Flexible Jacket Matrices for Cooperative Multi-Agent Network

Transcription

1 Procdgs of th th WSEAS Itratoal ofrc o Multda Systs & Sgal Procssg agzhou ha Arl - Flxbl act Matrcs for ooratv Mult-Agt tor Moo o L Xuq ag Zhu h hag-hu ho Isttut of Iforato ad oucato hobu atoal Uvrsty ou - Kora ooho@chobuacr agxuq@hotalco chzhu@chobuacr blu9@chobuacr Abstract: - urrtly du to th grog ds oucatos of Mult-Agt tor DFT ad DT orthogoal trasfor hch s usd coucato systs th a fxd sz of s a r ad rsctvly do ot t th rqurts of futur srvc W roos th cocyclc act atrcs athatcally lt A a l b a atrx f A a T l th th atrx A s a act atrx hch has a flxbl atrx sz tructo th Krocr tructo thod ad sl lt vrs t s vry ortat th coucato of th ult-agt tor bcaus t ca rovd th agts dffrt data rat ad data lgth Ky-Words: - DFT DT Krocr roduct cocyclc act atrcs cooratv ult-agt systs Itroducto Rctly Mult-Agt syst MAS has rcvd drabl attto - I grally MAS sts of lots of autooous agts that d to coucat ad shar forato th ach othr to a a rght dcso autoatcally I ult-agt systs grous of agts ust coordat ffctvly ordr to solv robls allocat tass across a dstrbutd orgazato collctvly dstrbut oldg ad forato ad achv collctv goals Th orgazatoal structur of a ult-agt syst dctats th tractos aog th agts ad ca lay a sgfcat rol th ovrall rforac of a socty of agtsth rforac of th Mult-Agt syst also dds o th rforac of th coucato systs bt th agts I ths ar ould l to roos act atrcs hch ar ortat th coucato systs ad rov th flxablty of act atrcs a Flat Structur b rarchcal Structur cmodularstruct Structur of th Mult-Agt tor d oucato bt to agts Fg Structur of th ult-agt tor Mult-agt tor s a dstrbutd syst ad th coordato s achvd by coucato dffrt tor structur such as flat structur hrarchcal

2 Procdgs of th th WSEAS Itratoal ofrc o Multda Systs & Sgal Procssg agzhou ha Arl - 9 structur odular structur ar sho Fgabc ad coucato bt to agts s sho Fgd It s obvously that th data lgth trasttd bt to agts dds o th sz of th DFT/DT orthogoal trasfor - W roosd act trasfor th sl lt vrs ad flxbl sz hch s alays bttr tha th DFT/DT hch has a fxd sz Elt-Ws Ivrs act Matrcs Lt a squar atrx If ts vrs atrx s obtad sly by a lt-s T for vrs l / hr s a ozro tat th call a act atrx - such as atrx ad ts vrs s / / / / / / / / / hr s th oralzd valu for ths atrx ad T s th trasos Fast ocyclc act Matrcs Wth Ay Sz W o df a th vctor ovr GF as V hr ad s th dcal dx xrssd by hr Usg th sa dfto ca gt V th orato as lts ultly ad th odular athatcally t ca b sho as follog T W ca us th dx ag to truct cocyclc act atrcs of ordr as th follog thor Thor Lt b a atrx of ordr hr x / ad th th atrx of ordr gv by s a cocyclc act atrx ad th sybol rrsts th Krocr roduct Its factorzato s xrssd a A A A A hr A I I ad I s th dtfy atrx Proof: Bfor rovg frst troduc a roosto hch s uch hlful durg th roof Proosto If a atrx ca b rtt as th follog forula s s s s hr s a cocyclc act atrx for s a r ubr s Th th atrx s s s also a cocyclc act atrx Th roof of ths roosto ca b foud 9 Th atrx of Eq s a cocyclc act atrx sc V oarg th ad obvously t s a act atrx Th ll rov t s also a cocyclc act atrx as o th th orato + hch as lts add ad th odular th tradtoal { }

3 Procdgs of th th WSEAS Itratoal ofrc o Multda Systs & Sgal Procssg agzhou ha Arl - ultlcato th ros ad colus ar dxd by th lts of G udr th crasg ordr { } Lt G bas o th for hav Thrfor for ay gh also G hav gh g h gh gh + gh g h + + g h+ gh h g h h + + sc gh + g + h g h + + h so hav gh gh gh h Thrfor s a cocyclc atrx O th othr had hav hr Fro ca gt + Usg Proosto It s asy to s that also a cocyclc atrx So h s s a cocyclc act atrx th roof of Eq ad Eq s coltd Th ll troduc a slar ay gv to rov Eq ad Eq9W us ducto o th dx h t s clarly tru: A I I I I Assu th hyothss s tru for ad th sho t ust thrfor hold for + For obta th follog fro th hyothss: A + I I + I I I I I I A I ad A I I I + + W ca rt A A A A A A I A I A I I A A A A I 9 I ths rocss cog fro basd o th forula AB D A BD hch ca b foud oar th th Eq9 o th Eq s rght so hav fshd th roof of Thor I t also rsts a tructo of cocyclc act atrcs basd o q -ary frst-ordr Rd Mullr cods hch hav so slarty th th abov aroach Ths ca b ald to dsg fast dcodg algorth for RM hr s a r ubr W ca a a xal for th 9-by-9 cocyclc act atrx Lt th ft fld of q lts F { } RM s as follog RM! Lt b a rtv thrd root of uty Th cocyclc act atrx obtad by

4 Procdgs of th th WSEAS Itratoal ofrc o Multda Systs & Sgal Procssg agzhou ha Arl - It s th sa th th atrx rstd th Tabl Fro th forula 9 ca factorz ths atrx ad th fast cocyclc act trasfor ca b rtt as A A hr A I A I thus hav A A " Fro ths sars atrcs ca asly dra th sgal flo grah as sho Fg a As o arbtrary ubr ca b dcoosd by r ubr W ll sho that th hghr ordr cocyclc act atrcs ca b tructd by th lor r ordr cocyclc act atrcs Thor ust troduc a scal cas: o ll rst a or gral thod hch satsfd all th sz Thor If th cocyclc act atrcs of ordr th hr s a r ubr ad Its factorzato s xrssd as A A A Whr A I I I I I I + + Proof: W hav alrady rovd th s cocyclc act atrx Thor Bas o th Proosto s also cocyclc act atrx As for Eq ad th roof s slar th that of Eq ad 9 oly d to chag I I I th I ad I I I th th carry out + + I roof by th sa thod Scally h so ad ca gt # I I 9 It s th scal cas dscrbd by Thor Exal Th fast cocyclc act trasfor th th ordr so Usg Thor t s asy to o A A A I I I I I I A A A A B A A A A B A A A A B A A A A B hr $ $ % % % A $ A $ B % % % $ $ % % % Th sgal flo grah of fast algorth s as sho Fgb

5 Procdgs of th th WSEAS Itratoal ofrc o Multda Systs & Sgal Procssg agzhou ha Arl - a ordr-9 b ordr- Fg Fast cocyclc act trasfor sgal flo For clarly so tructo aroachs for cocyclc act atrcs ar rstd th Tabl th tabl th scod colu s th dcoosto aroachs for ubrs ad th thrd colu s th tructo aroachs for cocyclc act atrcs larly all ths d of atrcs ca b tructd usg lor r ordr atrcs hr s a r ubr Tabl Dcoostos of ubrs ad Th ocyclc act Matrcs Th Mult-Agt Systs Fgur s o xal of Systs hch d dffrt coucato data rats ad data lgths to trast dffrt ds of forato As ca b s Thor ad Tabl that ocyclc act Matrcs th arbtrary sz ca b dcoosd to sallr act Matrcs th sz of r ubrs That as ca rovd arbtrary data rat ad lgth for th coucato th ooratv Mult-Agt Systs Fg Exal of Mult-Agt Mobl oucato Syst Tabl : oar th DFT DT adaard ad act atrcs

6 x X / / / > + F / adaard tr Wghtd : adaard : / / F / / / / DFT DFT DFT DT DT DT adaard act r Arbtrary It s sho th Tabl abov that th sz of th DFT/DT ar s a r ad rsctvly ca ot b xadd by th rocr roduct th sz of th s fxd ovr th act atrcs ca hav arbtrary atrx sz th Krocr roduct I coucato systs cludg th coucato th Mult-Agt cooratv systs th data rat ad data lgth dd o th sz of DFT/DT orthogoal trasfor th roosd act trasfor has a bttr flxblty ad slr vrs thod tha th DFT/DT orthogoal trasfor ocluso Th sz of th DFT s s a r ad th sz of th DT s rsctvly ad ca ot tructd by th Krocr roduct But th sz of act atrcs ca b arbtrary th Krocr roduct of dtty atrcs ad succssvly lor ordr act Matrcs ad that s vry usful dffrt data lgth for ult-agt tor Th vrs of th act atrx s fro lt s vrs hch ca a th rcvr of th agt lo colxty Th cotrbuto of ths or ls rovdg a d of act atrcs ca rovd flxblty coard th DFT ad DT hch s ortat th coucat chal th ooratv ult-agt tor Acoldgt Ths rsarch as suortd art by Mstry of Iforato ad oucato MI Kora udr th IT Forg Scalst Ivtg Progra ITSIPITSO Itratoal ooratv Rsarch by Mstry of Scc ad Tchology KOTEF ad d stag Bra Kora Rfrcs: Dcr K S Dstrbutd robl-solvg tchqus a survy IEEE Tras 9 SM-: 9 Pa Y Tbau M A tllgt agt fraor for trrs tgrato IEEE Tras 99 SM-: 9 gs R otrollg cooratv robl solvg dustral ult-agt syst usg ot ttos Artfcal Itllgc 99 : 9 L F Woha W M O obsrvablty of dscrt vt systs Iforato Sccs 9: 9 L Yqg Dstrbutd Structur ad Moto Plag for Autooous Robots hs: dssrtato Guagzhou: South ha Uvrsty of Tchology 99 Procdgs of th th WSEAS Itratoal ofrc o Multda Systs & Sgal Procssg agzhou ha Arl -

7 Procdgs of th th WSEAS Itratoal ofrc o Multda Systs & Sgal Procssg agzhou ha Arl - Ahd ad KRRao Orthogoal Trasfors for Dgtal Sgal Procssg Yor Srgr-Vrlag 9 Yag Y Xa Thory ad Alcato of ghr-dsoal adaard Matrcs Klur Acadc Publshrs Athoy VGrata fr Sbrry Orthogoal Dsgs Quadratc fors ad adaard Matrcs Marcl Dr Ic99 9 GL Fg ad Moo o L A xlct ostructo of o-cyclc act Matrcs th Ay Sz th Shagha cofrc obatorcsha Shagha ao Tog Uvrsty May - S Wcr Error otrol Systs for Dgtal oucato ad Storag Prtc all Itratoal Ic 99 F MacWllas ad A Sloa Th Thory of Error-orrctg ods Elsvr Scc Publshrs BV 9 Moo o L Yur Borssor h Zhu Fast act Trasfor Aroach to th Frst-Ordr q -arry Rd-Mullr ods Subttd to IEEE Iforato Thory ofrcisit uly -9 c Frac Moo o L "A Rvrs act Trasfor ad Its Fast Algorth" IEEE Tras o rcut ad Syst vol o 9- a Moo o L B S Raa ad u Yog Par A Gralzd Rvrs act Trasfor IEEE Tras rcuts Syst II vol o -9 uly Moo o L ad K Flayso A Sl Elt Ivrs act Trasfor odg Iforato Thory Worsho ITW Proc of IEEE ITW Aug- St Zalad also aar by IEEE Sgal Procssg Lttrs Volo March Moo o L ad a ou Fast Bloc Ivrs act Trasfor IEEE Sgal Procssg Lttrs Vol o -Aug Moo o L act Matrcs Yougl Publshd oay Kora