Neural Network Controller For The Inverted Pendulum

1(85$/1(7:25.&21752//(5)257+(,19(57('3(1'8/80 (QULTXH')HUUHLUD (GXDUGR53ODQFKRQ &DUORV'7URFKRQ

,QVWLWXWRGH,QJHQLHUtD(OpFWULFD)DFXOWDGGH,QJHQLHUtD8QLYHUVLGDGGHOD5HS~EOLFD &DVLOODGH&RUUHR0RQWHYLGHR¤8UXJXD\

$EVWUDFW

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

7KH XVH RI QHXUDO QHWZRUNV WR FRQWURO WKH ,QYHUWHG 3HQGXOXPLVDOVRDNQRZQWDVN,WFDQEHPHQWLRQHGWKHZRUNRI VHYHUDO DXWKRUV DV :LGURZ >@ *XH] DQG 6HOLQVN\ >@ 7RODW DQG :LGURZ >@ %DUWR 6XWWRQ DQG $QGHUVRQ >@ DQG $QGHUVRQ >@ +RZHYHU WKHUH KDYH QRW EHHQ SK\VLFDO LPSOHPHQWDWLRQV RI FRQWUROOHUV XVLQJ WKH &0$& QHXUDO QHWZRUN ,,7+(,19(57('3(1'8/80

,Q RUGHU WR PDNH WKH SK\VLFDO V\VWHP VXLWDEOH WR WKH SXUSRVH RI WKH SURMHFW WKHUH KDV EHHQ GHYHORSHG D PRGXODU VWUXFWXUHDVVKRZQLQWKHILJ

7KLVILHOGRIVWXG\KDVFRPHIURP%LRORJ\ZKLFKWULHV WRGLVFRYHUWKHSURFHVVHVLQYROYHGZLWKLQ WKHELRORJLFDOQHXUDO VWUXFWXUHV+RZHYHUWKH1HXUDO1HWZRUNVWXGLHGKHUHLVDYHU\ VLPSOLILHGPRGHORIRQHRIWKHP 7KH &0$& 1HXUDO 1HWZRUN  &HUHEHOODU 0RGHO $ULWKPHWLF &RPSXWHU  ZDV VWXGLHG LQLWLDOO\ E\ $OEXV >@>@ /DWHU 0LOOHU DQG *ODQ] >@ .UDIW DQG &DPSDJQD >@ DQG +DQGHOPDQ/DQHDQG*HOIDQG>@KDYHGHYHORSHGLWVSRWHQWLD OLWLHVDSSOLHGWRUHDOWLPHFRQWURORIG\QDPLFDOV\VWHPV 7KH&0$&FDQEHFDUDFWHUL]HGDVDQDVRFLDWLYHQHXUDO QHWZRUNLQWKHVHQVHWKDWDWDJLYHQWLPHLWVRXWSXWLVLQIOXHQFHG E\DVPDOOVXEVHWRIZHLJKWVRIWKHQHWWKDWDUHDGGUHVVHGE\LWV LQSXWV/RFDOJHQHUDOL]DWLRQLVDVVXUHGE\WKHPDSVXVHG+HQFH



)LJ 6\VWHP6WUXFWXUH

0HFKDQLFDOPRGXOH

,W FRQVLVWV RI D PHWDO EDU OLQNHG WR D FDUW WKURXJK D F\OLQGULFDODUWLFXODWLRQVZLQJLQJ ZLWKLQ D YHUWLFDO SODQH7KXV WKHSRVLWLRQLQZKLFK WKHEDULVYHUWLFDOZLWK LWV XSSHUH[WUHPH IUHH WR PRYH LV XQVWDEOH 7KH FDUW FDQ PRYH DORQJ D VWUDLJKW PHWDO JXLGH 7KH V\VWHP DOVR LQFOXGHV D FRQWLQXRXV FXUUHQW PRWRUWKHQHFHVVDU\HOHPHQWVWRWUDQVPLWWKHPRWRU VFRXSOHWR WKH FDUW DQG WKH WUDQVGXFHUV WKDW FRQYHUWV WKH VWDWH YDULDEOHV UHSUHVHQWLQJWKHSRVLWLRQRIWKHFDUW[ DQGWKHSRVLWLRQRIWKH EDUT LQWRHOHFWULFDOVLJQDOV $VKRUWVFKHPHRIWKLVPRGXOHLVVKRZQLQILJ

 [

 T

    . Y U 9  I T T  J[ [     J VLQ T  EcT  [ FRV [ /

7KH IULFWLRQ IRUFH )U FRQVWLWXWHV WKH VWURQJHVW QRQOLQHDULW\RIWKHV\VWHP,WZDVPRGHOHGE\WKHH[SUHVLRQ

  [ [ [  [ )U ) ) )  [   G  VLQ G  [  G 

DQG)[ DVVKRZQLQILJ

)LJ 0HFKDQLFDO0RGXOH $QDORJ0RGXOH

,W LQFOXGHV WKH EDVLF KDUGZDUH HTXLSPHQW WR DUUDQJH WKHVLJQDOVWKDWFRPHIURPWKHPHFKDQLFDOPRGXOHDQGJRWRWKH GLJLWDO PRGXOH %HVLGHV LW LQFOXGHV WKH PRWRU GULYH ZKLFK LV FRQWUROOHGE\DVLJQDOWKDWFRPHVIURPWKHGLJLWDOPRGXOH 'LJLWDO0RGXOH

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

7KH H[SUHVLRQV EHORZ GHVFULEHG WKH PDWKHPDWLFDO PRGHODGRSWHGIRUWKHSK\VLFDOV\VWHP 

)LJ )ULFWLRQIRUFHGHSHQGHQWRIG[GW

7KH SDUDPHWHUV WKDW FDUDFWHUL]HV WKH PRGHO ZHUH HVWLPDWHG E\ VHULHV RI H[SHULPHQWV 7KH YDOXHV REWDLQHG DUH OLVWHGEHORZ NY  -P  EP  G  G  G  E© 

,,,

1P9 1PV 1PV

&0$&1(85$/1(7:25.

7KH &HUHEHOODU 0RGHO $ULWKPHWLF &RPSXWHU FDQ EH GHVFULEHG DV VKRZQ LQ WKH ILJ  DV WKH FRPSRVLWLRQ RI WZR PDSVDQGDQDGGHU7KHILUVWPDSIL[HGDVRFLDWHHDFKHOHPHQW

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

7KLV SURSHUW\ FRQVWLWXWHV WKH PRVW LPSRUWDQW FKDUDFWHULVWLF RI WKH QHXUDO QHWZRUNV ,W FRQVLVWV LQ WKH SRVVLELOLW\ RI DGDSWLQJ WKH ZHLJKWV ZLWK D VSHFLILF DLP ,Q WKLV FDVH LW LV GHVLUH WR UHSURGXFH D SUHGHWHUPLQHG LQSXWRXWSXW UHODWLRQVKLS7KLVLVFDOOHGVXSHUYLVHGOHDUQLQJ,WFDQEHGRQHLQ WKHIROORZLQJZD\

7KH PDLQ DSSOLFDWLRQV UHSRUWHG XS WR QRZ DUH LQ WKH ILHOG RI 5RERWLFV 0LOOHU >@ UHDFKHG LQGXVWULDO SHUIRUPDQFH UHVXOWV LQ WKH SUREOHP RI WUDFNLQJ REMHFWV E\ D FDPHUD URERW 7KHUH DUH VRPH SDSHUV UHSRUWHG LQ WKH ILHOG RI SDWWHUQ UHFRJQLWLRQVSHHFKUHFRJQLWLRQDQGVLJQDOSURFHVVLQJ*ODQ] 0LOOHU>@  ,9

&0$&,03/(0(17$7,21

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

)LJ &0$&1HXUDO1HWZRUN

*LYHQ WKH LQSXW YHFWRU [ WR WKH QHWZRUN WKH FRUUHVSRQGLQJ RXWSXW X FDQ EH HYDOXDWHG WKURXJK WKH PHWKRG H[SODLQHGDERYHNQRZLQJWKHDFWXDOYDOXHVRIWKHZHLJWKVZ,I WKHGHVLUHGRXWSXWWRWKHJLYHQLQSXW[ LV\WKHQWKHDFWXDOL]DWLRQ DOJRULWPLV

Z M N   Z M N 

7KH IDFW WKDW RQO\ J ZHLJKWV DUH XSGDWHG LQ HDFK OHDUQLQJVWHSDQGQRWDOODVLQWKHWUDGLWLRQDODOJRULWKPVGRQRW SHUPLW WKLV QHWZRUN WR KDYH WKH SURSHUW\ RI JOREDO JHQHUDOL]DWLRQ+RZHYHU LW VSHHGV WKH DOJRULWKPZKLFK FDQ EH XVHGLQUHDOWLPHDSSOLFDWLRQV

E  \N  XN J

ZKHUH N UHSUHVHQWV WKH DFWXDOL]DWLRQ VWHSV DQG WKH VXELQGH[ M SRLQWV WR WKH ZHLJKW HOHPHQWV PDSSHG E\ WKH DFWXDO LQSXW [ 7KXV RQO\ J ZHLJKWV DUH XSGDWHG 7KH FRHILFLHQW E LV FDOOHG OHDUQLQJIDFWRUDQGLVOHVVWKDQWKHXQLW\

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



9M

L

TL  M @ J d M d J

M   J (> 

 d TL d T P  

ZKHUH TL LV WKHGLVFUHWHYDOXH RI [L   M LV WKH YHFWRU LQGH[ DQG (>@ LV WKH LQWHJHU SDUW RI LWV DUJXPHQW 7KHUHIRUH WKHUH DUH Q YHFWRUV9M RIJ FRPSRQHQWVHDFK7KHJ SRLQWHUVZHUHREWDLQHG FRQFDWHQDWLQJ WKH FRPSRQHQWV RI WKH YHFWRUV ZLWK WKH VDPH LQGH[

)LJ

&0$&6WUXFWXUH

%HFDXVHWKHSK\VLFDOV\VWHPVSDQVRYHUDOLWWOHUHJLRQ RI WKH VWDWH VSDFH FRQVLGHUHG LW ZDV XVHIXO WR FRPSULVH WKH DGGUHVVHV RYHU WKH ZHLJKW DUUD\ UHGXFLQJ LWV VL]H 7KH FRP SULVLQJPHWKRGVHOHFWHGLVFDOOHG+DVKFRGLQJ>@>@ +RZHYHUWKLVPHWKRGKDVDGLVDGYDQWDJH,WSURGXFHV ZKDW LV FDOOHG FROLVLRQV 7KLV LV WKH RYHUODSSLQJ RI ZHLJKW LQGH[HV IRU FRPSOHWHO\ GLIIHUHQW LQSXW YHFWRUV )RUWXQDWHO\ WKH SUREDELOLW\ RI VXFK FROLVLRQV LV UHODWLYHO\ VPDOO IRU SUDFWLFDO YDOXHV RI WKH VL]H RI WKH ZHLJKW YHFWRU : $OEXV >@ UHSRUWHG SUREDELOLWLHVRIIRU: JDQGIRU: J

DOVR LPSURYH WKH QHWZRUN SHUIRUPDQFH +RZHYHU WKH &0$& QHXUDO QHWZRUN LV LPLWDWLQJ DQRWKHU FRQWUROOHU 7KHQ LWV SHUIRUPDQFHFDQEHDWEHVWDVJRRGDVWKHRQHWKDWLVXVHGDV WKH WXWRU ,Q WKH QH[W SDUDJUDSK ZH SURSRVHG DQRWKHU FRQWURO VWUDWHJ\WRLPSURYHWKH&5(SHUIRUPDQFHXVHGDVWKHWXWRU

,Q WKH SUHVHQW UHSRUW WKH IROORZLQJ YDOXHV RI WKH SDUDPHWHUV WKDW GHILQHV WKH &0$& QHXUDO QHWZRUN ZHUH VHOHFWHGTP  J  E JLYHQVXFFHVIXO UHVXOWV 9 ),567&21752/6758&785(

,W FRQVLVWV LQ WUDLQLQJ D &0$& QHXUDO QHWZRUN WR FRQWUROWKHSK\VLFDOV\VWHPLPLWDWLQJDFRQWUROWXWRU,QWKLVFDVH WKHWXWRULVDOLQHDUFRQWUROOHU7KXVDIRXUUHDOLQSXWRQHUHDO RXWSXW &0$& ZDV LPSOHPHQWHG (DFK LQSXW FRUUHVSRQGV WR HDFK VWDWH YDULDEOH DQG WKH RXWSXW FRUUHVSRQGV WR WKH FRQWURO DFWLRQ7KHGHVLJQSDUDPHWHUVZHUH: TP J  E DQGWKHVDPSOHLQWHUYDO7 V7KHVXSHUYLVLRQ VLJQDO FRUUHVSRQGV WR WKH FRQWURO DFWLRQ JLYHQ E\ WKH OLQHDU FRQWUROOHU)LJVKRZVWKHVFKHPHSURSRVHG

)LJD7WUDMHFWRULHVIRU&5(&RQWUROOHU

$IWHU D IHZ PLQXWHV RI RIIOLQH WUDLQLQJ WKH QHXUDO QHWZRUN ZDV DEOH WR FRQWURO WKH V\VWHP DOPRVW DV ZHOO DV WKH WXWRU,QWKH)LJDFRPSDULVRQEHWZHHQWKHWUDMHFWRULHVIROOR ZHGE\WKHV\VWHPZLWKERWKFRQWUROOHUVLVVKRZQ

)LJE7UDMHFWRULHVIRU&0$&&RQWUROOHU 9, 6(&21'&21752/6758&785(

)LJ

&0$&OHDUQLQJIURPDWXWRU

$EHWWHUSHUIRUPDQFHWKDQWKHRQHVKRZQLQWKHILJXUH FRXOGEHREWDLQHGXVLQJDQRQOLQHDUGLVFUHWL]DWLRQZLWKDJUHDWHU QXPEHU RI GLVFUHWH YDOXHV QHDU WKH XQVWDEOH HTXLOLEULXP SRVLWLRQ8VLQJDEHWWHUWXWRUFRQWUROOHUDVDQRQOLQHDURQHFDQ



7KH VHFRQG FRQWURO VWUDWHJ\ FRQVLVWV LQ WUDLQLQJ D &0$&QHXUDOQHWZRUNWROHDUQWKHSODQWLQYHUVHLQRUGHUWRJLYH WKHDGHFXDWHFRQWURODFWLRQWRPRYHWKHV\VWHPIURPWKHVWDWH[N WRWKHGHVLUHVWDWH[N JLYHQE\DWUDMHFWRU\SODQQHU 7KHUHIRUH LW LV QHFHVVDU\ D QHW ZLWK HLJKW UHDO LQSXWV FRUUHVSRQGLQJ WR WKH IRXU VWDWH YDULDEOHV LQ WZR FRQVHFXWLYH VDPSOHWLPHVDQGDUHDORXWSXWZKLFKJLYHVWKHFRQWURODFWLRQ 7KHGHVLJQSDUDPHWHUVXVHGZHUH

TP J : WV VHF )LJVKRZVDJHQHUDOVFKHPHRIWKLVFRQWUROVWUXFWXUH

'LVFXVLRQ

7KLV VHFRQG FRQWURO VWUDWHJ\ EDVHG RQ WKH SODQW LQYHUVH LGHQWLILFDWLRQ XVLQJ QHXUDO QHWZRUNV KDV VHYHUDO GLIIHUHQFHVIURPWKH&5(

 ,WV DGDSWDWLYHQHVV 8VLQJ QHXUDO QHWZRUNV LQYROYHV WKH IDFW WKDW WKH\ DUH IOH[LEOH VWUXFWXUHV ZKLFK FDQ DGDSW WKHPVHOYHV WKURXJK WLPH WR UHDFK D VSHFLILHG WDUJHW +HUH WKH &0$& LV DGDSWLQJ LWV ZHLJKWV LQ RUGHU WR JLYH WKH FRQWURO DFWLRQ PRVW DSSURSLDWHWRPDNHWKHV\VWHPIROORZDGHVLUHWUDMHFWRU\  1RQOLQHDULW\%HFDXVHRIWKHDGGUHVVLQJPHWKRGWKHFRQWURO DFWLRQLVDQRQOLQHDUIXQFWLRQRIWKHQHWLQSXWV

)LJ

 7KHXVHRIDWUDMHFWRU\SODQQHU7KHFRQWUROPHWKRGVHOHFWHG LQYROYHVWKHXVHRIDWUDMHFWRU\SODQQHUEDVHGRQDSODQWPRGHO DQGDOLQHDUFRQWUROOHU,WLPSOLHVWKDWWKHWDUJHWLVDOLQHDUIXQF WLRQRIWKHREVHUYDWLRQVLQWKHSUHYLRXVWLPHVWHS

6HFRQGFRQWUROPHWKRG

7KHILJXUHVEHORZVKRZWKHOLPLWF\FOHVRIWKHV\VWHP FRQWUROOHG E\ WKH &5( DQG E\ WKH VHFRQG VWUXFWXUH 7KH SURMHFWLRQRIWKHOLPLWF\FOHLQERWKSODQHVLVUHGXFHGVSHFLDOO\ LQWKHSODQH[G[GW 9,, &21&/86,216

$VSHFLILHGW\SHRIQHXUDOQHWZRUNFDOOHG&0$&ZDV SUHVHQWHG VKRZLQJ LWV PDLQ FKDUDFWHULVWLFV DQG DSSOLFDWLRQV WR HQJLQHHU SUREOHPV ,W ZDV DSSO\ WR FRQWURO DQ ,QYHUWHG 3HQGXOXPZKLFKZDVSK\VLFDOO\LPSOHPHQWHG )LJ

/HDUQLQJSURFHVV

7KHOHDUQLQJSURFHVVZDV GLYLGHGLQWZRVWHSV,QWKH ILUVW VWHS WKH SODQW LV FRQWUROOHG E\ WKH &5( DQG WKH QHXUDO QHWZRUN LV RQO\ OHDUQLQJ ZKLOH LQ WKH VHFRQG RQH WKH &0$& FRQWLQXHV DGDSWLQJ LWV ZHLJKWV DQG WDNHV WKH FRQWURO RI WKH V\VWHP%RWKVWHSVDUHUHSUHVHQWLQJLQWKH)LJ

,QWKHILUVWSDUWRIWKHWUDLQLQJSKDVHQRLVHZDV DGGHG WRWKHFRQWURODFWLRQLQRUGHUWRDOORZWKHV\VWHPWRPRYHRYHUD ZLGH UHJLRQ RI WKH VWDWH VSDFH WR LPSURYH OHDUQLQJ 7KH GHOD\ EORFNVDUH QHFHVVDU\ EHFDXVH DW WLPH VWHS N WKH VWDWH YDULDEOHV [N DUH QRW NQRZQ 7KH WUDMHFWRULHV XVHG FRPH IURP D OLQHDU PRGHO RI WKH SODQW FRQWUROOHG E\ D OLQHDU FRQWUROOHU ,GHDO WUDMHFWRULHVWKDWUHGXFHWKHOLPLWF\FOHZHUHDOVRH[SHULPHQWHG



7KH FRQWURO RI DQ LQYHUWHG SHQGXOXP XVLQJ QHXUDO QHWZRUNVLVDQH[DPSOHRIWKHODUJHVHWRISRVVLEOHDSSOLFDWLRQV ZLWKLQ WKH HQJLQHHU ILHOG +RZHYHU WKLV LV D GLIILFXOW RQH EHFDXVH RI LWV XQVWDELOLW\ DQG QRQOLQHDULW\ ZKLFK PDNHV LW DWWUDFWLYHWRLQYHVWLJDWHQHZFRQWUROHVWUDWUHJLHV

$ FRPSDULVRQ EHWZHHQWKH FRQWURO VWUDWHJLHV UHSRUWHG KHUH DQG D OLQHDU FRQWUROOHU GHVLJQHG E\ %HO]DUHQD %RQLQR &KDYDUULD >@ ZDV PDGH 7KHUHVXOWV FRQILUP WKH IDFW WKDW WKLV WRROLVDSSURSLDWHWRERWKLPLWDWHRWKHUFRQWUROOHUVDQGJHQHUDWH JRRGFRQWURODFWLRQV%HVLGHVLWFDQEHDSSOLHGWRRWKHUSODQWV VSHFLDOO\ WKRVH ZKLFK DUH GLIILFXOW WR PRGHO RU KDYH FRPSXWDWLRQDO UHVWULFWLRQV ZLWK WKH FRQYHQWLRQDO FRQWURO PHWKRGV 7KHQHXUDOQHWZRUNVXVHGLQWKLVSDSHUZHUHVLPXODWHG LQ D 3& FRPSDWLEOH FRPSXWHU ,W LV XQGHUVWRRG WKDW KDUGZDUH LPSOHPHQWDWLRQ LV QHFHVVDU\ WR WDNH IXOO DGYDQWDJH RI WKLV SRZHUIXOWRRO

6LJPD;L7KH6FLHQWLILF5HVHDUK6RFLHW\ 5()(5(1&(6

)LJ D&5(T OLPLWF\FOH

)LJD

&0$& T OLPLWF\FOH

)LJE&5([ OLPLWF\FOH

)LJE &0$&OLPLWF\FOH 9,,, $&.12:/('*(0(176

7KH DXWKRUV ZRXOG OLNH WR WKDQN WR WKH VWDII RI WKH (OHFWULFDO (QJLQHHULQJ 'HSDUWPHQW )DFXOW\ RI (QJLQHHULQJ 0RQWHYLGHR 8UXJXD\7KLVUHVHDFKZDV SDUWLDOO\VXSSRUWHGE\



>@ $OEXV -6 D  $ 1HZ $SSURDFK WR 0DQLSXODWRU &RQWURO7KH&HUHEHOODU0RGHO$UWLFXODWLRQ&RQWUROOHU,((( 7UDQV$60(6HULH*9RO >@$OEXV-6E 'DWD6WRUDJHLQWKH&HUHEHOODU0RGHO $UWLFXODWLRQ&RQWUROOHU,(((7UDQV$60(6HULH*9RO  >@ $QGHUVRQ &:   /HDUQLQJ WR &RQWURO DQ ,QYHUWHG 3HQGXOXP 8VLQJ 1HXUDO 1HWZRUNV,((( &RQWU 6\VW 0DJ 9ROQR >@ %DUWR $%  6XWWRQ 56  $QGHUVRQ &:   1HXURQOLNH $GDSWLYH (OHPHQWV WKDW FDQ 6ROYH 'LIILFXOW /HDUQLQJ&RQWURO3UREOHPV,((( 7UDQV60& 9RO QR  >@%HO]DUHQD3 %RQLQR( &KDYDUUtD3 &RQWURO GHO 3p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