Abstract
This paper studies the extremum seeking problem for static maps with the inputs of the maps generated by a nonlinear uncertain system. A new small-gain approach is developed which uses an extremum seeking strategy to generate a reference signal, and employs a control law for reference-tracking of the nonlinear uncertain systems. The notions of input-to-state stability (ISS) and input-to-output stability (IOS) are used to characterize the interconnection between the extremum seeking strategy and the reference-tracking controller, and the nonlinear small-gain theorem is employed to guarantee the stability of the closed-loop extremum seeking system. With the proposed approach, the extremum seeking problem for a complex nonlinear system is solvable as long as one can design a proper reference-tracking controller for the system. Examples are given to show the feasibility of the proposed approach, and a numerical simulation is employed to show the effectiveness of the proposed design.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 5411-5416 |
| Number of pages | 6 |
| Journal | IFAC-PapersOnLine |
| Volume | 53 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2020 |
| Event | 21st IFAC World Congress 2020 - Berlin, Germany Duration: Jul 12 2020 → Jul 17 2020 |
Keywords
- Extremum seeking
- Semi-global practical stabilization
- Small-gain theorem
ASJC Scopus subject areas
- Control and Systems Engineering
Access to Document
Other files and links
Fingerprint Dive into the research topics of 'Extremum seeking for nonlinear uncertain systems: A small-gain synthesis'. Together they form a unique fingerprint.
Cite this
- APA
- Standard
- Harvard
- Vancouver
- Author
- BIBTEX
- RIS
Extremum seeking for nonlinear uncertain systems : A small-gain synthesis. / Wang, Qiyue; Qin, Zhengyan; Liu, Tengfei; Jiang, Zhong Ping.
In: IFAC-PapersOnLine, Vol. 53, No. 2, 2020, p. 5411-5416.Research output: Contribution to journal › Conference article › peer-review
}
TY - JOUR
T1 - Extremum seeking for nonlinear uncertain systems
T2 - 21st IFAC World Congress 2020
AU - Wang, Qiyue
AU - Qin, Zhengyan
AU - Liu, Tengfei
AU - Jiang, Zhong Ping
N1 - Funding Information: seemkii-nggflobbyafleannfladrgiflnogbatfhl,eanradndgeaoflifni ogpΩeritahtiopnflasnftirsoΩmitflhocmaflotroe t to refierence-tracking error, and the robustness ofi the sceoemmkipi-ngflegflˇobbdyayflenananflmadrigcisflno.gbTathfhl,eeatnroadonfldsgeeianofclifnifluogdpΩienrigtahtsiiopnnfglasunfftliarsorΩmpietfrlhotcumarfblotraoe- teftieorernecfieer-ternaccek-itnragckcainpgabeirflirtoyr,Ωaitnhd rtehspe ercotbtuosttnheesschoafintghees sceomip-gfleflˇobdayflnaanmdigcsflo.bTahfl,eatnodofldseianfclinflugdΩinigthsipnfglaunftlasrΩpietrhtumrborae-refierence-tracking capabiflity Ωith respect to the changes sctieoomnip-agflenflˇodbdaayfvlneaarnamdgiigcnsflgo.bTKahfrl,estatin´codoafldsnedianfWclinfluagdnΩignigt(h2s0ipn0fgl0au)n;ftlasKrΩupitetarhdtuimnrabotraae- refifireerfeienrceen-cterascikginnagflsc.aMpaobreifolivtyer,Ωnitohnflriensepaercgtatinostahreecuhsaendgteos ctioomnpaflenˇddayvnearamgiicnsg.TKhresttićooaflsndinWcfluadnigng(2s0in0g0u);flaKrupteardtuinrabtaa-ofirefierencesignafls.Moreover,nonflineargainsareusedto cteiotomnapfl.aflen(ˇd20da1yv7ne)ar,amgLiiycnsag.pTuKnhroesvtti´comoaflesntdihnoWcdflusadnHignag(r2isn0ing0g0ua);nfladKrupJteoarhdtauinnrsabetana- ofei srcerfiiebreentchee sinigtneracflso.nMneocrteioovnesr,,annodntflhineenaorngflainineasrasrme aufslfle-gdatino teitonafl.an(d20a1v7e)r,agLiynagpuKnrosvtićmaentdhoWdsanHga(r2in0g00a);ndKuJtoahdainnsaetna describe the interconnections, and the nonflinear smaflfl-gain ete(i2to0nafla1f7l..a)n,((d2017)2s0ma1va7ef)lfrl,,-aggLLaiiyynnaagpptuuKhnnerooosvvtrie´cmmetmaenTtdhhaoonWdsdesatnHarHgaafl.(r2ii(nn02gg0000ana)6;n)dd,KsuJJttohoahcdhanaiannssensatetinac theesocrriebme tJhieaningteertcaofnl.n(e1c9t9io4n)si,saenmd pthfloeynedontfloingeaurarsamnatfelfle-gtahine e(2t0a1f7l.),(2s0m1a7f)lfl,-gLaiynaptuhneoovremmeTthaondestHaafl.ri(n2g00a6n)d, sJtoohchaanssteinc theorem Jiang et afl. (1994) is empfloyed to guarantee the ((a2017)2tn0aa1flyf7l.s)i,,(s2smaflsM0m1aa7nf)lflfl,z-gai-gieLaiyannanpdttuhhKneoreoorvsrtemeim´mc(eTT2t0haa0onn9d)etes;tLHaflaiaufl..ria((n2006)2g0d0aK6n)rd,,ststsiJt´cooo(hcc2hha0astan1ss0teii)ncc, thtaeboirfleitmy oJfiiatnhge ectfloasfel.d(-1flo9o9p4)eiˇstreemmpuflomyesdeetkoinguasyrastnetmee, tsheee (a2n0a1fly7s)i,ssMmaanflflz-gieaianndthKeorsrteimć(T20a0n9)e;tLaiufl. a(n20d0K6)r,stsitćo(c2h0a1s0ti)c, stabiflity ofi the cflosed-floop eˇtremum seeking system, see (at2inm0a1efly7-vs)ai,srsyMminaagnflflze-gisetaiiamnnadtthiKoenorsrGteim´cua(yT20aa0nn9d)e;tDLoaicufl.haa(n2in0d0(K62)0r,1st5sit)´coa(cn2hd0a1sL0ti)ce, stoanbtiafligty(2o0fi0t7h)eacnflodseJdi-aflnogopaneˇdtrLeimuu(m20s1e8e)kifinogr tsuysttoermia,flsseoefi atinmaefly-vsaisryMinagnzeisetiamnadtiKonrsGtićua(y20a0n9d);DLoicuhaanind(K20r1st5i)ća(n2d01L0i)e, ∆ontag (2007) and Jiang and Liu (2018) fior tutoriafls ofi atainflmgaeeflby-vrsaaisrDyMiu¨nargnrzeeisettiamnfl.adt(i2Ko0nr1s7Gt)i´cu;aL(y2a0ab0na9dr);eDLtoiacufhl.a(ni2nd0(1K290r)1sth5i)´acva(en2d0b1eL0ei)ne, I∆o∆ntaangd(t2h0e07n)onafnlindeaJriasnmgaaflfnl-gdaiLniuth(e2o0r1e8m).fior tutoriafls ofi taiflmgeeb-vrarDyiünrgreesttiamfl.at(i2o0n17G)u; aLyaabnadr eDtoacfhl.a(i2n0(1290)1h5)avaendbeLeine I∆∆ and the nonflinear smaflfl-gain theorem. aflainiflmgebgtreeob-dvrraauacrDDyediuu¨¨nrrgtrroeetesttthieaflamflf..laitt((ei2017)2or0an1t7Gu)ru;;ea.LabLyaabnaradreteDtoaflacfhl..a((i2019)2n0(1290)1hh5)aavvaeendbbeeneLeine I∆n∆tahnisd pthaepenro, naflineasrsusmmapfltfl-iognainisthuesoerdemto. represent the ainflgtreobdraucDedu¨rtroettheaflf.lit(e2r0a1t7u)r;e.Labaretafl.(2019)havebeen I∆n∆tahnisd pthaepenro, naflineasrsusmmapfltfl-iognainisthuesoerdemto. represent the iinnflgttrreoobducdraucDeeddu¨rtotroethttheeaflflitef.lit(e2rar0a1turet7u)r;e..Labaretafl.(2019)havebeen IInnefietthisrheinsceppa-tarppaeecrr,k,inaagnn caasspssauumbmifpplitttioyionnofiiissthuuseseecddonttotororreflefleppredressseeynnstttemtthehse, ★introducedtothefliterature. Inefietrheinscep-tarpaecrk,inagn caspsaubmifplittyionofiisthuesecdonttororfleflepdreseynstemthse, InehfieitcrhheinsicsepΩ-taerpaekcrek,rintaghnancastpshauebmcifoplinttyidointoifoiinstshuiensemcdoantntoyroorflfeflieptdhreesseyˇnsittsetmtinhsge, ★ This work was supported in part by NSFC grants 61633007, rehfieicrhenicseΩ-terakcekrintghancatphaebcifolintyditoifoi ntshien mcoanntyrooflfflietdheseyˇsitsetminsg, ★61733018, 61533007 and U1911401, in part by NSF grant EPCN- reehfsieuicrflhetnsi,csseΩu-tcerhaakcaeksriKntghrastnciáctphaaenbdcifolWintydaintogifoi (n2tsh0ie0n0m)c;oaAnntryrioyofulffliertdhaensdeyˇsKitsertmsitnisgć, ★61733018,This wo61533rk wa007s suppandortedU1911401,in partinbparty NSbFyCNSFgrangtrsan61633007,t EPCN- rehsuicflhtsi,ssΩucehakaesrKthrastnićthaendcoWndaintgio(n2s0i0n0m);aAnryiyoufirthaendeˇKisrtsitnigć 1903781, ,an6d15i3n3p0a0r7t abnydStUa1te91K14ey01L, aibnorpaatrotrybyofNInStFellgigraennt CEoPnCtrNo-l r2ehs0ui0cf3lht)si;,ssTΩuacenhakeaetsraKtflh.ras(t2ni0ćt0ha6en)d;coGWnudaaintygioa(nn2sd0i0nD0m)o;caAhnaryiiynoufi(rt2ha0en1d5e)ˇK.isTrtsihtniigćs 61733018,1903781,and61533inpart007 andbyStateU1911401,KeyLabinoraparttorybyofNInSFtellgigraennttCEoPnCNtro-l r2es0u0f3lt)s;,sTuacnheatsaKfl.rs(t2i0´c0a6n)d; GWuaanyga(n2d00D0)o;cAhariiynu(r2a0n1d5)K. Trshti´cs 61733018,an0d3D78e1c,isaion61533ndoinfCp007aormtpandblyexStUSay1911401,tseteKmesyaLtainBboITrparta.torybyofNInSFtellgigraennttCEoPnCNtro-l r2es0u0f3lt)s;,sTuacnheatsaKfl.rs(t2i0´c0a6n)d; GWuaanyga(n2d00D0)o;cAhariiynu(r2a0n1d5)K. Trshtii´cs 1903781,,an6d15i3n3p0a0r7tabnydStUa1te91K14ey01L,aibnorpaatrotrybyofNInStFellgigraenntCEoPnCtrNo-l (2003);Tanetafl.(2006);GuayandDochain(2015).This 1903781, and in part by State Key Laboratory of Intelligent Control (2003); Tan et afl. (2006); Guay and Dochain (2015). This andan0d3DecisionD78e1c,isaionndofoinf ComplexCpaormtpblyexStSySaytstemsseteKmesyataLtaBIBboIT.Tra.tory of Intelligent Control (2003); Tan et afl. (2006); Guay and Dochain (2015). This and Decision of Complex Systems at BIT. and2405-8963 Copyright Decision of Complex© 2020 The Authors. This is an open access article under the CC BY-NC-ND licenseSystems at BIT. . Publisher Copyright: Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license
PY - 2020
Y1 - 2020
N2 - This paper studies the extremum seeking problem for static maps with the inputs of the maps generated by a nonlinear uncertain system. A new small-gain approach is developed which uses an extremum seeking strategy to generate a reference signal, and employs a control law for reference-tracking of the nonlinear uncertain systems. The notions of input-to-state stability (ISS) and input-to-output stability (IOS) are used to characterize the interconnection between the extremum seeking strategy and the reference-tracking controller, and the nonlinear small-gain theorem is employed to guarantee the stability of the closed-loop extremum seeking system. With the proposed approach, the extremum seeking problem for a complex nonlinear system is solvable as long as one can design a proper reference-tracking controller for the system. Examples are given to show the feasibility of the proposed approach, and a numerical simulation is employed to show the effectiveness of the proposed design.
AB - This paper studies the extremum seeking problem for static maps with the inputs of the maps generated by a nonlinear uncertain system. A new small-gain approach is developed which uses an extremum seeking strategy to generate a reference signal, and employs a control law for reference-tracking of the nonlinear uncertain systems. The notions of input-to-state stability (ISS) and input-to-output stability (IOS) are used to characterize the interconnection between the extremum seeking strategy and the reference-tracking controller, and the nonlinear small-gain theorem is employed to guarantee the stability of the closed-loop extremum seeking system. With the proposed approach, the extremum seeking problem for a complex nonlinear system is solvable as long as one can design a proper reference-tracking controller for the system. Examples are given to show the feasibility of the proposed approach, and a numerical simulation is employed to show the effectiveness of the proposed design.
KW - Extremum seeking
KW - Semi-global practical stabilization
KW - Small-gain theorem
UR - http://www.scopus.com/inward/record.url?scp=85105064342&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85105064342&partnerID=8YFLogxK
U2 - 10.1016/j.ifacol.2020.12.1535
DO - 10.1016/j.ifacol.2020.12.1535
M3 - Conference article
AN - SCOPUS:85105064342
VL - 53
SP - 5411
EP - 5416
JO - IFAC-PapersOnLine
JF - IFAC-PapersOnLine
SN - 2405-8963
IS - 2
Y2 - 12 July 2020 through 17 July 2020
ER -