Automatica 50 (2014) 1254–1263
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Automatica
journal homepage: www.elsevier.com/locate/automatica
Brief paper
Distributed adaptive control for consensus tracking with application
to formation control of nonholonomic mobile robots
✩
Wei Wang
a
, Jiangshuai Huang
b
, Changyun Wen
b
, Huijin Fan
c,1
a
Department of Automation, Tsinghua University, Beijing 100084, China
b
School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore
c
Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
a r t i c l e i n f o
Article history:
Received 6 February 2013
Received in revised form
7 October 2013
Accepted 27 January 2014
Available online 18 March 2014
Keywords:
Distributed coordination
Adaptive control
Consensus tracking
Nonlinear systems
Nonholonomic mobile robots
a b s t r a c t
In this paper, we investigate the output consensus problem of tracking a desired trajectory for a class of
systems consisting of multiple nonlinear subsystems with intrinsic mismatched unknown parameters.
The subsystems are allowed to have non-identical dynamics, whereas with similar structures and
the same yet arbitrary system order. And the communication status among the subsystems can be
represented by a directed graph. Different from the traditional centralized tracking control problem,
only a subset of the subsystems can obtain the desired trajectory information directly. A distributed
adaptive control approach based on backstepping technique is proposed. By introducing the estimates
to account for the parametric uncertainties of the desired trajectory and its neighbors’ dynamics into
the local controller of each subsystem, information exchanges of online parameter estimates and local
synchronization errors among linked subsystems can be avoided. It is proved that the boundedness of all
closed-loop signals and the asymptotically consensus tracking for all the subsystems’ outputs are ensured.
A numerical example is illustrated to show the effectiveness of the proposed control scheme. Moreover,
the design strategy is successfully applied to solve a formation control problem for multiple nonholonomic
mobile robots.
© 2014 Elsevier Ltd. All rights reserved.
1. Introduction
Because of its widespread potential applications in various
fields such as mobile robot networks, intelligent transportation
management, surveillance and monitoring, distributed coordina-
tion of multiple dynamic subsystems (also known as multi-agent
systems) has achieved rapid development during the past decades.
Consensus is one of the most popular topics in this area, which has
received significant attention by numerous researchers. It is often
aimed to achieve an agreement for certain variables of the subsys-
tems in a group. A large number of effective control approaches
✩
This work was supported by National Natural Science Foundation of China
under grant nos. 61203068, 61290324 and 61174079. The material in this paper
was not presented at any conference. This paper was recommended for publication
in revised form by Associate Editor Raul Ordóñez under the direction of Editor
Miroslav Krstic.
E-mail addresses: wwang28@tsinghua.edu.cn (W. Wang),
jhuang2@e.ntu.edu.sg (J. Huang), ecywen@ntu.edu.sg (C. Wen),
ehjfan@mail.hust.edu.cn (H. Fan).
1
Tel.: +86 27 87543130; fax: +86 27 87543130.
have been proposed to solve the consensus problems (see Arcak,
2007; Bai, Arcak, & Wen, 2008, 2009; Hong, Hu, & Gao, 2006; Jad-
babaie, Lin, & Morse, 2003; Moreau, 2005; Ren, 2007; Ren & Beard,
2005, for instance). According to whether the desired consensus
values are determined by exogenous inputs, which are sometimes
regarded as virtual leaders, these approaches are often classified
as leaderless consensus and leader-following consensus solutions
(see Kaizuka & Tsumura, 2011; Ni & Cheng, 2010; Song, Cao, & Yu,
2010; Zhang, Chen, & Stan, 2011, and the references therein). Be-
sides, many of the early works were established for systems with
first-order dynamics, whereas more results have been reported in
recent years such as Ni and Cheng (2010), Ren, Moore, and Chen
(2007), Seo, Shim, and Back (2009) and Yu, Chen, Ren, Kurths, and
Zheng (2011) for systems with second or higher-order dynamics.
A comprehensive overview of the state of the art in consensus
control can be found in Ren and Cao (2010), in which the results
on some other interesting topics including finite-time consensus
and consensus under limited communication conditions including
time delays, asynchronization and quantization are also discussed.
It is worth mentioning that except for Kaizuka and Tsumura
(2011), all the aforementioned results are developed based on the
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