Passivity-baseddecentralizedstabilizationofmulti-agentsystemswithuncertaintyandmixeddelays(2013年)资源-CSDN文库

工程技术

论文

需积分: 5 7 浏览量 2021-05-11 14:46:46 上传评论收藏 443KB PDF 举报

资源推荐

资源详情

资源评论

J Control Theory

Appl

2013

(4) 579-585

DOI

10.1007/s11768-013-2040

亿

Passivity-based decentralized stabilization of

multi-agent systems with uncertainty

and

mixed delays

anzeng

，针，

Xuebo

CHEN

Huaguang

ZHANG

School

lnformation

Science

and

Engine

巳

ring

，

Northeastern

University

Shenyang

Liaoning

110004

China;

2.School

Electronics

and

Information

Engin

巳

ering

，

University

Science

and

Technology

aoning

Anshan

Liaoning

114051

China

Abstract:

this paper,

巳

investigate

a decentralized stabilization

probl

巳

ofunc

巳

rtain

multi-ag

巳

nt syst

巳

with

rnixed delays in

uding

discret

巳

and

distributed time-varying delays based

passivity stability.

巳

design

a decentralized

stat

巳

feedback

stabilization

sch

巳

such that the family of

osed-loop feedback

subsyst

巳

enjoys the delay-dependent

passivity stability for each subsystem. Then

巳

mploying

new

Lyapunov-Krasovskii function, a

near matrix inequality

(LMI) approach is

develop

巳

to establish

巳

delay-dependent

crit

巳

ria

for

巳

passivity

stability

multi-ag

巳

systems. The

suffici

巳

condition

given for

巳

cking

巳

passivity

stability. The proposed LMI result is computationally

effici

巳 n

巳

xample

is given to show the

effectiven

巳

method.

Keywords: Multi-agent systems; Passivity stability; Decentralized stabilization; Time-delay systems

1 Introduction

Multi-agent

systems

hav

巳

found

successful applications

many

areas

such

problem

solving,

multi-agent

simula-

tion

construction

synthetic worlds

and

collective robotics

etc.

[1]. Stability is a basic qualitative property

multi-

agent

systems

since

it is

not

present

may

impos-

sible for

the

multi-ag

巳

to achieve

any

other

group

时巳

c

tive. Stability

analysis

multi-agent

systems

is still

open

problem

[2-5].

recent

巳

ars

，

has

巳

recognized

that

time

delay is

oft

巳

one

巳

main

sources

instability

and

poor

performance.

Sinc

巳

multi-agent

systems usually

have a spatial

nature

and

a variety

communication

chan-

nels,

desired

model

them

introducing

continu-

ously

distributed delays

over

a certainly duration

time,

such

that

distant

past

has

less

influenc

巳

compared

to the re-

cent

behavior

the

state

[6-9].

Therefor

巳，

when

model

multi-ag

巳

systems

both

time-varying

discrete delay

and

distributed

delays

should

巳

taken

into

accoun

practice

there

are

inevitably

some

uncertainties

due

to inaccuracy in

mathematical

model

and

paramet

巳

fluctuations.

Thus

great

importance

to investigate

the

stability

problem

for

unc

巳

rtain

multi-agent

syst

巳

with

both

discrete

and

dis-

tributed

time-varying

delays.

known

that

巳

dynamics

multi-agent

systems are

very

complicated

and

hard

design

the

collective

behavior

studying

individual

agent

dynamics

and

vari-

able

intra-agent

couplings.

Dynamic

graphs

are

巳

the

巳旺

órts.

Referenc

巳

[10]

discussed

the

controllability

dy-

namic

graphs

multi-agent

networks

while

[11] consid-

ered

the

cas

巳

when

the

arcs

the

graphs

can

described

巳

ceived

March

2012;

revised

May

2012

by dynamics.

this

pap

巳

，

巳

mathematical

model

[11]

and

analyze passivity stability properties

multi-

agent

systems.

The

passivity theory, intimately

circuit

analysis

method

has

received a

lot

attention

from

the

control

com-

munity

during

the

last

several

巳

cades

2-13].

provides

nice

tool

for

analyzing

the

stability

systems.

In this

pap

町，

use

巳

passivity

theory to

analyze

巳

decentralized

stability

uncertain

multi-agent

systems

with

both

discret

巳

and

distributed

time-varying

delays. We

consider

an interconnection

巳

nts

which

have local

con-

trol inputs

and

are nonlinearly

connected

each

other.

The

inputs are

used

stabiliz

巳

each

individual

agent

decen-

tralized manner.

Notations

Throughout

this

paper

and

nxm

de-

饨，

respectively, the

n-dim

巳

nsional

idean

spac

巳

and

the

set

a11

n x m real matrices.

The

superscript

‘T'

巳

notes matrix transposition.

The

identity matrices

and

z巳

matrices are

denoted

and

巳

spectively.

The

notion

:):

(resp

巳

ctively

，

Y))

means

that

and

巳

symmetric

matrices,

and

that X - Y is positive

semidefinit

巳

(respectively, positive definite).

2 Problem formulation

Let

consider

multi-agent

system

which

composed

agent

(scalar

subsyst巳

ms)

，

and

each

subsystem

巳

scribed as follows:

:白(肚

(αz

十

Aαz)zz(t)+;

二

(e;j

ße;j

)fj

(Xj

(t))

•

Corresponding

author.

E-mail:

m1zhxm@sina.com.

l.:

+86-412-5929741;

fax:

+86-412-5929129.

This

work

was

suppo

口

the

Nationa1

Natural

Sci

巳

nce

Foundation

China

(Nos.

60874017

50977008

60821063

61034005)

巳

National

High

，巳

chnology

Research

and

Deve10pment

Program

China

(No.

2009AA04Z127)

and

the

National

Basic

巳

Program

China

(No

2009CB32060

1).

South

China

University

Techno1ogy

and

Academy

Mathematics

and

Systems

Science

CAS

and

Springer-Verlag

Berlin

Heide1berg

2013

580

al.

/ J Control Theory Appl

2013

(4)

579-585

十三

(eL+AEi)93(Z30

一

T(t)))

十汇

(e:;

+ße:J

,.,

(Xj

(s))ds

十

Ui(

吗?

j=1'

叮

一

(t)

Yi(t)

且

(Xi(t))

，

i =

，

，...，风

，

，...，

，

+(E

ßE

刊二

(t)h(z(s))ds+

叫

以

均)

伊

x(t

例

功)川)

•

The following assumptions are made in this paper.

(4)

(1) A

Tnhe

time-varying uncertainties

ßD

ßE

，

牛

and

ùEJ

are

出

form:

ßD

月

(t)

且

，

ßE

(t)E

ßE

= H3F3(t)E3,

ßE

(t)E4,

where

H1' H2'

H4'

E1' E2'

are known constant

matrices that characterize

tl1

e structure

the uncertainties,

and

Fì

(t) , F

(t) ,

(t)

，

且

(t)

are unknown time-varying

matrices with Lebesgue measurable elements bounded by

)Fi(t)

运

，

= 1,2,3,4.

orth

巳

whole

system is

土

(t)

= (A +

ßA)x(t)

ßE

)f(x(t))

+(E

ßE2)g(x(t

- T(t)))

+(E

ßE

)

,.,

h(x(s))ds + u(t),

(t)

f(x(t))

(2) A2) For

iε1

，

. . . ,n,

tl1

e subsystem nonlinear inter-

where

x(t) =

[X1(t)

X2(t)

...

xn(t)]T is

multi

吨

ent

state

vector

f(x(t))

[h(X1(t))

…

fn(xn(t))]T

εRn?

h(x(t)) = [h1(X1(t))

...

hn(xn(t))]T

εRn

，

g(x(t - T(t)))

= [g1(xdt - T(t)))

...

gn(xn(t -

T(t)))]T

lR，

are the output nonlinear interconnected functions includ-

ing time-varying delay

, u(t) =

[U1(t)

...

un(t)

lR，

is multi-agent input vector,

y(t)

巳

output

vectoζ

diag{α1

，

. . . , a

} is a diagonal matrix,

)nxn,

(ε;

，

)nxn and

，

)nxn

are the interconnec-

lJ'

tion weight matrices representing the strength

coupling

between the individual subsystems.

ßA

ßE

and

ßE3

are time-varying parametric uncertainties, T(t) and

(t)

denote the discrete time-varying delay and the dis-

tributed time-varying delay

, respectively, and are assumed

to satisfy 0

运

T(t)

, 0

运

(t)

~σm

，

where T

and

σm

are constants.

The initial condition associated with system

(1) is

Xi(S)

队

(s)

，

where

if>

i(S) is bounded and continuously

differ

巳

ntialon

[一

，

]，

ρ=

maX{T

，

m}.

note that the subsystems are unstable and we use a

巳

cent

时

巳

state feedback

-(k

+ ßki)Xi + ri

to stabilize each subsystem independently.

ßk

tl1

e con-

troller gain perturbations.

choose the feedback gain

向

and

ßk

向

ßd

leav

巳

the

reference

input

ri (bias)

fr.

巳

but constan

Therefore, we obtain

巳

closed-Ioop

system

土

i(t)

-(d

十

ßdi)Xi(t)

+ζ(EL+AeL)ι(

句

(t))

(吨巳吃

+ A

气

ψ3υ

幻蚓

川(伊

句

一

叫咐咐

例

均)))

+主咿

叫

弓

ψ3

引

)ι

Lt_u(t

叫州

(ο(t)

(

吟)

i(t)

，

以

= fi(Xi(t)) ,

connected functions in (1) are bounded and satisfy

5-;

fi(xd

- fi(X2)

也~

Jt\~~1

Jt\~

'i(xd

gi(X2

)

lrz

二《

，

m-;

~仇

(xd

- hi

(X2)

，、电

咽

Remark

巳

constants

in A2) are allowed to be pos-

itive

, negative or zero. Lipschitz conditions are

just

出

spe-

cial cases

A2). Hence, the interconnected functions could

be non-monotonic and more general descriptions than

tl1

usual sigmoid functions. Note that assumption A2) is more

general than the sigmoid function which was used in

1].

Wedenote

= diag{

;t-

, .. . ,

才}，

占了十

5:;

十占士

占一

+5i

、

diag{.:::..!.

一

-L

，

一~:l

,...,

""n

'"'n

h, m1 and h, m2 are similar

出

form

and

, re-

spectively.

This paper adopts the following widely accepted deÍÌni-

tion

passivity [12].

Definition 1 System

(4) is called passive

these exists

a scalar

γ~

0 such that

2fuT(t)T(t)dt

-47(t)r(t)dt

for

注

and for all solution to (4) wi

tl1

L{~mma

[8]

Let

，

三

lR，

，

and P be a positive deÍÌ-

nite matrix

, then

2α

~二

Tp-

bTpb.

Lt~mma

2 [8] For given matrices H , E and F with

FTF

运

and a scalar E > 0, the following holds:

HFE

(HFE)T

~ε

-1E

Lt~mma

3 (Jensen inequality) For any constant matrix

lR,

nxn,

二

> 0, scalar h > 0, vector func-

tionω

•

lR,

n such that

巳

integrations

concemed

h …

are well

deÍÌn

叫

then

(儿

ω(

圳

s)~W(

儿

(s)ds)

n …

儿

~(s)W

(s)ds

Lf~mma

4 (Schur complement) Given symmetric ma-

(3) trices

and matrix E

, where E

and 0 <

土

(t)

一

ßD)x(t)

ßE

)f(x(t))

+(E

+ ßE2)g(X(t - T(t)))

, then E

< 0

and only

[叫

l[-M

< Oor I •

-E

I I E

剩余6页未读，继续阅读

评论收藏

内容反馈

weixin_38731145

粉丝: 4
资源: 940

Passivity-based decentralized stabilization of multi-agent syste...

最新资源

Passivity-based decentralized stabilization of multi-agent syste...

Passivity based Control of Euler_Lagrange Systems

Passivity-based robust control for nonlinear feedback systems using robust right coprime factorization

《工程电磁场与电磁波基础》简介.pdf

Approximation-of-large-scale-dynamical-system.djvu

Passivity-based robust control for uncertain nonlinear feedback systems

On-the-passivity-of-general-nonlinear-systems.rar_Windows编程_PDF_

MultibodySystemDynamics,Robotics and Control.zip

Passivity analysis and pinning control of multi-weighted complex dynamical networks

Passivity Analysis of Neural Networks with Discrete and Distributed Delays

Informatics in Control, Automation and Robotics (LNEE 430) 2018

Robust passivity analysis of neural networks with discrete and distributed delays

Robust Passivity and Feedback Design for Nonlinear Stochastic Systems with Structural Uncertainty

Passivity and synchronization of coupled reaction-diffusion Cohen-Grossberg neural networks with state coupling and spatial diffusion coupling

Intelligent Adaptive Control: Industrial Applications

Passivity analysis of coupled reaction-diffusion neural networks with Dirichlet boundary conditions

气动伺服摩擦补偿控制

Passivity based Robust Control - 对于双连杆机器人：基于被动的鲁棒控制，它表明这种方法不能很好地处理变化。-matlab开发

独立直流微电网中燃料电池与超级电容的功率协调控制

Input and output passivity of coupled reaction-diffusion neural networks with impulsive effects

不确定时延广义网络控制系统的保性能控制 (2012年)

Passivity of directed and undirected complex dynamical networks with adaptive coupling weights

Passivity and Passification for Delay Fuzzy System Based on Delay Partitioning Approach

Passivity Analysis and Design of a Haptic Interface

Further results on passivity analysis of neural networks with time-varying delay

基于无源性的直流微网虚拟惯性研究 .docx

最新资源