Letters
Leader-following consensus of discrete-time multi-agent systems
with observer-based protocols
Xiaole Xu
a,b
, Shengyong Chen
a
, Wei Huang
a
, Lixin Gao
c,
n
a
College of Information Engineering, Zhejiang University of Technology, Zhejiang 310023, China
b
Wenzhou Vocational College of Science & Technology, Zhejiang 325006, China
c
Institute of Intelligent Systems and Decision, Wenzhou University, Zhejiang 325027, China
article info
Article history:
Received 21 October 2012
Accepted 23 February 2013
Communicated by H. Jiang
Available online 23 March 2013
Keywords:
Multi-agent system
Leader-following consensus
Discrete-time system
Observer
Switching topology
abstract
This paper investigates the leader-following consensus problem of discrete-time multi-agent systems.
The dynamics of the leader and all following agents adopt the same general form of a linear model that
can be of any order. The interconnection topology among the agents is assumed to be switching and
undirected. To track the active leader, two kinds of distributed observer-based consensus protocols are
proposed for each following agent, whose distributed observers are used to estimate the leader's state
and the tracking error based on the relative outputs of neighboring agents, respectively. In light of the
modified discrete-time algebraic Riccati equality and Lyapunov method, we prove that the discrete-time
leader-following consensus problem can be solved by proposing the distributed observer-based
consensus protocol under switching topologies. Finally, a numerical example is given to illustrate the
obtained result.
& 2013 Elsevier B.V. All rights reserved.
1. Introduction
Distributed coordination control of multi-agent systems has gained
much int erest in v arious scientific communities due to broad applica-
tions in man y areas including formation control [1],distributedsensor
networks [2],robotics[3–5], flocking [6], surveillance, distributed
computation, and synchronization of coupled chaotic oscillators.
Consensus control is one of the most fundamental problems of
coordination control, which indicates that every agent will reach
agreement on their certain variables of common interest states
asymptotically or in finite time by designing a networked int eraction
protocol. In past decades, much study has been conducted on this
problem. In the fields of syst em and control, the development
of consensus theory is primarily impelled by [7,8]. To explain the
simulation result of the well-known Vicsek's model, Jadbabaie et al. [7]
provided a typical neighbor -based consensus control which updated
the heading of an ag ent by av eraging the headings of its neighbors.
Ren and Beard [9] extended the work of Jadbabaie et al. [7] to the case
of dir ected graphs. In [10], the authors studied the av erag e-consensus
problem and proposed a general control framew ork to the multi-agent
consensus pr oblem. A genera l analysis framework for the multi-agent
consensus problems in high-dimensional state space was provided
in [11]. T o track he second-order active leader , [1 2] proposed observer -
based control protocol for each first-or der follower -ag ent. Leader -
following consensus of multi-agent systems with second-order
dynamics was studied by [13]. For leader -following multi-agent
syst ems with general linear dynamics, Ni and Cheng [14] proposed a
distributed state feedback law to solve consensus problem. The
distributed H
2
and H
∞
consensus control problems of multi-agent
systems are investigated in [1 5,16]. Till now , consensus problems have
been extensi vely studied by numerous researchers from various
perspective s. Some relevant int eresting research topics include con-
sensus filtering [17], finite-time consensus [18],time-delay[1 9],
sampled-data control [20], communication constraint [2 1],rendezvous
[22],swarm[23,24], formatio n [25] and so on.
Compared with the continuous-time systems, discrete-time
systems are both more simple and more suitable by using
computer in calculations. Some interesting works related to the
topic of first-order discrete-time consensus stability had been
reported in [7,9,26,27]. By using probability limit theory and
algebraic graph theory, Li et al. [28] investigate the average
consensus problem of first-order discrete-time multi-agent net-
works in uncertain communication environments. Gao et al. [29]
studied the consensus problem of multiple agents with discrete-
time second-order dynamics and showed that there exist con-
troller gains to make the systems achieve consensus for any
bounded time-delays. Sun et al. [30] studied the convergence
and convergence speed for the second-order and the high-order
discrete-time multi-agent systems with random networks and
arbitrary weights.
For many practical multi-agent systems, some variables which may
lead the system to achieve a prescribed group behavior cannot be
measured by agent directly. Thus, the agent has to estimate these
variables via the measured output. An neighbor -based estimation
Contents lists available at SciVerse ScienceDirect
journal homepage: www.elsevier.com/locate/neucom
Neurocomputing
0925-2312/$ - see front matter & 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.neucom.2013.02.023
n
Corresponding author. Tel.: þ86 577 86689214.
E-mail addresses: gao-lixin@163.com, lxgao@wzu.edu.cn (L. Gao).
Neurocomputing 118 (2013) 334–341