906 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 24, NO. 4, AUGUST 2016
Fuzzy Observed-Based Adaptive Consensus Tracking
Control for Second-Order Multiagent Systems With
Heterogeneous Nonlinear Dynamics
C. L. Philip Chen, Fellow, IEEE, Chang-E Ren, and Tao Du
Abstract—In this paper, the consensus tracking control prob-
lem of second-order multiagent systems with unknown nonlinear
dynamics, immeasurable states, and disturbances is investigated.
The nonlinear dynamics in multiagent systems do not satisfy the
matched condition. In this paper, fuzzy logic system is introduced to
approximate the unknown nonlinear dynamics, and adaptive high-
gain observer is designed to estimate the unmeasured states. Based
on backstepping approach and Lyapunov theory, a new adaptive
fuzzy distributed controller is proposed for each agent only us-
ing the information of itself and its neighbors. Then the consen-
sus tracking is achieved under the designed distributed controller.
Moreover, it is proved that all the signals in the multiagent systems
are semiglobally uniformly ultimately bounded, and the consensus
tracking error converges to a small neighborhood of the origin that
can be designed as small as possible. Finally, the simulation result
illustrates the effectiveness of the designed controller.
Index Terms—Adaptive fuzzy control, consensus tracking con-
trol, fuzzy observer, multiagent systems, second-order nonlinear
systems.
I. INTRODUCTION
D
UE to the broad applications of distributed coordination,
the research of cooperative control of multiagent systems
has attracted much attention. The corresponding applications
have penetrated into many areas, such as the formation con-
trol of robots, unmanned air vehicles and spacecrafts, flocking,
rendezvous, information fusion of wireless sensor, and so on
[1]. Distributed consensus control of multiagent systems, as one
of the important topics of the distributed cooperative control,
has been intensively investigated over the past decade. If all the
agents in one group can reach an agreement, such as the same
position, velocity, attitude, and rendezvous, then the agents are
said to reach the consensus. Different from the centralized con-
trol, the distributed consensus controller for each agent can only
use its local information, i.e., the information from itself and its
Manuscript received April 08, 2015; revised August 02, 2015; accepted
September 15, 2015. Date of publication October 05, 2015; date of current
version August 02, 2016. This research was supported in part by the University
of Macau MYRG and the National Nature Science Foundation of China under
Grant 61572540.
C. L. Philip Chen and C.-E. Ren are with the Department of Computer and
Information Science, Faculty of Science and Technology, University of Macau,
Macau 999078, China (e-mail: philip.chen@ieee.org; dtlrce@gmail.com).
T. Du is with the School of Automation, Southeast University, KeyLaboratory
of Measurement and Control of CSE, Ministry of Education, Nanjing 210018,
China (e-mail: dtlysd@sina.com).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TFUZZ.2015.2486817
neighbors. Compared with centralized control, the distributed
consensus control has many virtues, for example, flexibility,
robustness, and low cost.
Some influential study on consensus control for multiagent
systems has been done, e.g., [2]–[5]; although, they assume that
the model of multiagent systems is accurate. However, the prac-
tical model of the physical systems is imprecise [6]–[10], and
the uncertainties may come from the actual uncertainty about the
plant (e.g., unknown plant parameters), or from the purposeful
choice of a simplified representation of the system’s dynamics,
or from the environmental uncertainties. The uncertainties may
have undesirable effects on multiagent systems, i.e., the uncer-
tainties may influence or destroy the consensus of multiagent
systems. For example, the distributed consensus controller in [2]
cannot steer the multiagent systems to achieve the average con-
sensus, when there are communication noises which is uncertain
from the external environment [11]. Hence, it is significant to
consider the uncertainty in the model of multiagent systems. In
[12] and [13], the consensus control problem of the multiagent
systems with environmental uncertainties has been studied. In
[13], in order to solve the consensus tracking problem of second-
order linear multiagent systems with disturbances, a distributed
observer is utilized.
In recent years, some studies investigating the consensus of
multiagent systems with unknown nonlinear dynamics and/or
external disturbance have been finished, e.g., [1], [14]–[21]. In
[14]–[16], the nonlinear dynamics have a common feature, that
is, they must be homogeneous, i.e., for the different agents, they
have an identical nonlinear dynamics; in addition, the nonlinear
dynamics satisfy the Lipschitz condition or Lipschitz-likecondi-
tion. However, the different agents may have different nonlinear
dynamics. In [1], [17]–[20], and [22] the multiagent systems
with heterogeneous nonlinear dynamics are considered. Com-
pared with the multiagent systems with homogeneous dynamics,
the consensus problem of multiagent systems with heteroge-
neous nonlinear dynamics is more complicated. In order to deal
with this problem, the fuzzy logic system (FLS) and neural net-
works (NN) are employed. In [1], [17], and [18], the NN are used
to compensate for the unknown nonlinear dynamics for the first-
order nonlinear multiagent systems with external disturbance or
state time delay. The consensus control of first-order nonlin-
ear multiagent systems is stretched to the consensus control of
second-order or higher-order nonlinear multiagent systems in
[18], [19], and [22].
In the abovementioned cases, it should be noted that all the
states of each agent are used to implement the proposed con-
1063-6706 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications
standards/publications/rights/index.html for more information.
Authorized licensed use limited to: SOUTH CHINA UNIVERSITY OF TECHNOLOGY. Downloaded on March 28,2020 at 12:20:01 UTC from IEEE Xplore. Restrictions apply.