Systems & Control Letters 73 (2014) 58–66
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Systems & Control Letters
journal homepage: www.elsevier.com/locate/sysconle
Consensus control of nonlinear leader–follower multi-agent systems
with actuating disturbances
✩
Xinghu Wang
a
, Dabo Xu
b,∗
, Yiguang Hong
a
a
Key Laboratory of Systems and Control, Institute of Systems Science, Chinese Academy of Sciences, Beijing 100190, China
b
School of Automation, Nanjing University of Science & Technology, Nanjing 210094, China
a r t i c l e i n f o
Article history:
Received 8 February 2014
Received in revised form
3 July 2014
Accepted 9 September 2014
Available online 11 October 2014
Keywords:
Multi-agent systems
Disturbances
Distributed control
Networked control
a b s t r a c t
This paper studies a semi-global asymptotic consensus problem of nonlinear multi-agent systems with
local actuating disturbances. For a modest nonlinear scenario, a consensus protocol is proposed based on
a viable two-layer network. The consensus problem is treated as distributed output regulation, which is
resolved by a joint decomposition of the zero-error constraint inputs and a configuration of a flexible
internal model network. An illustrative example is also given to show the efficiency of the two-layer
networked design.
© 2014 Elsevier B.V. All rights reserved.
1. Introduction
In the past few years, cooperative control of multi-agent
systems has gained increasing research interest and a major
development. One of the central problems is that of controlling
all agents in order to make their outputs converge to a common
output trajectory. This problem usually refers to as consensus
or output synchronization. Since the fundamental study of
consensus protocols for single-integrator agents (see [1]), a
number of effective techniques have been proposed for multi-
agent systems from linear to nonlinear in many directions, see
for instances [2–7] and references therein. At the present stage,
to the best of our knowledge, there is a lack of particular studies
on consensus control with external disturbances appearing at
individual agent dynamics. Relevant results may be found in [8–
10]. In particular, [9,10] proposed an observer-based control by
viewing the disturbances as exosystem outputs and [8] studied the
problem by a non-smooth control technique. It is noted that the
✩
The work was substantially supported by NNSF of China under Grant 61304009
and Grant 61174071, and under A Project Funded by the Priority Academic
Program Development of Jiangsu Higher Education Institutions and the Program for
Changjiang Scholars and Innovative Research Team in University (No. IRT13072).
A preliminary version of the paper was presented at the 11th IEEE International
Conference on Control & Automation [31].
∗
Corresponding author. Tel.: +86 25 8431 5872.
E-mail addresses: wxh@amss.ac.cn (X. Wang), dabo.xu@ymail.com,
xu.dabo@gmail.com (D. Xu), yghong@iss.ac.cn (Y. Hong).
methods developed in the aforementioned literature rely on the
absolute state information in addition to the neighbor information.
Also, the result of [8] is a practical consensus design, not leading
to asymptotic consensus. In view of these existing studies,
consensus control with exogenous disturbances deserves further
investigation, particularly for nonlinear multi-agent networks.
It is known that, to cope with asymptotic tracking and/or dis-
turbance rejection of uncertain systems, in the terminology of
robust output regulation, the device of internal model plays an in-
dispensable role, see [11–16]. Recently, a lot of efforts have been
made to distributed control of the leader–follower multi-agent sys-
tems with uncertainties by applying the output regulation the-
ory; see, for instances [17–19]. In accordance with these results,
an individual internal model should be embedded in each local
controller to succeed the consensus with node uncertainties and
disturbances. Recall that in output regulation, the exosystem is of-
ten used to model references and disturbances as well. In the usual
centralized or decentralized setup, there is no need to treat them
separately. Nonetheless, regarding multi-agent systems in the dis-
tributed fashion, things are basically inconsistent due to limited
interactions or communications. To adapt this situation, the leader
in leader–follower type networks can be viewed as an exosystem
to produce references relating to certain collective behaviors. Con-
trary to references, local disturbances certainly have a negative
effect to the control goal. These two types of signals thus have op-
posite effects with respect to the control goal. This fact basically
motivates us to develop more flexible strategies that can manage
http://dx.doi.org/10.1016/j.sysconle.2014.09.004
0167-6911/© 2014 Elsevier B.V. All rights reserved.