Article
Transactions of the Institute of
Measurement and Control
2015, Vol. 37(9) 1041–1048
Ó The Author(s) 2014
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DOI: 10.1177/0142331214554676
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Distributed cooperative tracking of
multi-agent systems with actuator
faults
Jianzhen Li
Abstract
This paper deals with the fault-tolerant cooperative tracking problem for multi-agent systems with actuator faults. First, the fault-free case is consid-
ered. A novel cooperative tracking algorithm is proposed, together with a sufficient condition for the followers to track the leader. Then, based on the
proposed cooperative tracking algorithm, a fault-tolerant cooperative tracking algorithm is provided, for multi-agent systems subject to a loss of actua-
tor effectiveness. In this algorithm, an estimator is adopted to estimate the effectiveness rate of each actuator, and effect of actuator loss is compen-
sated for by adjusting a compensate gain in the control law. It is shown that all of the followers can track the leader with ultimately bounded tracking
errors, if parameters in the cooperative tracking algorithm are chosen properly. Finally, a numerical example is given to illustrate the effectiveness of
the proposed algorithms.
Keywords
Cooperative tracking, multi-agent systems, actuator faults
Introduction
Distributed cooperative control of multi-agent systems has
attracted much attention in recent years. Potential application
areas of this problem include multi-robot systems, flocking,
unmanned air vehicles, wireless sensor networks, smart micro-
grids, etc. (see Beard et al., 2001; Fax and Murray, 2004;
Saber and Shamma, 2005; Saber et al., 2007; Su et al., 2008;
Wang and Gu, 2012; Bidram et al., 2013, and references
therein). The consensus problem is a fundamental problem in
the cooperative control problem. For multi-agent systems,
consensus means the group of agents asymptotically agree
upon certain quantities of interest that depends on the states
of all agents (Saber et al., 2007). Based on some fundamental
work by Saber and Murray (2004) and Ren and Beard (2005),
many results have been reported in the past few years (see Yu
et al., 2010; Yuan et al., 2010a; Liu et al., 2011; You and Xie,
2011; Zhao et al., 2012; Yuan et al., 2010b, and references
therein).
The cooperative tracking problem is another important
problem in cooperative control of multi-agent systems, which
is also called consensus tracking problem or leader-following
consensus problem. The objective of the cooperative tracking
problem is to design distributed tracking algorithm for the
followers to track the leader. Due to the communication con-
straints, only a part of the followers can access information
from the leader. Therefore, the cooperative tracking problem
is a very challenging problem. The cooperative tracking prob-
lem for first-order and second-order multi-agent systems was
investigated by Cao and Ren (2012), Hong et al. (2008), Ren
(2007) and Zhao et al. (2012), while the high-order case is
addressed by Wen et al. (2013). Wen et al. (2013) assumed the
control input of the leader to be zero. The cooperative track-
ing problem for high-order multi-agent systems with dynamic
leader was considered by Zhang and Lewis (2012) and Li et
al. (2013). It is worth mentioning that the sliding-mode tech-
nique was adopted by Zhang and Lewis (2012) and Li et al.
(2013) so control inputs of the followers are discontinuous.
However, this kind of control input may lead to a chatting
phenomenon in practice. To deal with this problem, a coop-
erative tracking algorithm with continuous control input was
given by Li et al. (2012).
An actuator fault is a common phenomenon in control
practice. Therefore, fault detection and fault accommodation
problems are extensively investigated Jiang et al. (see 2006);
Ding (see 2008); Li et al. (see 2014, and references therein).
Fault-detection and fault-tolerant consensus problems of
multi-agent systems have attracted the attention of researchers
in the last few years. The fault-detection problem for discrete-
time multi-agent systems with first-order dynamics was con-
sidered by Pasqualetti et al. (2012), while the continuous-time
second-order multi-agent systems were considered by Shames
et al. (2011). The fault tolerant consensus problem for first-
order multi-agent systems was investigated by Yang et al.
School of Electronics and Information, Jiangsu University of Science and
Technology, Zhenjiang, Jiangsu, P. R. China
Corresponding author:
Jianzhen Li, School of Electronics and Information, Jiangsu University of
Science and Technology, Zhenjiang, 212003, Jiangsu, P. R. China.
Email: jzlijust@gmail.com
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