无速度测量的二阶多主体系统分布式观测器共识研究

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本文主要探讨了二阶多主体系统的共识问题，特别关注的是在不依赖于各个主体的速度测量情况下实现共识。论文标题"没有速度测量的二阶多主体系统基于观察者的共识"明确指出了研究的核心议题，即针对二阶动态模型（包括双积分器和谐振子）的多主体系统，设计一种仅依赖于位置信息而非速度信息的分布式观测器协议。作者Chenglin Wang、Fang Liu、Qiang Song和Xiaoliang Feng分别来自河南科技大学电气工程学院和黄淮大学信息工程学院，他们在研究中提出了一个创新的方法，通过利用多主体的位置数据，来解决带有或无时滞的二阶系统共识问题。这种方法的关键在于将观测器技术融入到共识策略中，从而使得系统能够在缺乏速度信息的情况下，依然能够达到全局协调一致的状态。文章的历程显示，它于2015年9月2日初次接收，经过修订后在同年10月24日再次接收，并于11月27日获得接受，最后在2015年12月17日在线发布。关键词包括"二阶共识"、"多主体系统"、"分布式观测器"、"双积分器"、"谐振子"以及"时间延迟"，这些都是论文讨论的重点领域。该研究的主要贡献在于理论分析和方法设计，旨在解决实际应用中可能遇到的挑战，如在通信受限或无法获取精确速度信息的情境下，如何确保多主体系统能够通过观测器机制达到稳定的共识状态。这对于推进多机器人协作、网络同步等领域具有重要的理论价值和实践意义。通过深入理解文中提出的算法和理论，读者可以了解到如何在实际工程中有效地处理这类复杂的系统问题。

Observer-based consensus of second-order multi-agent systems

without velocity measurements

Chenglin Wen

, Fang Liu

, Qiang Song

, Xiaoliang Feng

College of Electrical Engineering, Henan University of Technology, Zhengzhou 450001, China

School of Information Engineering, Huanghuai University, Zhumadian, Henan 463000, China

article info

Article history:

Received 2 September 2015

Received in revised form

24 October 2015

Accepted 27 November 2015

Communicated by Guang Wu Zheng

Available online 17 December 2015

Keywords:

Second-order consensus

Multi-agent system

Distributed observer

Double integrator

Harmonic oscillator

Time delay

abstract

This paper investigates the consensus of second-order multi-agent systems without measuring the

velocity states of the agents, where each agent can be either a double integrator or a harmonic oscillator.

By utilizing the position information of the agents, a distributed observer-based protocol is proposed to

solve the second-order consensus problem of multi-agent systems with or without time delay. The

observer-based consensus problem is converted to the stability analysis for a set of second-order quasi-

polynomials through coordinate transform and system decomposition. Then, some necessary and suf-

ﬁcient conditions are derived for reaching second-order consensus in multi-agent systems with or

without time delay, respectively, and it is shown that the consensus can be achieved if and only if the

communication delay is less than a critical value. Simulation examples are given to verify the theoretical

analysis.

1. Introduction

In the past few decades, the consensus problem has been a

focal point of many different disciplines due to its important role

in the investigation of the distributed coordination of multi-agent

systems. The consensus in a multi-agent system is said to be

reached if all the agents can eventually agree on some common

value under some control algorithms based on local information.

Much progress has been made in the consensus of multi-agent

systems with ﬁrst-order dynamics [1–3], second-order dynamics

[4–9], higher-order dynamics [10–13] and fractional-order

dynamics [14,15]. In particular, much effort has been devoted to

the second-order consensus problem due to many practical

applications of second-order multi-agent systems, such as the

ﬂocking of unmanned air vehicles [16,17] and the formation con-

trol of multiple mobile robots [18,19]. It is worth mentioning that

the ﬁrst-order consensus problem is closely related to the syn-

chronization problem of complex networks [20–23].

A second-order linear multi-agent system is composed of a set

of interconnected systems, where each agent may be a double

integrator [4–6], a spring-mass system [24], or a harmonic oscil-

lator [25,26]. Moreover, it is worth mentioning that a harmonic

oscillator and a double integrator can be described by a uniﬁed

mathematical model. Some fundamental results have been

obtained to address the second-order consensus of multi-agent

systems with double-integrator dynamics [4–6]. In recent years,

the consensus problem of coupled harmonic oscillators has been

intensively investigated by using many different control strategies

[25–29]. It is now well known that the existence of a directed

spanning tree in network topology is a necessary condition for

reaching second-order consensus [4], and both the real and ima-

ginary parts of the nonzero eigenvalues of network Laplacian

matrix are important to discuss the consensus problem [5].

Since the time delay is inevitable in many physical systems

[30–32], some researchers have studied the consensus in a net-

work of double integrators or harmonic oscillators with time

delay. For coupled double-integrators, Yu et al. [5] showed that the

communication delay should be less than some critical value and

Meng et al. [6] further analyzed the effects of input and commu-

nication delays on second-order consensus. As for coupled har-

monic oscillators, Zhang et al. [27] considered the consensus in the

network with delayed velocity coupling, while Song et al. [29]

investigated the consensus using delayed position information and

proved that the time delay should be chosen from a set of bounded

intervals.

Note that most consensus protocols for coupled double inte-

grators [4–6] and coupled harmonic oscillators all require velocity

states [25–28]. However, for a second-order multi-agent system

without being equipped with velocity sensors, the velocity infor-

mation will not be available. Moreover, in some practical cases, the

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/neucom

Neurocomputing

http://dx.doi.org/10.1016/j.neucom.2015.11.087

Corresponding author.

E-mail address: qsongseu@gmail.com (Q. Song).

Neurocomputing 179 (2016) 298–306

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