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Fuzzy Adaptive Iterative Learning Control for Consensus of Multi...
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不精确通信拓扑结构的多智能体系统一致性的模糊自适应迭代学习控制,陈家喜,李俊民,研究了一类具有不精确通信拓扑结构的一阶线性参数化多智能体系统的自适应一致性问题。提出了描述不精确通信拓扑结构的头从结点多
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˖ڍመڙጲ
http://www.paper.edu.cn
不精确通信拓扑结构的多智能体系统一致性
的模糊自适应迭代学习控制
陈家喜,李俊民,李金沙
西安电子科技大学数学与统计学院,西安市 710126
摘要:研究了一类具有不精确通信拓扑结构的一阶线性参数化多智能体系统的自适应一致性问
题。提出了描述不精确通信拓扑结构的头从结点多智能体系统的 T-S 模糊模型,设计出了一
种模糊分布式自适应迭代学习控制协议。对于头结点的动态系统未知情况,所提出的协议保
证,从节点可以一致跟踪头结点在 [0, T ]。基于 Lyapunov 稳定性理论,给出了闭环多智能体
多智能体系统一致性的充分条件。最后,给出了一个仿真实例说明了该方法的有效性。
关键词:自适应迭代学习,一致性算法,多智能体系统,T-S 模糊系统,不精确拓扑结构
中图分类号: O231.2
Fuzzy Adaptive Iterative Learning Control for
Consensus of Multi-Agent Systems with
Imprecise Communication Topology Structure
Jiaxi Chen, Junmin Li, Jinsha Li
School of Mathematics and Statistics, Xidian University, xi’an 710126
Abstract: This paper investigates the adaptive consensus problem of first-order linearly para
-meterized multi-agent systems (MASs) with imprecise communication topology structure. T
-S fuzzy models are presented to describe leader-followers MASs with imprecise communicati
-on topology structure, and a fuzzy distributed adaptive iterative learning control protocol is
proposed. With the dynamic of leader unknown to any of the agent, the proposed protocol gu
-arantees that the follower agents can track the leader uniformly on [0, T ] for consensus prob
-lem. A sufficient condition of the consensus for the closed-loop multi-agent system (MAS) is
given based on Lyapunov stability theory. Finally, a simulation example is given to illustrate
the effectiveness of the proposed method in this sudy.
Key words: AILC, consensus algorithm, MAS, T-S fuzzy system, Imprecise Communication
Topology Structure.
Foundations: The National Nature Science Foundation of China under Grant 61573013, 61603286 and by Ph.D. Pragrams
Foundation of Ministry of Education of China under Grant 20130203110021
Author Introduction: Chen Jiaxi (1990-),male,master, major research direction:adaptive control, learning con-
trol of MAS, and T-S fuzzy systems. Correspondence author:Li Junmin(1964-),male,professor, major research di-
rection:adaptive control, learning control of MAS, hybrid system control theory and the networked control systems, etc,
e-mail:jmli@mail.xidian.edu.cn. Li Jinsha(1987-),famale, lecturer,major research direction:iterative learning control;
cooperative control of multi-agent systems.
- 1 -
˖ڍመڙጲ
http://www.paper.edu.cn
0 Introduction
Research on distributed control for multi-agent systems has attracted increasingly signifi-
cant interest because of its broad applications among the unmanned air vehicles [1], formation
control [2], flocking [3], congestion control in communication network [4] and distributed sensor
networks [5]. For all the agents to reach a consensus, the most important thing is to design a
distributed control for the multi-agent systems. In [6]-[11], the consensus problem of leader-
followers MASs has been extensively researched. In the consensus of real multi-agent systems,
various uncertainties are always appear. As an important research topic, the consensus for
uncertain MASs receives significant attention in the control filed.
As we all known, iterative learning control (ILC) is an effective way to handle repeated
control problems. Compared with other control methods, ILC has simplicial structure and
effective learning ability. Nowadays, ILC has been highly applied in industries which consist
of repetitive motions, such as robot, hard disk drives, chemical plants, and so on [12]-[14].
Nowadays, researchers has applied ILC to multi-agent systems. The result that the agents of
MAS reach consensus by using iterative learning control firstly appears in [15], where MAS
formation problem is considered. In [16], two coordination algorithms that is proposed by
using ILC are represented for the consensus of the distributed multi-agent system. Researchers
study the finite-time consensus of multi-agent systems with higher-order dynamics in [17]. Some
distributed algorithms, which were constructed mainly based on the communication information
among individual of the distributed systems, are represented to reach the objective. For the
consensus of MAS with switching topology, a distributed ILC scheme is proposed in [18] . When
communication topology graph of systems is not accurate, the consensus problem of MASs can
not be reached by using the above control method.
In the literature related to AILC for the consensus problem of MASs, communication
topology graph is often set to time-varying stochastic or switching. However, in practical
applications, the connections between the nodes are variable, even are imprecise. In [19], T-S
fuzzy models are applied to describe a MAS with uncertain communication topology structure.
The subsystems of MASs are given, which involve no parameter uncertainty. In a practical
MASs, unknown parameters and disturbances may arise naturally. As far as authors know, the
AILC for the consensus problem of MAS with imprecise connected graph is seldom investigated.
In this paper, we make further efforts to study the AILC for consensus problem of MASs with a
specific model and imprecise communication topology structure. At first, the dynamic of each
agent is nonlinear. Moreover, there has unknown parameter in the dynamic, and any follower
agent can not get the dynamic of the leader. We propose a new distributed adaptive iterative
learning control protocol for all followers in the MAS can track the leader in the finite time
interval.
The structure of the paper is following. In Section 2, some definitions about undirect-
- 2 -
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ed graph are presented. In Section 3, 4 and 5, T-S fuzzy systems are presented to address
multi-agent models with uncertain communication topology structure. The simulations in Sec-
tion 5 demonstrate the effectiveness of proposed consensus algorithms in this paper. Finally,
Conclusions are presented in Section 6.
1 Graph properties
We use undirected graph G = (V, E, A), where V = {v
1
, v
2
, . . . , v
n
} is the nodes set and
E ⊆ V × V is the edge set, to model the communication topology among the n nodes. Let
A = [a
ij
] ∈ ℜ
n×n
is the adjacency matrix with G. Let the edges have weights a
ij
= a
ji
≥ 0,
with a
ij
= a
ji
> 0 if (v
j
, v
i
) ∈ E, and a
ij
= a
ji
= 0 otherwise. Note a
ii
= 0. The set of
neighbours of a node v
i
is N
i
= {v
j
: (v
j
, v
i
) ∈ E}. Define the Laplacian matrix L = D − A
where d
i
=
n
j=1
a
ij
and D = diag (d
1
, . . . , d
n
). The undirected graph G is said to be connected
if there exists a path between any two distinct vertices of the graph
To study the leader-following consensus problem, we consider a leader-following MAS
consisting of n + 1 notes, in which an leader agent and n followers (graph G). The leader-
following MAS is conveniently studied by a interaction topology graph
¯
G =
¯
V ,
¯
E,
¯
A
, where
¯
V = {¯v
0
, ¯v
1
, . . . , ¯v
n
} and
¯
A =
0 0 · · · 0
a
10
a
11
· · · a
1n
.
.
.
.
.
.
.
.
.
.
.
.
a
n0
a
n1
· · · a
nn
∈ R
(n+1)×(n+1)
Define a diagonal matrix B = diag {b
1
, b
2
, . . . , b
n
} to be the leader adjacency matrix associated
with
¯
G, where b
i
= a
i0
≥ 0 and b
i
> 0 if (v
0
, v
i
) ∈
¯
E.
Lemma 1[20]: If graph
¯
G is connected, then the symmetric matrix H = L + B associated with
¯
G is positive definite.
2 Problem Formulation
In practical application, the connection between the nodes may become unreliable due to
the system uncertainty and disturbances subject to some inherent and external influences. It
is very difficult to clearly describe these effects. Here, we will explore these affections, which
can be regard as a fuzzy set. We construct T-S fuzzy models to describe multi-agent systems
with uncertain communication topology structure.
- 3 -
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