制度:新 ; 報告番号:甲3441号 ; 学位の種類:博士(工学) ; 授与年月日:15-Sep-11 ; 早大学位記番号:新576

Wang Lan

English

制度:新 ; 報告番号:甲3441号 ; 学位の種類:博士(工学) ; 授与年月日:15-Sep-11 ; 早大学位記番号:新5765textthesi

Wang, Lan

32430

Waseda University Repository

Study on adaptive control of nonlinear dynamical systems based on quansi-ARX models

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 早稲田大学大学院情報生産システム研究科     博 士 論 文 概 要         論  文  題  目   Study on Adaptive Control of Nonlinear Dynamical Systems Based on Quasi-ARX Models      申  請  者   WANG, Lan   情報生産システム工学専攻 ニューロコンピューティング研究      2011 年 6 月  2 Adap t ive  con t ro l  i s  a  ve ry  impor t an t  f i e ld  o f  sys t em con t ro l  and  has  a t t r ac t ed  a  l o t  o f  i n t e r es t  f rom re sea rche r s  i n  r ecen t  yea r s .  L inea r  sys t e m theory  i s  ve r y  deve loped  and  the re  ex i s t  many  exce l l en t  adap t ive  con t ro l  r e su l t s  fo r  l i nea r  sys t ems .  On  the  o the r  hand ,  mos t  o f  r ea l  p l an t s  a re  non l inea r  and  l inea r  approx ima t ive  mode l s  can  no t  do  we l l  i n  t he  accuracy  p rob lem o f  t hese  p l an t s .  The re fo re ,  many  non l inea r  b l ack -box  mode l s  (neura l  ne tworks ,  wave le t  ne tworks ,  adap t ive  fuzzy  sys t ems ,  e t c . )  have  been  used  to  con t ro l  o f  non l inea r  sys t ems .  However ,  t he re  a re  two  p roblems  fo r  t hese  non l inea r  mode l s :  t he  con t ro l l e r  des ign ing  and  the  s t ab i l i t y  o f  co r respond ing  con t ro l  sys t em.  The  con t ro l l e r s  based  on  these  non l inea r  mode l s  a re  more  d i f f i cu l t  t o  be  ob ta ined  than  based  on  the  l i nea r  mo de l s .  S t ab i l i t y  and  accuracy  o f  t he  con t ro l  sys t em fo r  non l inea r  sys t ems  a re  d i f f i cu l t  t o  be  ensu red  in  one  me thod  o r  one  non l inea r  mode l .    A  quas i - l i nea r  b l ack -box  mode l ing  scheme  has  been  p roposed  wi th  wh ich  the  t echn iques  based  on  we l l  deve loped  l inea r  sys t em theo ry  cou ld  be  ex tended  to  non l inea r  sys t ems .  I t  cons t ruc t s  mode l s  cons i s t ing  o f  two  pa r t s :  a  macro-pa r t  and  a  ke rne l -pa r t .  The  macro-pa r t  i s  a  u se r - f r i end ly  in t e r face  cons t ruc t ed  us ing  the  spec i f i c  knowledge  and  the  cha rac te r i s t i c s  o f  ne twork  s t ruc tu re ;  t he  e f fo r t s  o f  th i s  pa r t  a re  to  in t roduce  some  prope r t i e s  f avorab le  t o  ce r t a in  app l i ca t ions ,  such  a s  con t ro l l e r  des ign ing .  In  th i s  t hes i s ,  Au toRegress ive  eXogenous  (ARX)  mode l  s t ruc tu re  i s  chosen  a s  macro -pa r t  because  o f  va r ious  use fu l  l i nea r i ty  p rope r t i e s .  Th i s  macro  s t ruc tu re  makes  the  p roposed  con t ro l l e r  eas i ly  ge t  an d  use  l i ke  based  on  ARX model .  The  ke rne l -pa r t  i s  a  non l inea r  b l ack -box  mode l  which  i s  used  to  r ep re sen t  t he  compl i ca t ed  coe f f i c i en t s  o f  mac ro-pa r t s .  In  th i s  t hes i s ,  neu ra l  ne tworks ,  r ad ia l  bas i s  func t ion  ne tworks ,  and  neura l  fuzzy  ne tworks  a re  chosen  a s  t he  ke rne l -pa r t s  which  improve  the  con t ro l  accu racy .  Obv ious ly ,  t he  above  mode l ing  scheme  can  cons t ruc t  d i f fe r en t  mac ro-pa r t s  and  ke rne l -pa r t s  wi th  app ly ing  spec i f i c  knowledge  fo r  d i f f e r en t  app l i ca t ion  in t e re s t s .  However ,  t he  s t ab i l i t y  i s  s t i l l  a  p rob lem which  mus t  be  so lved  i f  t he  con t ro l l e r s  based  on  the  quas i - l i nea r  b l ack -box  mode l ing  sche me  wan t  to  be  used  in  t he  rea l  wor ld .   The  mot iva t ion  o f  t h i s  t hes i s  i s  i n t ended  to  r esea rch  on  adap t ive  con t ro l  o f  non l inea r  dyna mica l  sys tems  based  on  the  quas i -ARX b lack-box  mode l s .  Accord ing  to  the  quas i -ARX mode l ing  scheme ,  seve ra l  i mproved  quas i -ARX b lack-box  mode l s  a re  p roposed  fo r  d i f f e ren t  non l inear  con t ro l  r equ i r emen t .  The  ob ta ined  quas i -ARX b lack -box  mode l  i s  cons ide red  to  have  two  p rope r t i e s :  t he  l i nea r  p rope r ty  and  the  non l inea r  p rope r ty .  Based  on  the  mode l  3 cha rac te r i s t i c s ,  two  con t ro l l e r s  can  be  ob ta ined :  one  l i nea r  con t ro l l e r  and  one  non l inea r  con t ro l l e r .  The  l i nea r  con t ro l l e r  i s  used  to  ensure  t he  con t ro l  s t ab i l i t y  and  the  non l inea r  con t ro l l e r  i s  u t i l i zed  to  improve  the  con t ro l  accuracy .  A  swi t ch ing  mechan i sm i s  p roposed  be tween  the  two  con t ro l l e r s .  In  the  p re mise  o f  s t ab i l i t y ,  t he  swi t ch ing  mechan i sm wi l l  t end  to  choose  the  non l inea r  con t ro l l e r  fo r  t he  accuracy .  On  the  o the r  hand ,  t he  swi t ch ing  mechan i sm wi l l  r e tu rn  to  l inea r  con t ro l l e r  t o  ensu re  s t ab i l i t y  when  the  s t ab i l i t y  o f  con t ro l  sys t e m i s  des t royed .  The re fore ,  t he  s t ab i l i t y  and  accuracy  p rob lems  in  adap t ive  con t ro l  p rocess  a re  so lved  by  one  mode l  fo l lowing  the  quas i -ARX mode l ing  scheme .  Inves t iga t ions  a re  made  to  do  sys t em iden t i f i ca t ion ,  con t ro l  des ign  fo r  non l inea r  sys t ems  and  s t ab i l i t y  ana lys i s  o f  con t ro l  sys t em unde r  t he  f r a mework  o f  l i nea r  con t ro l  t heo ry  based  on  the  new mo de l ing  sche me .   Chapter  1  br i e f ly  in t roduces  sys t em,  sys t e m iden t i f i ca t ion ,  con t ro l ,  s t ab i l i t y  and  accuracy  p rob lems ,  quas i -ARX mode l ing ,  ou r  mot iva t ion ,  goa l s  o f  t h i s  work  and  ou t l i ne  o f  t he  thes i s .   Chapter  2  p roposes  a  quas i -ARX neura l  ne twork  fo l lowing  the  quas i - l i nea r  b l ack -box  mode l ing  sche me  and  d i scusses  i t s  app l i ca t ion  fo r  s t ab i l i t y  adap t ive  con t ro l  o f  non l inea r  sys t ems .  Th i s  con t ro l  me thod  focuses  on  r ea l i z ing  the  s t ab i l i t y  and  accuracy  based  on  one  quas i -ARX neura l  ne twork  mode l .  The  ob ta ined  quas i -ARX neura l  ne twork  mode l  i s  d iv ided  in to  two  pa r t s :  t he  l i nea r  pa r t  i s  u sed  to  ensure  the  non l inea r  con t ro l  s t ab i l i t y ,  and  the  non l inea r  pa r t  i s  u t i l i zed  to  i mprove  the  con t ro l  accuracy .  One  l i nea r  con t ro l l e r  i s  ob ta ined  based  on  the  l i nea r  par t  and  one  non l inea r  con t ro l l e r  i s  g iven  based  on  the  quas i -ARX neura l  ne twork  mode l .  In  o rde r  t o  combine  bo th  the  s t ab i l i t y  and  un ive r sa l  approx ima t ion  capab i l i t y ,  a  0 /1  swi t ch ing  l aw i s  e s t ab l i shed  in  ou r  p roposed  con t ro l  sys t em by  a  swi t ch ing  c r i t e r ion  func t ion  based  on  sys t e m inpu t -ou tpu t  va r i ab le s  and  p red ic t ion  e r ro r s .  An  adap t ive  con t ro l l e r  i s  des igned  fo r  non l inea r  dynamica l  sys t ems  based  on  two  ob ta ined  con t ro l l e r s  and  the  p roposed  swi t ch ing  mechan i s m.  At  f ina l ly ,  t he  s t ab i l i t y  o f  t he  p roposed  con t ro l  sys te m i s  ana lyzed .   Chapter  3  exp lo res  a  fuzzy  swi t ch ing  adap t ive  con t ro l  approach  th rough  propos ing  a  fuzzy  swi t ch ing  mechan i sm and  d -d i f f e rence  ope ra to r  based  on  the  quas i -ARX RBFN mode l .  Three  i mprovemen t s  a r e  g iven  to  the  quas i -ARX mode l  i n  th i s  chap te r .  F i r s t ly ,  a  fuzzy  swi t ch ing  mechan i sm i s  cons t ruc t ed  on  the  sys t em swi t ch ing  c r i t e r ion  func t ion .  Th i s  mechani sm can  improve  con t ro l  pe r fo r mance  than  the  0 /1  swi t ch ing  l aw bo th  on  accuracy  and  s t ab i l i t y .  4 Second ly ,  a  d -d i f f e rence  ope ra to r  i s  u sed  in  the  ARX- l ike  express ion  o f  sys t em to  r e l ax  the  a s sumpt ion  o f  g loba l  boundedness  on  h ighe r -o rde r  non l inea r  t e rms .  Th i s  makes  t he  mode l  can  be  use fu l  fo r  more  compl i ca t ed  non l inea r  sys t ems .   At  f i na l ly ,  RBFN i s  used  to  r ep l ace  the  NN in  the  quas i -ARX b lack-box  mode l  wh ich  i s  unde r s t andab le  in  t e rms  o f  pa rame te r s  and  i s  no t  an  abso lu te  b l ack -box  mode l ,  compared  wi th  NN.  A pr ior  knowledge  can  be  used  to  conf i rm the  pa ra mete r s  o f  RBFN which  can  dec rease  t he  nu mber  o f  on - l ine  ad jus t ed  pa ra me te r s .    Chapter  4  proposes  a  Mul t ip l e - Inpu t  Mul t ip l e -Output  (MIMO)  quas i -ARX mode l  and  a  mul t iva r i ab l e  decoup l ing  Propor t ion  In t eg ra t ion  Di f fe ren t i a t i on  (P ID)  con t ro l l e r .  The  p roposed  MIMO quas i -ARX mode l  improves  the  quas i -ARX mode l  wh ich  can  be  used  a s  the  p red ic to r  o f  MIMO non l inea r  sys t ems .  The  adap t ive  mul t iva r i ab le  PID con t ro l l e r  w i th  a  decoup l ing  compensa to r  and  a  f eed - fo rward  compensa to r  i s  p r e sen ted  fo r  t he  con t ro l  o f  non l inea r  MIMO sys t ems  us ing  the  p roposed  MIMO quas i -ARX RBFN pred ic t ion  mode l .  The  pa ramete r s  o f  such  con t ro l l e r  a r e  s e l ec t ed  based  on  the  gene ra l i zed  min imum con t ro l  va r i ance .  In  th i s  chap te r ,  t he  co r re spond ing  s t ab i l i t y  ana lys i s  i s  g iven .  The  p roposed  con t ro l  method  can  sa t i s fy  accuracy ,  s t ab i l i t y  and  decoup l ing  r equ i remen t s  fo r  MIMO nonl inea r  sys t ems .   Chapter  5  i n t roduces  a  Non l inear  P r inc ipa l  Componen t  Ana lys i s  (NPCA)  to  improve  the  iden t i f i ca t ion  o f  t he  quas i -ARX Neuro- fuzzy  Ne tworks  (NFNs)  mode l .  When  NFN i s  u sed  a s  ke rne l -pa r t ,  va r i ab le s  and  the  o rde r  o f  t he  mode l  i nc reases ,  t he  complex i ty  o f  i npu t -ou tpu t  des ign ing  the  NFN a l so  inc reases .  The  NPCA ne twork  t r a ined  by  Ar t i f i c i a l  Neura l  Ne twork  (ANN)  re so lves  the  d i mens ion  p rob lem in  the  iden t i f i ca t ion  p rocess  when  the  inpu t  va r i ab l e s  o f  NFN a re  non l inea r  cor re l a t ion ,  i n s t ead  o f  PCA ne twork .  The  con t ro l  me thod  i s  g iven  based  on  the  i mproved  quas i -ARX NFN mode l  wi th  NPCA.  Thi s  me thod  r educes  the  number  o f  con t ro l l e r  pa ra me te r s  and  i mproves  the  con t ro l  pe r fo r mance  o f  t he  con t ro l l e r  based  on  the  quas i -ARX mode l .   Chapter  6  conc ludes  th i s  work ,  su mmar izes  the  thes i s  and  g ives  so me  po ten t i a l  t op i c s  fo r  ou r  fu r the r  r esea rch .  

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Study on adaptive control of nonlinear dynamical systems based on quansi-ARX models

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