Wilamowski B.M., Irwin J.D. The Industrial Electronics Handbook. Second Edition: Industrial Communication Systems

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23-6 Industrial Communication Systems

23.2.3 Impulsive Control for Chaos Synchronization via Partial States

In.the.continuous.synchronization.control.strategies.like.the.linear.feedback.control.and.adaptive.

cont

rol

.abov

.cont

inuous

.tran

smission

.of.stat

.vari

ables

.of.the.driv

ing

.syst

.is.requ

ired

.to.obta

sync

hronization

.cont

rol

.signa

.in.impl

ementation.

. us,.the.secu

rity

.leve

.is.signi

cantly

.decr

eased

.if.

the.sche

.is.appl

ied

.to.secu

.comm

unication.

.On.the.othe

.hand

.a.pure

.impu

lsive

.sync

hronization

sche

.is.impl

emented

.by.tran

sferring

.the.stat

.info

rmation

.of.the.driv

ing

.syst

.only.at.disc

rete

impu

lsive

.inst

ants,

.ther

efore,

.is.much.more.feasi

ble

.in.secu

.comm

unication

.to.enha

nce

.tran

smission

secu

rity

.and.also.to.impr

ove

.the.tran

smission

.eci

ency.

.In.addi

tion,

.a.secu

.comm

unication

.syst

base

.on.impu

lsive

.sync

hronization

.has.anot

her

.adva

ntage

.of.bein

.less.sensi

tive

.to.chan

nel

.nois

.than.

that.bas

.on.con

tinuous

.syn

chronization.

Suppose

.that.the.driv

ing

.syst

.is.give

.by.(23.

1).

. e.resp

onse

.syst

.with.impu

lsive

.cont

rol

.adde

to.par

tial

.sta

tes

.of.the.sys

tem

.at.onl

.cer

tain

.dis

crete-time

.ins

tants

.τ

.is.given.as





  





 

…

X AX f X Y h t

Y g X Y h t t l

= − + +

= + ≠ =

( , ) ( ),

( , ) ( ), , , , , ,

0 1 2τ

 

Y Y U t t

l l l l

( ) ( ) ( ), ,τ τ τ

+ −

= + =











(23.

where

.{τ

}.is.a.discrete-time.set.satisfying.that.0.<.τ

.<.τ

.<.

…

.<.τ

l+1

.<.

…

.and.τ

.→.∞.as.l.→.∞.

and.τ

.is.called.an.impulsive.instant.. e.design.of.impulsive.controller.involves.the.choices.of.the.

cont

rol

.law.U

(t).and.impulsive.instant.τ

..According.to.[WWSG09],.U

(t).is.chosen.in.such.a.way.that.

0( )τ

.. is.gives

U t E

l l

( ) ( ) .= −

−

(23.

With

.such.a.cont

rol,

.∆

  

Y Y Y

l l

+ −

= − ≠

τ τ( ) ( ) 0,.and.thus.there.is.a.“jump”.of.the.state.vector

at.τ

To.ensu

.that.syst

.(23.

.and.(23.

.are.asym

ptotically

.sync

hronized

.with.the.cont

rol

.in.(23.

8),

.the.

impu

lsive

.ins

tant

.τ

.should.be.chosen.from.the.following.strategy.[WWSG09].

Strategy for the choice of impulsive instant