通过脉冲控制仅具有位置信息的多智能体系统的共识和性能优化资源-CSDN文库

研究论文

45 浏览量 2021-03-16 02:24:49 上传评论收藏 1.52MB PDF 举报

资源推荐

资源详情

资源评论

Published in IET Control Theory and Applications

Received on 24th June 2012

Revised on 6th October 2012

Accepted on 30th October 2012

doi: 10.1049/iet-cta.2012.0461

ISSN 1751-8644

Consensus and performance optimisation of

multi-agent systems with position-only information

via impulsive control

Li Ding

, Pian Yu

, Zhi-Wei Liu

, Zhi-Hong Guan

School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, People’s Republic of China

Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074,

People’s Republic of China

E-mail: liding@whu.edu.cn

Abstract: In this study, the consensus problem of second-order multi-agent systems (MAS) with position-only information is

studied. Allowable sampling period for which second-order consensus can be achieved is obtained with two impulsive

consensus algorithms. It is shown that if there is at least one eigenvalue of the Laplcian matrix with a non-zero imaginary

part, consensus cannot be achieved for sufﬁciently small or large impulsive periods for both algorithms. Furthermore, the

convergence performance of the MAS is optimised. Convergence speed, asymptotical decay factor and per-step decay factor

of the error energy are utilised to investigate the convergence performance, and the relationship among impulsive period,

topology structure and convergence performance is derived. Finally, numerical examples are given to validate our theoretical

results.

1 Introduction

During the past several decades, the research on cooperative

collective behaviour in biological community, such as

ﬂocking of birds, schooling of ﬁsh and swarming of bees

gave us much insight into the distributed control of

multi-agent systems (MAS). In many practical situations,

agents communicate and share information with their

neighbours to reach an agreement on certain quantities of

interest eventually, which is referred as consensus problem.

The consensus problem has attracted increasing attention

recently because of its broad applications ranging from

scheduling of automated highway systems, formation

control of multiple vehicles, coordination and control of

distributed sensor networks and attitude alignment of

satellite clusters, etc.

In the literatures dealing with the consensus problem, several

topics have been addressed, including lead-following

consensus [1], ﬁnite-time [2, 3] and asynchronous consensus

[4], average consensus [5], second-order or high-order

consensus [6–10] etc. Many valuable results have been

obtained with special features, such as communication

delay [11, 12], noises in transmission channels [13],

limited communication date rate [14] and non-linear dynamics

[15–17].

In recent years, owing to the development of digital sensors

and the constraints of transmission bandwidth of networks,

sampling and impulsive control have been developed and

widely applied in many areas. In most of the work dealing

with sampling or impulsive control consen sus, it is assumed

that each agent can obtain the information of its and others

full states [18, 19]. However, the velocity states of agents

are often unavailable in practice because of the technical

limitations or communication constraints. Therefore

consensus algorithms using only position information have

been proposed recently [20–23].

In these works, one of the m ost challenging job is the

investigation of the effect of sampling period or impulsive

period on the stability and performance of consensus for

the analysis of MAS. In [20], an impulsive consensus

algorithm was proposed in which the current position data

of its neighbours and the past position data of its own

state were ut ilised. In [21], a hybrid control algorithm was

considered in which both current and sampled position

data of its neigh bours were utilised. Sufﬁcient or necessary

and sufﬁcient conditions for consensus was obtained.

However, the explicit expression of impulsive period or

sampling period for consensus was not provided.

Motivated by the above considerations, two consensus

algorithms with position-only information via i mpulsive

control are studied in this paper. Our main contributions

are summarised as follows. First, we derive the explicit

impulsive period for achieving second-order consensus

and it is shown that the impulsive period is restricted not

only by an upper bound but also by a lower bound for

general directed networks with the proposed two

algorithms. Second, the convergence performance

optimisation problem has been addressed. The relationship

between topology structure, impulsive period and

convergence performance has been derived based on the

www.ietdl.org

16 IET Control Theory Appl., 2013, Vol. 7, Iss. 1, pp. 16–24

The Institution of Engineering and Technology 2013 doi: 10.1049/iet-cta.2012.0461

analysis of convergence speed and the decay factor of error

energy.

The following of this paper is organised as follows. In

Section 2, the preliminaries and problem formulation are

presented. In Section 3, two impulsive consensus

algorithms using position-only information is proposed and

the explicit allowable impulsive period for consensus is

derived. Convergence performance optimisation problem is

discussed in Section 4. In Section 5, numerical examples

are presented to validate our theoretical results. Conclusions

are drawn in Section 6.

2 Preliminaries and problems formulation

In this section, some basic concepts and results are

introduced. First, the following notations are used

throughout this paper. Denote Z as the set of all positive

integer and R

as the set of real vectors with dimension n.

Given a complex number

[ C, Re(λ), Im(λ), |λ| are the

real part, the imaginary part and the modulus of λ,

respectively, i denotes the imaginary unit. In addition, I

the identity matrix with order N,1

= [1, 1, ..., 1]

[ R

denotes the square matrix with order N in which each of

its element is zero, ρ(·) and det(·) denote the spectral radius

and determinant of a matrix, respectively, and ⊗ is the

Kronecker product.

2.1 Preliminaries

Let G={V, E, A} be an unweighted directed graph with

adjacency matrix denoted by A=(a

)

N×N

. Here, V is the

set of all nodes and E [ V×V is the set of al l directed

edges. If there is an edge from nodes i to j, then we say that

node j can obtain the information from node i and a

= 1,

otherwise a

= 0. The graph G is called a connected graph

if for any i, j [ V, there is a path from i to j. In this paper,

we do not consider graphs with loops, namely, a

= 0 for

all i = 1, 2, ..., N. The set of neighbours of the node i is

denoted by V

. A root r is a node having the property that

for each node i different from r, there is a directed path

from r to i. A directed tree is a directed graph, in which

there is exactly one root and every node except for this

node has exactly one parent. We say a directed graph has a

directed spanning tree if there is a directed tree, which

consists of all the nodes and some edges in G.

The Laplacian matrix l = (l

)

N×N

is deﬁned by



j=1, j=i

, l

=−a

, i = j

Then it has some properties as follows.

1. Zero is an eigenvalue of L, and 1

is the associated right

eigenvector.

2. If G is an undirected graph (a

= a

), the Laplacian matrix

L is a symmetric matrix, then all the eigenvalues of L are real.

3. If G contains a directed spanning tree, then

is an

algebraically simple eigenvalue of L and all the other

eigenvalues are with positive real parts.

In what follows, some lemmas about the Laplacian L and

stability criteria are given.

Lemma 1 [24]: Deﬁne matrix

L = (

)

(N−1)×(N − 1)

− l

... l

− l

...

− l

... l

− l

⎛

⎜

⎝

⎞

⎟

⎠

(1)

Denote the eigenvalues of Laplacian matrix L and the matrix

L, respectively, by

, ...,

and

, ...,

N−1

where 0 =|

|≤|

|≤···≤|

| and |

|≤|

|≤···≤

N−1

|, then

, ...,

N−1

Lemma 2 ([25]): The polynomial

+ az + b = 0

where a, b [ C, has all roots within the unit circle if and only

if all roots of

(1 + a + b)t

+ 2(1 − b)t + b − a + 1 = 0

are in the open left half-plane (LHP).

Lemma 3 ([21, 26]): Given a complex coefﬁcient polynomial

of order two as follows

g(s) = s

+ (

i)s +

where

are real constants. Then, g(s) is stable if

and only if

. 0 and

−

. 0.

2.2 Problems formulation

Consider a system consists of N-identical agents with

second-order dynamics

(t) = v

(t),

(t) = u

(t) (2)

where i = 1, 2, ..., N, x

[ R

, v

[ R

are the position and

velocity states of the ith agent, respectively, u

[ R

is th e

control input referred to the consensus algorithm.

In this paper, two second-order consensus algorithms using

position-only information are studied which are

(t) =−



k=1



j[V

(t) − x

(t))



+ p

(t) − x

k−1

))}

(t − t

)

(3)

and

(t) =−



k=1



j[V

(t) − x

(t))



−p



j[V

k−1

) − x

k−1

))



(t − t

)

(4)

where t [ ( t

k−1

, t

], p

. 0, p

. 0 are the control gains,

(·)

is Dirac impulsive function, the impulsive time sequence

satisﬁes 0 , t

, t

, ···, lim

k1

= 1. The uniform

www.ietdl.org

IET Control Theory Appl., 2013, Vol. 7, Iss. 1, pp. 16–24 17

doi: 10.1049/iet-cta.2012.0461

The Institution of Engineering and Technology 2013

剩余8页未读，继续阅读

评论收藏

内容反馈

weixin_38660295

粉丝: 6
资源: 910

通过脉冲控制仅具有位置信息的多智能体系统的共识和性能优化

通过脉冲控制在联合连接的拓扑结构上混合混合多智能体系统的共识

通过采样数据控制实现具有加速目标的多智能体系统的渐近有界共识跟踪

多智能体系统的仿真_matlab源码.zip

脉冲与切换控制有通讯延迟的多智能体系统.rar

基于量化脉冲控制策略的领导跟随多智能体系统的固定时间一致性.pdf

基于脉冲控制的线性多智能体系统的二部一致性.pdf

非线性多智能体系统在脉冲控制下的部分分量一致性.pdf

有向拓扑图下基于脉冲协议的离散非线性多智能体系统一致性.pdf

二阶多智能体系统的领导-跟随异步脉冲一致性.pdf

二阶非线性多智能体系统的脉冲一致性.rar

一阶非线性多智能体系统的脉冲编队跟踪仿真

二阶非线性多智能体系统的脉冲一致性.pdf

人工智人-家居设计-多智能体系统预测协同控制研究.pdf

事件触发脉冲控制的多智能体系统分群一致性.docx

相对位置多段脉冲控制PLSR.rar

脉冲与切换控制有通讯延迟的多智能体系统.pdf

随机时延下非线性多智能体系统的一致性控制研究.pdf

分布式脉冲控制的非线性多智能体系统基于网络的领导者遵循共识

智能灯光控制系统PWM调光平滑性优化.pdf

【多智能体控制】脉冲控制多智能体一致性仿真【含Matlab源码 8793期】.zip

【多智能体控制】脉冲控制多智能体一致性仿真【含Matlab源码 8792期】.zip

多智能体脉冲控制仿真程序

仅具有采样位置的多主体系统的脉冲共识

STM32步进电机脉冲控制

基于PLC控制的脉冲除尘系统的升级设计.pdf

基于STM32的脉冲激光器智能控制系统设计.pdf

pulse_除尘器脉冲控制器_

脉冲微分方程_脉冲微分_脉冲系统代码_微分方程_

最新资源