Distributed Design of Glocal Controllers Hampe pei i Sasahar - - PowerPoint PPT Presentation

Hierarchical Model Decomposition for Distributed Design of Glocal Controllers

IEEE E CDC 2019 19 Distrib tribute uted d Contr ntrol

• l I/ ThA20

A20

Karl l Henrik rik Johansson ansson (KTH) Hampe pei i Sasahar ahara a (KTH), ), Takayuk uki i Ishiza hizaki (Tok

• kyoT
• Tec

ech) Jun-ic ichi hi Imura a (TokyoT

• Tec

ech), ), Henrik rik Sandb dber erg g (KTH) H)

1.

• 1. Intr

troduct duction ion an and Res esea earch h Object ectiv ive 2.

• 2. Glocal

cal Co Contr troll

• ller

er De Design n Pr Problem em

• 3. So

Solution tion via H a Hier erar archi hical cal Model el De Deco compos position ition 4.

• 4. Numeri

merical cal Ex Exam ample

• Centr

ntrali alized/Dis ed/Distrib tribute uted d Design ign

• Motiv

tivating ing Example ple

• Resear

search h Ob Object ectiv ive

• System

em Description scription

• Pr

Problem lem Formula ulation tion

• Hier

erar archical hical Model del Decompo composition ition

• Existence

stence Condition ndition

• Ex

Explici licit t Representa sentation tion

Ce Centr ntraliz alized/D ed/Distri istribut uted ed De Desi sign gn

1/14

Ce Centr traliz alized ed De Design Di Distr tributed uted De Design

• unique

ique contr ntroller

• ller designe

igner

• simulta

ultane neous

• us design

ign of subcon controller

• llers
• multiple

tiple cont ntroller

• ller designer

igners

• indepe

pendent ndent design ign

unde der r devel elopmen

• pment

Retr trof

• fit

it Co Cont ntrol

• l

2/14

’s viewpoint

[1] T. Ishi hiza zaki, , et al., Automa

• matica

tica, 2018. 2018. [2] T. Ishi hiza zaki, , et al., Arxiv iv, 2019. 2019.

Existing ting Metho thod: d: Retr trof

• fit

it Contr trol

• l [1,2

,2]

Retr trof

• fit

it Co Cont ntrol

• l

2/14

’s viewpoint Retr trof

• fit

it Contr troller

• ller

Def.: .: stability ility preser serving ving cont ntroller

• ller for any possib

sible le Premis mise: e: the entir tire e system em witho thout ut

[1] T. Ishi hiza zaki, , et al., Automa

• matica

tica, 2018. 2018. [2] T. Ishi hiza zaki, , et al., Arxiv iv, 2019. 2019.

retr trof

• fit

it contr ntroller

• ller works

s for r local cal beha havi vior

• r in

global bal behavior vior is not t fully ly contr ntrolled

• lled

is stable le Existing ting Metho thod: d: Retr trof

• fit

it Contr trol

• l [1,2

,2]

Pr Prob

• blem

lem in in Ex Exis istin ing g Me Method hod

3/14

second

• nd-or
• rder

der netw twor

• rk

k system em subsystem’s dynamics heter terog

• geneous

eneous, , but same e shape pe same e paramet ameters damping ping term: rm: large free ee response sponse retr trof

• fit

it contr ntrol

• l

good (for

• r initial

tial distur turbance bance in )

Pr Prob

• blem

lem in in Ex Exis istin ing g Me Method hod

3/14

second

• nd-or
• rder

der netw twor

• rk

k system em subsystem’s dynamics heter terog

• geneous

eneous, , but same e shape pe same e paramet ameters damping ping term: rm: small ll free ee response sponse retr trof

• fit

it contr ntrol

• l

st steady ady osc scill illation tion (for

• r initial

tial distur turbance bance in )

Pr Prob

• blem

lem in in Ex Exis istin ing g Me Method hod

4/14

Obser ervation tion global bal sy synchr hroniz

• nized

ed behavi vior

• r in each

h clust uster r (box) x) How w to suppr press ess it? Idea ea

co comb mbini ining ng global/local bal/local co contr trol

• ller

lers intr trodu

• ducing

cing a g a globa

• ball

lly working ing co cont ntroll

• ller

er

detail tail of the e steady ady oscill illation tion

Pr Prop

• pose
• sed

d Glo local al St Structur ucture

5/14

dist strib ibute uted d des esign gn for r glocal cal co contr ntrol

[3] S. Hara, a, et al., Proc. . MSC, 2015. 2015.

• bjectiv

ective local cally ly oper erating ting subcontr controller

• llers

globally bally oper erating ing subcon contr troller

• ller

glo local cal co contr ntrol

• l [3

[3]

1.

• 1. Intr

troduct duction ion an and Res esea earch h Object ectiv ive 2.

• 2. Glocal

cal Co Contr troll

• ller

er De Design n Pr Problem em

• 3. So

Solution tion via H a Hier erar archi hical cal Model el De Deco compos position ition 4.

• 4. Numeri

merical cal Ex Exam ample

• Centr

ntrali alized/Dis ed/Distrib tribute uted d Design ign

• Motiv

tivating ing Example ple

• Resear

search h Ob Object ectiv ive

• System

em Description scription

• Pr

Problem lem Formula ulation tion

• Hier

erar archical hical Model del Decompo composition ition

• Existence

stence Condition ndition

• Ex

Explici licit t Representa sentation tion

Sy Syst stem m De Desc scription iption

6/14

th th su subsy system: stem: # of contr troller

• ller designer

igners: s: cluster sters dynamics amics of subsystems tems in : inter ercon connection nection signal nal : contr trol input put : measur surement ment outpu put netw twor

• rk

th th clust uster: entir tire e sy syst stem em : embedding edding matrix trix state: te:

Glo local al Co Cont ntrol

• l St

Structur ucture

7/14

local cal contr ntroller

• llers

global bal contr troller

• ller

local cal contr ntrol/measur

• l/measuremen

ement global bal contr trol/

• l/meas

measur urement ement global bal local cal whole

• le contr

ntrol

• l input

ut (meas easur uremen ement: : dual al form) rm) informa

• rmation

tion struct uctur ure e of contr ntroller

• ller
• broadc
• adcast

ast contr ntrol

• l
• aggregate

e measur suremen ement ,

Pr Prob

• blem

lem For

• rmula

ulation tion

8/14

• bjectiv

ective: e: distrib tributed uted design gn of glocal cal contr troller

• llers

the e condition dition depends ends only y on

al allows ws independent pendent des esign n of subco contr ntroll

• ller

ers

Remar mark (for

• r rigor
• rous

us form rmula ulation, tion, se see our r paper) er) (inde dependent pendent of the e other er contr ntroller

• llers)

s) Design ign sets s of subcon contr troller

• llers

for any y such h that the e closed sed-loop loop system em

e.g., ., stabi bili lity ty, , pe perf rforma

• rmance

nce bo bound

Problem lem design ign paramet ameter er is not t subcon controller

• ller itself

elf but se sets s of su subcontr controller

• llers

has a prescribed escribed proper perty ty

1.

• 1. Intr

troduct duction ion an and Res esea earch h Object ectiv ive 2.

• 2. Glocal

cal Co Contr troll

• ller

er De Design n Pr Problem em

• 3. So

Solution tion via H a Hier erar archi hical cal Model el De Deco compos position ition 4.

• 4. Numeri

merical cal Ex Exam ample

• Centr

ntrali alized/Dis ed/Distrib tribute uted d Design ign

• Motiv

tivating ing Example ple

• Resear

search h Ob Object ectiv ive

• System

em Description scription

• Pr

Problem lem Formula ulation tion

• Hier

erar archical hical Model del Decompo composition ition

• Existence

stence Condition ndition

• Ex

Explici licit t Representa sentation tion

Basic ic Idea ea equiv ivalent alent system em descri cription ption composed posed only ly of seria ial/par /parallel allel inter ercon connect ected d reduced uced-or

• rder

der models els

• hier

erar archica hical l struct ucture

• reduced

duced-or

• rder

der models els scala lable le design gn stabil bility ity of the e whole

• le system

em Design ign sets s of admissib issible le contr troller

• llers

for r each h subsystem stem

Hi Hier erar archic hical al Mod

• del

el Dec ecompo

• mpositi

sition

• n 9/14

Hi Hier erar archic hical al Mod

• del

el Dec ecompo

• mpositi

sition

• n10/14

14

Definition inition For a given n system em is called led a hier erar archica hical model del decomposition

• mposition if

if for r any under der Questions stions

• Does

es it exist? t?

• How

w to constr nstruc uct t it?

• existence

stence condition dition

• implicit

licit repr presenta esentation tion (original riginal state te = super erposition position of the substa states es) and embedding bedding matric trices es ,

Theor

• rem

em 2 The sy syst stem em is s a hier erar archical hical model el decomposi composition tion possib sible le to deriv rive e of a given n system em

Ex Exis istence nce and nd Repr presenta esentation tion

11/14 14

existence tence Theor

• rem

em 1 Ther ere e exist sts s a hier erar archical hical model del decomposi composition tion wher ere is the contr ntrolla

• llable

le subspace space implicit licit repr presenta esentation tion : char aract acteriza rization tion through

• ugh contr

ntrolla

• llable

le subspace pace Remar mark: : subcon controller

• llers can

n be implement lemented d through

• ugh

linear ear funct nctional ional obser erver ers s (Theor eorems ems 3,4) 4) : linea ear r matr trix ix equation ions

Pr Prop

• pose
• sed

d Glo local al Co Cont ntrol

• l

12/14 14

• 1. For a given

en sy syst stem em and clust usters, , chec eck k exist stence nce of a hier erar archica hical model del decomposition

• mposition based

ed on Theor

• rem

m 1

• 2. Deri

rive e a specif cific ic repr prese esenta ntation tion based ed on Theor

• rem

em 2

• 3. Implement

lement subco cont ntrolle

• llers through
• ugh funct

nctional ional obser erver ers distrib tribute uted d design ign is achie ieved ed

• ex. for

r stabi bility lity stabilizing bilizing each h loop the e entir ire e system em is stable le dist strib ributed uted design sign of subcon controller

• llers

(Theor eorems ems 3,4) 4)

1.

• 1. Intr

troduct duction ion an and Res esea earch h Object ectiv ive 2.

• 2. Glocal

cal Co Contr troll

• ller

er De Design n Pr Problem em

• 3. So

Solution tion via H a Hier erar archi hical cal Model el De Deco compos position ition 4.

• 4. Numeri

merical cal Ex Exam ample

• Centr

ntrali alized/Dis ed/Distrib tribute uted d Design ign

• Motiv

tivating ing Example ple

• Resear

search h Ob Object ectiv ive

• System

em Description scription

• Pr

Problem lem Formula ulation tion

• Hier

erar archical hical Model del Decompo composition ition

• Existence

stence Condition ndition

• Ex

Explici licit t Representa sentation tion

Nu Numerical erical Ex Exampl ple

13/14 14

sec econd nd-or

• rder

der net etwor

• rk

free ee res espons

• nse

ret etrof

• fit

it co contr trol

• l

(l (loca cal l co contr trol) sy synchroniz

• nized

ed osc scillation tion

damping ping term: rm: small ll

syste tem res espons

• nse

Nu Numerical erical Ex Exampl ple

13/14 14

syste tem res espons

• nse

global bal co contr trol

• l

glocal cal co contr trol

• l

loca cal osc scillati tion

• n

no osc scilla lation tion sec econd nd-or

• rder

der net etwor

• rk

damping ping term: rm: small ll

Co Conc nclusion lusion

14/14 14

Su Summary ary Res esea earch h Di Direc ecti tions

• ns
• cluste

teri ring ng met ethod hod

• robus

ustne tness ss an anal alysi sis dist strib ibute uted d des esign gn goal al: co contr trol

• l str

tructur cture: e: glocal cal str truct ctur ure des esign gn met ethod hod

• hier

erar archi hical cal model el dec ecomposi mposition tion