IEEE E CDC 2019 19 Distrib tribute uted d Contr ntrol ol I/ ThA20 A20 Hierarchical Model Decomposition for Distributed Design of Glocal Controllers Hampe pei i Sasahar ahara a (KTH), ), Takayuk uki i Ishiza hizaki (Tok okyoT oTec ech) Jun-ic ichi hi Imura a (TokyoT oTec ech), ), Henrik rik Sandb dber erg g (KTH) H) Karl l Henrik rik Johansson ansson (KTH)
1. 1. Intr troduct duction ion an and Res esea earch h Object ectiv ive - Centr ntrali alized/Dis ed/Distrib tribute uted d Design ign - Motiv tivating ing Example ple - Resear search h Ob Object ectiv ive 2. 2. Glocal cal Co Contr troll oller er De Design n Pr Problem em - System em Description scription - Pr Problem lem Formula ulation tion 3. So Solution tion via H a Hier erar archi hical cal Model el De Deco compos position ition - Hier erar archical hical Model del Decompo composition ition - Existence stence Condition ndition - Ex Explici licit t Representa sentation tion 4. Numeri 4. merical cal Ex Exam ample
Ce Centr ntraliz alized/D ed/Distri istribut uted ed De Desi sign gn 1/14 Ce Centr traliz alized ed De Design - unique ique contr ntroller oller designe igner - simulta ultane neous ous design ign of subcon controller ollers Distr Di tributed uted De Design - multiple tiple cont ntroller oller designer igners - indepe pendent ndent design ign unde der r devel elopmen opment
Retr trof ofit it Co Cont ntrol ol 2/14 Existing ting Metho thod: d: Retr trof ofit it Contr trol ol [1,2 ,2] ’s viewpoint [1] T. Ishi hiza zaki, , et al., Automa omatica tica, 2018. 2018. [2] T. Ishi hiza zaki, , et al., Arxiv iv, 2019. 2019.
Retr trof ofit it Co Cont ntrol ol 2/14 Existing ting Metho thod: d: Retr trof ofit it Contr trol ol [1,2 ,2] ’s viewpoint Retr trof ofit it Contr troller oller Premis mise: e: the entir tire e system em witho thout ut is stable le Def.: .: stability ility preser serving ving cont ntroller oller for any possib sible le retr trof ofit it contr ntroller oller works s for r local cal beha havi vior or in global bal behavior vior is not t fully ly contr ntrolled olled [1] T. Ishi hiza zaki, , et al., Automa omatica tica, 2018. 2018. [2] T. Ishi hiza zaki, , et al., Arxiv iv, 2019. 2019.
Pr Prob oblem lem in in Ex Exis istin ing g Me Method hod 3/14 second ond-or order der netw twor ork k system em subsystem’s dynamics heter terog ogeneous eneous, , but same e shape pe same e paramet ameters damping ping term: rm: large (for or initial tial distur turbance bance in ) free ee response sponse good retr trof ofit it contr ntrol ol
Pr Prob oblem lem in in Ex Exis istin ing g Me Method hod 3/14 second ond-or order der netw twor ork k system em subsystem’s dynamics heter terog ogeneous eneous, , but same e shape pe same e paramet ameters damping ping term: rm: small ll (for or initial tial distur turbance bance in ) free ee response sponse st steady ady osc scill illation tion retr trof ofit it contr ntrol ol
Pr Prob oblem lem in in Ex Exis istin ing g Me Method hod 4/14 detail tail of the e steady ady oscill illation tion Obser ervation tion global bal sy synchr hroniz onized ed behavi vior or in each h clust uster r (box) x) How w to suppr press ess it? intr trodu oducing cing a g a globa oball lly working ing co cont ntroll oller er Idea ea co comb mbini ining ng global/local bal/local co contr trol oller lers
Pr Prop opose osed d Glo local al St Structur ucture 5/14 local cally ly oper erating ting subcontr controller ollers globally bally oper erating ing subcon contr troller oller glo local cal co contr ntrol ol [3 [3] dist strib ibute uted d des esign gn for r glocal cal co contr ntrol objectiv ective [3] S. Hara, a, et al., Proc. . MSC, 2015. 2015.
1. 1. Intr troduct duction ion an and Res esea earch h Object ectiv ive - Centr ntrali alized/Dis ed/Distrib tribute uted d Design ign - Motiv tivating ing Example ple - Resear search h Ob Object ectiv ive 2. 2. Glocal cal Co Contr troll oller er De Design n Pr Problem em - System em Description scription - Pr Problem lem Formula ulation tion 3. So Solution tion via H a Hier erar archi hical cal Model el De Deco compos position ition - Hier erar archical hical Model del Decompo composition ition - Existence stence Condition ndition - Ex Explici licit t Representa sentation tion 4. Numeri 4. merical cal Ex Exam ample
Sy Syst stem m De Desc scription iption 6/14 th su th subsy system: stem: # of contr troller oller designer igners: s: cluster sters dynamics amics of subsystems tems in th th clust uster: : contr trol input put : measur surement ment outpu put : inter ercon connection nection signal nal entir tire e sy syst stem em netw twor ork state: te: : embedding edding matrix trix
Glo local al Co Cont ntrol ol St Structur ucture 7/14 informa ormation tion struct uctur ure e of contr ntroller oller local cal contr ntroller ollers local cal contr ntrol/measur ol/measuremen ement global bal contr troller oller global bal contr trol/ ol/meas measur urement ement - broadc oadcast ast contr ntrol ol - aggregate e measur suremen ement whole ole contr ntrol ol input ut , global bal local cal (meas easur uremen ement: : dual al form) rm)
Pr Prob oblem lem For ormula ulation tion 8/14 objectiv ective: e: distrib tributed uted design gn of glocal cal contr troller ollers Problem lem Design ign sets s of subcon contr troller ollers for any y such h that the e closed sed-loop loop system em has a prescribed escribed proper perty ty e.g., ., stabi bili lity ty, , pe perf rforma ormance nce bo bound design ign paramet ameter er is not t subcon controller oller itself elf but se sets s of su subcontr controller ollers Remar mark the e condition dition depends ends only y on (inde dependent pendent of the e other er contr ntroller ollers) s) allows al ws independent pendent des esign n of subco contr ntroll oller ers (for or rigor orous us form rmula ulation, tion, se see our r paper) er)
1. 1. Intr troduct duction ion an and Res esea earch h Object ectiv ive - Centr ntrali alized/Dis ed/Distrib tribute uted d Design ign - Motiv tivating ing Example ple - Resear search h Ob Object ectiv ive 2. 2. Glocal cal Co Contr troll oller er De Design n Pr Problem em - System em Description scription - Pr Problem lem Formula ulation tion 3. So Solution tion via H a Hier erar archi hical cal Model el De Deco compos position ition - Hier erar archical hical Model del Decompo composition ition - Existence stence Condition ndition - Ex Explici licit t Representa sentation tion 4. Numeri 4. merical cal Ex Exam ample
Hi Hier erar archic hical al Mod odel el Dec ecompo ompositi sition on 9/14 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 order der models els Design ign sets s of admissib issible le contr troller ollers for r each h subsystem stem - hier erar archica hical l struct ucture stabil bility ity of the e whole ole system em - reduced duced-or order der models els scala lable le design gn
Hi Hier erar archic hical al Mod odel el Dec ecompo ompositi sition on 10/14 14 Definition inition For a given n system em and embedding bedding matric trices es , is called led a hier erar archica hical model del decomposition omposition if if for r any under der (original riginal state te = super erposition position of the substa states es) Questions stions - existence stence condition dition - Does es it exist? t? - implicit licit repr presenta esentation tion - How w to constr nstruc uct t it?
Exis Ex istence nce and nd Repr presenta esentation tion 11/14 14 : char aract acteriza rization tion through ough contr ntrolla ollable le subspace pace existence tence Theor orem em 1 Ther ere e exist sts s a hier erar archical hical model del decomposi composition tion wher ere is the contr ntrolla ollable le subspace space implicit licit repr presenta esentation tion : linea ear r matr trix ix equation ions Theor orem 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 Remar mark: : subcon controller ollers can n be implement lemented d through ough linear ear funct nctional ional obser erver ers s (Theor eorems ems 3,4) 4)
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