Robust H
∞
Almost Output Consensus Design for Heterogeneous
Nonlinear Multi-Agent Systems
Xinghu Wang
1
,DaboXu
2
and Haibo Ji
1
Abstract— This paper considers robust H
∞
almost output
consensus for a class of heterogeneous multi-agent nonlinear
systems subjected to unmodelled external disturbances. A
Lyapunov method is proposed to derive a distributed output-
feedback control protocol. It renders the closed-loop system
an L
2
disturbance attenuation property with certain internally
stability.
I. INTRODUCTION
Consensus control of multi-agent systems with the goal
of controlling all agents to track to a common trajectory
has received considerable attention in the past decade. Many
interesting results have been obtained from various direc-
tions, see for instances [6], [15], [19], [25] and references
therein. Particularly, to handle consensus of heterogeneous
multi-agent nonlinear systems, a number of effective output
regulation methods have been developed in literature. For
the nonlinear multi-agent systems in output-feedback form
with unity relative degree case, [21] considered a semi-global
asymptotic consensus control by using a two-layer networked
design, and [2], [24] developed global consensus controls
under different assumptions on the interaction topology,
where [2] considered the case of a loop-free digraph, [3]
required the induced subgraph by the follower agents to
be undirected (bidirected), and [20], [24] assumed that the
interaction digraph contains a spanning tree with the leader
node being its root.
Recently, a few interesting studies have been carried
out towards H
∞
consensus; see [13], [16], [17], which
achieves consensus with disturbance attenuation. In this
case, the agents are subject to external disturbances that
cannot be modelled through an exosystem in a way as [7],
[8]. Therefore, distributed control needs to achieve global
consensus with a guaranteed H
∞
performance, which is
usually described by the H
∞
norm of transfer function from
disturbances to an average of the weighted relative outputs of
the agents, or a suitably defined disagreement output. By vir-
tual of linear matrix inequalities, [13], [16] presented several
effective distributed control designs to minimizing the H
∞
norm. To reduce impact of disturbances on the consensus
*This work was supported in part by the NNSF of China under Grants No.
61503359, No. 61304009, No. 61273090, in part by the Fundamental Re-
search Funds for the Central Universities under Grant No. WK 2100100027,
and in part by the Anhui Provincial Natural Science Foundation under Grant
No. 1308085QF107.
1
X. Wang and H. Ji are with Department of Automation, Uni-
versity of Science and Technology of China, Hefei, 230027, China
{xinghuw,jihb}@ustc.edu.cn
2
D. Xu is is with School of Automation, Nanjing University of Science
and Technology, Nanjing, 210094, China
xu.dabo@gmail.com
error to any arbitrarily small value, [17], [18] developed
an H
∞
almost synchronization method. In view of these
references, so far, the H
∞
consensus only tackles the linear
multi-agent systems. However, to the best of our knowledge,
there is a lack of particular studies on disturbance attenuation
of nonlinear multi-agent systems with external disturbances.
Relevant result may be found in [22], which proposed a
robust almost output consensus control design for multi-
agent nonlinear systems affected by external disturbances.
In this paper, for a class of multi-agent nonlinear systems,
within the framework of [22], we investigate a robust H
∞
almost consensus problem. Specifically, we shall develop a
distributed output-feedback control achieving consensus of
multi-agent systems with L
2
disturbance attenuation. The
present study is challenging due to at least two aspects.
Firstly, the concerned agents are heterogeneous and un-
certain nonlinear systems. Hence, certain robust technique
is necessary. Secondly, our control goal is to make the
effect of disturbances and initial conditions on the consensus
error arbitrarily small. Thus is generally difficult to be done
because of the nonlinear system structure.
The main contribution is to present a distributed output-
feedback control design to handle the disturbance attenuation
for multi-agent nonlinear systems subjected to external dis-
turbances that cannot be modelled through an exosystem. A
certain L
2
disturbance attenuation property in H
∞
consensus
is also ensured.
The rest of this paper is organized as follows. Section II
shows the system description as well as the problem defini-
tion. Section III is devoted to the distributed control design
to achieve the consensus. Finally, Section IV concludes this
paper.
Notations: For column vectors x
1
, ··· ,x
n
,
col(x
1
, ··· ,x
n
) denotes
x
T
1
, ··· ,x
T
n
T
; B
x
ρ
:= {x ∈
R
n
: x≤ρ} for a constant ρ>0; for a constant c>0
and a smooth positive definite function W : R
n
→ R,
Ω
c
(W ):={x ∈ R
n
: W (x) ≤ c}.
II. F
ORMULATION
This paper concerns a network of N-multiple nonlinear
agents subject to unmodeled disturbances described by (see,
e.g., [11])
˙x
i
= A
i
x
i
+ g
o
i
(y
i
,w)+B
i
u
i
+ g
d
i
(y
i
,w),
y
i
= C
i
x
i
, 1 ≤ i ≤ N
(1)
where x
i
∈ R
n
i
is the state, y
i
∈ R is the output, and
u
i
∈ R is the control input. w ∈ W is some unknown
parameter (or parameter uncertainties) in a fixed compact set
12th IEEE International Conference on Control & Automation (ICCA)
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