分布式观测器与学习控制：不确定Euler-Lagrange系统多节点领导跟随协议

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本文主要探讨了2020年发表在《神经计算》(Neurocomputing)第405期上的研究，由Dong Liang和Jie Huang两位作者合作完成。他们的研究关注的是"领导者跟随"的二分图共识问题，针对多个不确定的欧拉-拉格朗日系统（Euler-Lagrange systems）在有符号切换网络上的应用。欧拉-拉格朗日系统广泛应用于机械工程、动力学等领域，特别是在复杂系统建模中。论文的核心贡献在于发展了一种分布式观测器理论，它将线性领导系统的观测器从静态连接网络扩展到了联合切换网络的情况。通过这种方法，他们能够处理网络中动态的连接变化，这对于实际应用中的通信网络具有重要意义，因为在许多情况下，网络连接并非固定不变，而是会根据需要频繁切换。在分析过程中，研究者利用了确定性等效原则，这是一个重要的控制理论工具，它允许在存在不确定性的情况下，通过转化问题来找到近似的解决方案。这一原则在处理多个不确定系统时尤为关键，因为它能够在一定程度上缓解不确定性对系统性能的影响。该论文的主要目标是设计一种学习控制策略，使得每个不确定的欧拉-拉格朗日系统能够通过与领导者保持一致，达到二分图共识。这意味着所有系统能够在遵循领导者运动的同时，相互之间也达到同步，即使在网络连接和系统参数存在变化时也能维持这种行为。此外，由于关键词包括"二分图共识"、"分布式观测器"、"学习控制"、"多个欧拉-拉格朗日系统"以及"有符号切换网络"，这表明研究不仅关注理论层面的创新，还关注实际应用中的可扩展性和鲁棒性，确保了在复杂和动态网络环境中系统的稳定性和有效性。这篇文章在控制理论和分布式系统领域具有较高的学术价值，为解决多代理系统中的领导者跟随问题提供了新的理论框架和技术方法，对于推进机器人控制、物联网设备协调以及复杂网络动态管理等领域的发展具有重要参考意义。

Neurocomputing 405 (2020) 96–102

Contents lists available at ScienceDirect

Neurocomputing

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

Leader-following bipartite consensus of multiple uncertain

Euler-Lagrange systems over signed switching digraphs

Dong Liang, Jie Huang

∗

Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, N.T., Hong Kong

a r t i c l e i n f o

Article history:

Received 8 January 2020

Revised 12 March 2020

Accepted 6 April 2020

Available online 11 May 2020

Communicated by Dr. Derui Ding

Keywords:

Bipartite consensus

Distributed observer

Learning control

Multiple Euler-Lagrange systems

Signed switching networks

a b s t r a c t

In this paper, we investigate the leader-following bipartite consensus problem of multiple uncertain Euler-

Lagrange (EL) systems over signed switching networks. We ﬁrst extend the distributed observer for a

linear leader system over signed communication networks from the static case to the jointly connected

switching case. Based on such a distributed observer and the certainty equivalence principle, we further

show that, under the assumptions that the signed switching network is structurally balanced and jointly

connected, the leader-following bipartite consensus problem of multiple uncertain EL systems over signed

switching networks is solvable by a class of distributed adaptive control law. Our result will then be

applied to the leader-following bipartite consensus problem of a group of two-link robot manipulators.

Introduction

Over the past few years, the distributed control of multi-agent

systems over signed graphs has received considerable attention. In

practice, a signed digraph can represent, say, allied/adversary re-

lationships such as two parties in politics since cooperation and

competition often coexist, trade war between countries or opin-

ion dynamics in trust-mistrust social networks [22] . A fundamen-

tal problem in the distributed control of multi-agent systems over

signed graphs is the so-called bipartite consensus, which is to de-

sign a distributed control law to achieve modulus consensus for

each agent with antagonistic interactions [1] .

Early work on the bipartite consensus focused on multiple

single-integrator systems. For example, in [1] , Altaﬁni showed that

the bipartite consensus for multiple single-integrator systems can

be achieved if and only if the signed graph is structurally bal-

anced and connected. The result in [1] was then extended to the

general linear multi-agent systems [6,23,24,26] . Like the consen-

sus problem over unsigned graphs, the bipartite consensus can

also be classiﬁed into leaderless case [1] and leader-following

case [11,13,20,21] . The bipartite tracking problem was studied in

[11] with a scalar leader system, and in [6,18,21] with a high-order

leader system. In [9] , the robust bipartite output regulation for a

∗

Corresponding author.

E-mail addresses: dliang@mae.cuhk.edu.hk (D. Liang), jhuang@mae.cuhk.edu.hk

(J. Huang).

class of general linear systems was studied, which aims to achieve

asymptotic modulus tracking in the presence of a class of distur-

bances. Almost all the publications mentioned above assumed that

the signed graphs were static. Recently, the distributed control of

multi-agent systems over signed switching graphs were consid-

ered in some papers. For example, the output bipartite consen-

sus of heterogeneous linear multi-agent systems was investigated

in [19] by a distributed dynamic output feedback control law. The

bipartite synchronization of a class of nonlinear systems satisfying

the one-sided Lipschitz condition over signed switching networks

was studied in [25] . Other relevant work on bipartite consensus

over signed switching topologies can be found in [7] .

EL systems are an important class of nonlinear systems that can

model robots, spacecraft systems, etc [8,10] . The cooperative con-

trol problems of multiple EL systems over unsigned communica-

tion networks have been thoroughly studied in quite a few papers

[3,4,14] . In particular, Ref. [3] solved the leader-following consensus

problem of multiple EL systems over jointly connected switching

networks via a distributed observer approach. More recently, the

study of the cooperative control problems of multiple EL systems

has been extended to the signed communication networks. For ex-

ample, Ref. [5] considered the swarming behaviors of multiple EL

systems with uncertain parameters over signed static communica-

tion networks.

In this paper, we will further study the leader-following bipar-

tite consensus problem of multiple EL systems over signed switch-

ing communication networks. Compared with [5] , our paper offers

at least three new features. First, our digraph is a signed switching

https://doi.org/10.1016/j.neucom.2020.04.050

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判断一个图是否欧拉图 若是欧拉图,则输出a is euler”; 若是半欧拉图,则输出a is semi-euler”; 若不是欧拉图,则输出“a is not euler”。 注意:该输出前后无空格,行尾回车。

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判断一个图是否欧拉图若是欧拉图,则输出a is euler”; 若是半欧拉图,则输出a is semi-euler”; 若不是欧拉图,则输出“a is not euler”。注意:该输出前后无空格,行尾回车。