向量权重下无向网络的结构可控性分析

需积分: 0 134 浏览量更新于2024-08-05 收藏 336KB PDF 举报

本文档探讨了"2020期刊 - 矢量加权结构可控性：无向扩散网络中的子系统控制问题"，发表在《IEEE 控制系统快报》(IEEE CONTROL SYSTEMS LETTERS) 第4卷第3期，由Han Gao和Guangchen Zhang共同署名。研究焦点在于考虑具有扩散耦合子系统的无向网络的结构可控性，每个子系统都遵循相同高阶单输入多输出动力学，但网络拓扑的连接权重是通过向量而非标量来表示的。主要贡献在于，作者提供了关于这种特殊网络系统是否具有结构可控性的判断条件。结构可控性意味着即使网络中的交互链接权重被几乎所有的向量值替代，对应的系统仍然保持可控。论文证明，网络系统具备结构可控性的必要和充分条件是：所有子系统既必须是可控的也是可观测的，并且网络拓扑对全局输入可达性有要求。这些结论扩展到了更复杂的情况，包括多输入多输出子系统动态、矩阵权重的边，以及网络中包含有向和无向交互链接。关键词：无向网络，扩散耦合，子系统控制，结构可控性，向量权重，全球输入可达性，多输入多输出系统，矩阵权重，有向与无向链接。这项工作对于理解复杂网络系统的设计和优化具有重要意义，特别是在系统工程、自动化控制和网络理论领域，它提供了一种方法来评估和设计具有高度结构稳定性的网络系统，这对于确保系统的鲁棒性和响应性能至关重要。通过这个研究，工程师们可以更好地构建和分析实际应用中的网络系统，如电力系统、交通网络或分布式控制系统，以实现高效的控制策略和管理。

596 IEEE CONTROL SYSTEMS LETTERS, VOL. 4, NO. 3, JULY 2020

Structural Controllability of Undirected Diffusive

Networks With Vector-Weighted Edges

Yuan Zhang , Yuanqing Xia , Han Gao, and Guangchen Zhang

Abstract—In this letter, controllability of undirected net-

worked systems with diffusively coupled subsystems is

considered, where each subsystem is of identically ﬁxed

general high-order single-input-multi-output dynamics. The

underlying graph of the network topology is vector-

weighted, rather than scalar-weighted. The aim is to ﬁnd

conditions under which the networked system is struc-

turally controllable, i.e., for almost all vector values for

interaction links of the network topology, the correspond-

ing system is controllable. It is proven that, the networked

system is structurally controllable, if and only if each sub-

system is controllable and observable, and the network

topology is globally input-reachable. These conditions are

further extended to the cases with multi-input-multi-output

subsystem dynamics and matrix-weighted edges, or where

both directed and undirected interaction links exist.

Index Terms—Undirected diffusive network, structural

controllability, network analysis and control, vector-

weighted Laplacian.

I. INTRODUCTION

NALYSIS and synthesize of networked systems with

diffusively coupled subsystems, also known as diffusive

networks, have received much attention in the ﬁelds of syn-

chronization, consensus, stability, as well as controllability and

observability [1]–[3]. This is because the diffusive coupling

mechanism frequently arises naturally in thermal systems,

power systems, car-following trafﬁc systems, etc. [2], [4]. As is

known to all, controllability is a fundamental system property.

Particularly, controllability of a leader-follower multi-agent

system (MAS) running the consensus protocol guarantees that

the system can reach agreement subspace arbitrarily fast [5].

Many works have focused on controllability of leader-

follower MASs [3], [5]–[7]. For example, [6] gave conditions

for controllability of such networked systems in terms of

eigenvectors of the Laplacian matrices. The works [3], [5], [7]

studied the same problem by means of graph-theoretic

tools. However, except [3], all the above works assume

that each subsystem is a single-integrator. On the other

hand, controllability of networks with high-order subsystems

Manuscript received January 9, 2020; revised March 9, 2020;

accepted March 27, 2020. Date of publication April 8, 2020; date of cur-

rent version April 28, 2020. Recommended by Senior Editor M. Arcak.

(Corresponding author: Yuan Zhang.)

The authors are with the School of Automation, Beijing Institute of

Technology, Beijing 100811, China (e-mail: zhangyuan14@bit.edu.cn;

xia_yuanqing@bit.edu.cn; gaohhit@163.com; guangchen_123@

126.com).

Digital Object Identiﬁer 10.1109/LCSYS.2020.2986250

has also attracted much research interests in [8]–[13]. To

be speciﬁc, [8], [11], [13] focused on networked systems

with identical subsystems (called homogeneous networks),

whiles [9], [10], [12] on networked systems with general

heterogeneous subsystems (called heterogeneous networks).

Particularly, controllability as a generic property for a net-

worked system is studied in [12], [13].

However, except [9], [10], [12] which focus on hetero-

geneous networks, almost all results on controllability of

homogeneous networks are built on the condition that all

weights of edges in the network topology belong to {0, 1} or

some given scalars [3], [5]–[8], [11], [13]. Notice that, when

each subsystem is not of single-input-single-output (SISO),

there is a typical situation that different interaction chan-

nels between two subsystems are weighted differently, either

because of differences in the nature of physical variables they

convey, or the variants of the channels themselves. For exam-

ple, in some networks consisting of both physical couplings

and cyber couplings, the physical channels and the cyber ones

between two subsystems can have different weights. See more

examples in [14]–[16]. If we use a graph to denote the sub-

system interaction topology, then each edge of the graph may

have a vector-valued or matrix-valued weight as introduced

in [14], [15]. In such case, some existing approaches for con-

trollability analysis for networks with scalar-weighted edges

may not be applicable (such as the spectrum-based approaches

in [3], [11]).

In this letter, we study structural controllability of an undi-

rected diffusive networked system with high-order subsystems,

where the underlying graph of the network topology has

symmetric vector-weighted edges. Our purpose is to ﬁnd

conditions under which the networked system is structurally

controllable, i.e., for almost all vector values for edges of

the network topology, the whole system is controllable. The

main contributions of this letter are three-fold. First, we

prove that, an undirected diffusive networked system with

identical single-input-multi-output (SIMO) subsystems (lead-

ing to vector-weighted edges) is structurally controllable,

if and only if each subsystem is controllable and observ-

able, and the network topology is globally input-reachable.

Second, we show that our conditions are still valid even

when both directed edges and undirected ones exist. Third,

we extend our results to the case with arbitrarily dimensional

matrix-weighted edges.

It is remarkable that some relations between connectivity

and observability have been revealed in [15] for a net-

worked system where subsystems are decoupled whereas

their outputs are relatively measured by sensor networks, and

each interconnection edge deﬁned therein has a semi-deﬁnite

2475-1456

 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.

See https://www.ieee.org/publications/rights/index.html for more information.

Authorized licensed use limited to: Qingdao University. Downloaded on October 29,2020 at 06:19:45 UTC from IEEE Xplore. Restrictions apply.

下载后可阅读完整内容，剩余5页未读，立即下载

章满莫

粉丝: 35
资源: 316

向量权重下无向网络的结构可控性分析

GIS数据转换器(矢量-矢量)V3.0.rar

GIS数据转换器(矢量-矢量)V2.2.rar

第一讲空间数据结构-矢量数据结构.ppt

天地图--矢量.zip

Weight-NRDV-Hop.zip_DV--HOP改进算法_DV-hop Matlab_dv-hop加权_改进 DV-Hop

亿图-矢量绘图

PPT图标素材大全-矢量图标

永磁同步电机矢量控制-弱磁控制-simulink

2020-2022年成都市矢量数据

基于MFCC和加权矢量量化的说话人识别系统-基于MFCC和加权矢量量化的说话人识别系.rar

最新资源