.
東北大學(xué)秦皇島分?？刂乒こ虒W(xué)院秦皇島 066004

基金項目: 國家自然科學(xué)基金(61573077, U1808205), 中央高?；究蒲袠I(yè)務(wù)費專(zhuān)項基金(N2023022)資助

詳細信息

作者簡(jiǎn)介:
曹連謙：東北大學(xué)秦皇島分校碩士研究生. 主要研究方向為復雜網(wǎng)絡(luò )能控性和網(wǎng)絡(luò )化系統控制. E-mail: caolianqian@neusoft.edu.cn

王立夫：東北大學(xué)秦皇島分校副教授. 主要研究方向為復雜網(wǎng)絡(luò ), 同步控制, 能控性, 交通網(wǎng)絡(luò ). 本文通信作者. E-mail: wlfkz@neuq.edu.cn

孔芝：東北大學(xué)秦皇島分校副教授. 主要研究方向為知識發(fā)現, 決策分析, 智能優(yōu)化算法, 復雜網(wǎng)絡(luò ). E-mail: kongz@neuq.edu.cn

郭戈：東北大學(xué)秦皇島分校教授. 主要研究方向為智能交通系統, 交通大數據分析, 人工智能應用, 信息物理系統. E-mail: geguo@yeah.net

計量
- 文章訪(fǎng)問(wèn)數: 1131
- HTML全文瀏覽量: 500
- PDF下載量: 92
- 被引次數: 0
出版歷程
- 收稿日期: 2021-07-14
- 修回日期: 2021-11-14
- 網(wǎng)絡(luò )出版日期: 2022-02-04
- 刊出日期: 2024-11-26

Controllability of Multi-layer Heterogeneous Complex Network Systems

CAO Lian-Qian^1
,,
WANG Li-Fu^1
,,
KONG Zhi^1
,,
GUO Ge^1
,

1.
School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004

Funds: Supported by National Natural Science Foundation of China (61573077, U1808205) and Fundamental Research Funds for the Central Universities (N2023022)

More Information

Author Bio:
CAO Lian-Qian　Master student of Northeastern University at Qinhuangdao. His research interest covers controllability of complex networks and control of networked systems

WANG Li-Fu　Associate professor of Northeastern University at Qinhuangdao. His research interest covers complex networks, synchronous control, controllability, and traffic networks. Corresponding author of this paper

KONG Zhi　Associate professor of Northeastern University at Qinhuangdao. Her research interest covers knowledge discovery, decision analysis, intelligent optimization algorithms, and complex networks

GUO Ge　Professor of Northeastern University at Qinhuangdao. His research interest covers intelligent transportation systems, traffic big data analysis, artificial intelligence applications, and information physical systems

摘要

摘要: 研究了節點(diǎn)狀態(tài)為高維的多層復雜網(wǎng)絡(luò )系統的能控性問(wèn)題. 討論了節點(diǎn)的異質(zhì)性、層間耦合和層內耦合對網(wǎng)絡(luò )能控性的影響. 研究發(fā)現當節點(diǎn)狀態(tài)由同質(zhì)變?yōu)楫愘|(zhì)、內耦合矩陣由相同變?yōu)椴煌瑫r(shí), 對網(wǎng)絡(luò )能控性均有影響(網(wǎng)絡(luò )可以由能控變?yōu)椴荒芸? 反之亦然). 對層間耦合模式為驅動(dòng)響應模式和相互依賴(lài)模式, 分別給出了網(wǎng)絡(luò )系統能控的充分條件或必要條件. 相比于直接應用經(jīng)典的能控性判據, 這些條件更易于驗證, 且驅動(dòng)響應模式比相互依賴(lài)模式實(shí)現系統完全能控所需的條件更弱.
- 網(wǎng)絡(luò )能控性 /
- 異質(zhì)網(wǎng)絡(luò ) /
- 多層網(wǎng)絡(luò ) /
- 內耦合矩陣
Abstract: This paper studies the controllability of multi-layer complex network systems with high-dimensional node states. We discuss the influence of node heterogeneity, inter-layer coupling, and intra-layer coupling on the controllability of the network. It is found that when the state of the node changes from homogeneous to heterogeneous or the inner-coupling matrix changes from identical to nonidentical, both have an impact on the controllability of the network (the network can be changed from controllable to uncontrollable, and vice versa). The sufficient or necessary conditions for the controllability of the networked system when the inter-layer coupling mode is the drive response mode and the interdependence mode are given, respectively. These conditions are easier to verify than using the classic controllability criteria directly, and the conditions that the drive response mode to achieve fully controllability are weaker than the conditions for the interdependence mode.
- Network controllability /
- heterogeneous network /
- multi-layer network /
- inner-coupling matrix

HTML全文

圖 1 層間耦合為驅動(dòng)響應模式的兩層網(wǎng)絡(luò )

Fig. 1 Two-layer networks with the inter-layer drive-response couplings

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圖 2 層間耦合為相互依賴(lài)模式的兩層網(wǎng)絡(luò )

Fig. 2 Two-layer networks with the inter-layer interdependent couplings

下載: 全尺寸圖片幻燈片

圖 3 層間耦合為驅動(dòng)響應模式的M層網(wǎng)絡(luò )結構示意圖

Fig. 3 The illustration of M-layer networks with the inter-layer drive-response couplings

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圖 4 層間耦合為相互依賴(lài)模式的3層網(wǎng)絡(luò )結構示意圖

Fig. 4 The illustration of three-layer networks with the inter-layer interdependent couplings

下載: 全尺寸圖片幻燈片

圖 5 驅動(dòng)層為鏈網(wǎng)絡(luò )、響應層為星形網(wǎng)絡(luò )的兩層網(wǎng)絡(luò )

Fig. 5 Two-layer networks with the topology of the drive-layer is a chain network, and the response layer is a star network

下載: 全尺寸圖片幻燈片

表 1 本文模型中所用的特殊符號

Table 1 Special notations used in the model of this paper

	特殊符號	含義
	${\boldsymbol{A}}_i^K$	第$ K $層網(wǎng)絡(luò )的第$ i $個(gè)節點(diǎn)的狀態(tài)矩陣
	${\boldsymbol{B}}_i^K$	第$ K $層網(wǎng)絡(luò )的第$ i $個(gè)節點(diǎn)的輸入矩陣
	${\boldsymbol{C}}_i^K$	第$ K $層網(wǎng)絡(luò )的第$ i $個(gè)節點(diǎn)的輸出矩陣
	${\boldsymbol{H}}_i^K$	第$ K $層網(wǎng)絡(luò )的第$ i $個(gè)節點(diǎn)與該層其他節點(diǎn)之間的內耦合矩陣
	${\boldsymbol{H}}_i^{KJ}$	第$ J $層網(wǎng)絡(luò )的第$ i $個(gè)節點(diǎn)與第$ K $層網(wǎng)絡(luò )的其他節點(diǎn)之間的內耦合矩陣
	${{\boldsymbol{W}}^K}$	第$ K $層的網(wǎng)絡(luò )拓撲
	${{\boldsymbol{D}}^{KJ} }$	第$ J $層到第$ K $層的網(wǎng)絡(luò )拓撲
	${\boldsymbol{x}}$	整個(gè)網(wǎng)絡(luò )系統的狀態(tài)
	${{\boldsymbol{x}}^K}$	第$ K $層網(wǎng)絡(luò )的狀態(tài)
	${\boldsymbol{u}}$	整個(gè)網(wǎng)絡(luò )系統的輸入
	${{\boldsymbol{u}}^K}$	第$ K $層網(wǎng)絡(luò )的輸入
	${\boldsymbol{ \Phi}}$	整個(gè)網(wǎng)絡(luò )系統的狀態(tài)矩陣
	${{\boldsymbol{\Phi}} _{KK} }$	第$ K $層網(wǎng)絡(luò )的狀態(tài)矩陣
	${{\boldsymbol{\Phi}} _{KJ} }$	第$ J $層到第$ K $層網(wǎng)絡(luò )的狀態(tài)矩陣
	${\boldsymbol{\Psi}}$	整個(gè)網(wǎng)絡(luò )系統的輸入矩陣
	${\boldsymbol{ \Xi}}$	整個(gè)網(wǎng)絡(luò )系統的輸出矩陣
	${{\boldsymbol{\Lambda}} ^K}$	以${\boldsymbol{A}}_1^K,\cdots,{\boldsymbol{A}}_N^K$為對角元的分塊對角矩陣
	${\boldsymbol{ \Delta}}$	對角矩陣${ {\text{diag} } } \{ {{\boldsymbol{\Delta}} ^1},\cdots,{{\boldsymbol{\Delta}} ^M}\}$
	${{\boldsymbol{\Delta}} ^K}$	對角矩陣${ {\text{diag} } } \{ \delta _1^K,\cdots,\delta _N^K\}$

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