AIAA Gudanc Navgaon and Conrol Confrnc and Eh - 3 Augus 7 Hlon H Souh Carolna AIAA 7-655 Adav Nural Nork Flgh Conrol Usng oh Currn and Rcordd Daa Grsh Chodhary * and Erc N. Johnson Darmn of Arosac Engnrng Gorga Insu of chnology Alana GA 333 Modrn arosac vhcls ar cd o rform yond hr convnonal flgh nvlos and h h rousnss and aaly o ora n uncran nvronmns. Augmnng rovn lor lvl conrol algorhms h av lmns ha h long rm larnng could hl n achvng r aaon rformanc hl rformng aggrssv manuvrs. h currn av mhodologs hch us Nural Nork asd conrol mhods us only h nsananous sas o un h av gans. hs rsuls n a rank on lmaon on h av la. In hs ar roos a novl aroach o av conrol hch uss h currn or h onln nformaon as ll as sord or ackground nformaon for aaon. sho ha usng a comnd onln and ackground larnng aroach s ossl o ovrcom h rank on lmaon on h av la rsulng n fasr aaon o h unknon dynamcs. Furhrmor sho ha usng comnd onln and ackground larnng mhods s ossl o guaran long rm larnng n h av flgh conrollr hch nhancs rformanc of h conrollr hn ncounrs a manuvr ha has n rformd n h as. us Lyaunov asd mhods for shong ounddnss of all sgnals for a roosd mhod. h rformanc of h roosd mhod s valu n h hgh fdly smulaon nvronmn for h GMAX UAS manand y h Gorga ch UAV la. h smulaon rsuls sho ha h roosd mhod hs long rm larnng and fasr aaon lng o r rformanc of h UAS flgh conrollr. I. Inroducon EURAL nork (NN conrollrs hav found many succssful alcaons n h Arosac ndusry. Nural N nork asd av flgh conrollr for uncran nonlnar dynamcal sysms lmna h nd for offln gan unng and schdulng mhods as ll as rduc h mony and ffor ndd o dnfy and modl sysm dynamcs. A nural nork can hough of as a aramrzd class of non-lnar mas. Mullayr fdforard nural norks ar caal of aromang any connuous unknon nonlnar funcon or mang on a comac s 6. Furhrmor Nural Norks hav onln aaon caals hch can usd o dsgn conrol las ha can handl uncrans and nonlnars n sysm dynamcs and h nvronmn. Adav nural nork conrollrs hav n ald o roo arm manulaor conrol y Ls Km and ohrs 6. Nural Nork conrollrs ar naural choc for Unmannd Aral Vhcl (UAV sysm conrol du o hr caaly o a o varyng dynamcs as of mlmnaon and rousnss rors. Usng Nural Nork av flgh conrollrs n UAV conrol sysms dsgn also rducs h ffor rqurd n modlng and flgh sysm dnfcaon of h flgh laform. Cals Johnson Kannan and ohrs hav mlmnd Nural Nork augmnd aroma modl nvrson conrollrs h sudo conrol hdgng succssfully for conrol of varous * Grua Rsarch Asssan Grsh.Chodhary@gach.du. Assosa Profssor Erc.Johnson@gach.du Amrcan Insu of Aronaucs and Asronaucs Coyrgh 7 y Gorga ch. Pulshd y h Amrcan Insu of Aronaucs and Asronaucs Inc. h rmsson.
fd ng as ll as roary ng UAV sysms h sgnfcan nonlnars and sauraons n h conrol loo -5. hs conrollrs hav rovn succssful vn n rformng hghly dmandng manuvrs rqurng fas aaon. h ncrasng dmand on rcson agly cooraon and safy n auonomous arosac sysms hr mvaran naur and h nrcacs of ral-orld oraons lm h ffcvnss of conrol archcurs mloyng only lor-lvl or sy-sa mhodologs. hl dndng on sound conrol hory concs s rmly moran; s clar ha ru vancs can only m y nsurng nllgnc aaon and long rm larnng n h cor conrol and dcson-makng archcur. Hovr h currn av las for nural norks (.g. -7 only us h nsananous knoldg for aaon. Hnc h currn av las hav no ral long rm mmory and hnc do no h any mrovmn n rformanc hn rformng manuvrs ha hav n rformd rvously. hs lmaon can also land y nong ha h rank of h NN gh dynamc s alays a mos on hn only currn daa s usd for NN ranng. If could ossl o augmn hs dynamcs o of a hghr rank or vn full rank hn h donal dgrs of frdom could usd o mrov h rformanc of h conrol sysm. In hs ar roos a novl aroach o h dsgn of Nural Nork av conrollrs hch ovrcoms h rank- lmaon and hs h rors of sm gloal larnng. accomlsh hs y comnng currn onln larnng algorhms h a ackground larnng mhodology hr h ackground larnng la s a rojcon of h currn larnng la no h nullsac of h currn larnng. sho ha on such mhod hch uss Lnar n h Paramr NN guarans ounddnss of all sgnals usng a Lyaunov saly aroach. Smulaon rsuls ar analyzd n ordr o valua h rformanc of h n aroach. Our ork ulds uon h ork of h scond Auhor and Sung-Mn Oh 8. II. Nural Nork Basd Adav Conrol A rf lanaon of a asln dynamc nvrson asd onln larnng Nural Nork asd av conrol sysm s gvn hr. h rr s rfrrd o [-7] for dald lanaons. A. Aroma Modl Invrson asd Adav Conrol Consdr a sysm of h form: f ( δ hr ( n δ R. nroduc a sudo conrol nu hch rrsns a dsrd ẋ and s cd o aromaly achvd y h acuang sgnal δ n h follong mannr: ẋ ( hr 3 f ( δ (3 In a modl nvrson schm h acual conrol nu δ s found y nvrng Eq.(3. Hovr snc h funcon s usually no acly knon or hard o nvr an aromaon s nroducd as: f ( δ 4 f ( ˆ δ. (4 Basd on h aromaon aov h acuaor command s drmnd y an aroma dynamc nvrson of h form ˆ ( 5 δ cmd f. (5 hs rsuls n a modlng rror n h sysm dynamcs ( δ 6 hr (6 Amrcan Insu of Aronaucs and Asronaucs
( δ δ ˆ( δ 7 f ( f (7 fˆ s chosn such ha an nvrs h rsc o δ ss. Fgur dcs a mor scfc h aromaon form of an aroma dynamc nvrson-asd Nural Nork av conrollr ncludng acuaor a PCH comnsaon. h fˆ ˆ δ δ rm rm c ˆ Rfrnc Modl crm f δ cmd Nonlnar Acuaor Dynamcs δ f rm Nural Nork δ Adaaon La d PD comnsaor Fgur Nural Nork Adav Conrol usng Aroma Modl Invrson and PCH comnsaon Basd on aromaon n Eq.(4 h acuaor command s drmnd y an aroma dynamc nvrson of h form ˆ ( 8 δ cmd f δ (8 hr s rmd h sudo-conrol and rrsns a dsrd ẋ ha s cd o aromaly achvd y δ cmd. hs dynamc nvrson assums rfc acuaor dynamcs and hnc dos no ak no accoun ffcs such as acuaor sauraon or ra lmaon. As a rsul h acual command may no qual h achvd command du o h characrscs of h acuaor (hch may furhr vary h m. Incororang h acuaor dynamcs n h acual nonlnar nvrson rsns ohr dffculs arsng du o varous dsconnuous acuaor characrscs such as acuaor sauraon dscr (quanzd conrol ra lmaon m dlays and unmodlld dynamcs. h Nural Nork lmn ll am o a o hs characrscs vn hn mgh no dsral o do so. Psudo Conrol Hdgng (PCH 4 s on mhod ha can handl hs rolm. hs mhod rvns h av lmns of h av conrol sysm from ryng o a o a class of unand lan nu characrscs. h sudo-conrol hdg sgnal ( h s dfnd as h dffrnc n h commandd sudo-conrol nu and h acually achvd sudo-conrol nu. hs dffrnc s comud y usng an sm acuaor oson asd on a modl or masurmn. hs sma s hn usd o g h sudo-conrol hdg as h dffrnc n commandd sudo-conrol and h sm acual sudo-conrol. 3 Amrcan Insu of Aronaucs and Asronaucs
ˆ( ˆ( ˆ ˆ 9 h f δ cmd f δ (9 Fgur llusras h mannr n hch sudo conrol hdgng can achvd for a oson and ra lmd acuaor. h PCH sgnal s nroducd as an don nu no h rfrnc modl forcng o mov ack. Hnc h rfrnc modl dynamcs h PCH com: ( rm crm rm rm c c h hr c c ( rrsn rnal commands. h nsananous sudo-conrol ouu of h rfrnc modl n h fd-forard ah s no changd y h us of PCH and s crm. crm frm ( rm rm c c ( B. Modl rackng Error Dynamcs h oal sudo-conrol sgnal for h sysm s no consrucd y h hr comonns: crm d hr ( crm s h sudo-conrol sgnal gnr y h rfrnc modl n Eq. ( d s h ouu of a can lnar comnsaor and s h Nural Nork aaon sgnal. h lnar comnsaor ( d dsgnd usng sandard lnar conrol dsgn chnqus hch rndr h closd loo sysm sal hs nclud P-D(Prooronal-Drvav comnsaon or LQR (Lnar Qurac Rgulaor comnsaon. For h scond ordr sysm PD comnsaon s rssd y 3 d [ K K d ] hr h rfrnc modl rackng rror s dfnd as: 4 rm rm h modl rackng rror dynamcs ar found y dffrnang : (3 [ ] 5 A B ( δ f ( δ fˆ( δ hr (4 (5 I 6 A B K Kd I 7 8 hr oh K and K d ar ral osv marcs. h h aov form A s Hurz. hn on assums ha h lan nus δ ar acly knon hn h rror dynamcs can rrsnd as: A B hr ( δ [ ( δ ( δ ] f ( δ fˆ( δ Is rgardd as h modl rror o arom and canclld y dfn h sgnal r as: (6 (7 h ouu of h Nural Nork. n r PB R 3 (8 4 Amrcan Insu of Aronaucs and Asronaucs
hr P n n R s h osv dfn soluon o h Lyaunov quaon: 9 P PA Q A (9 C. Nural Nork Basd Adaaon Sngl Hddn Layr (SHL Prcron NNs ar unvrsal aromaors. hy can aroma any smooh nonlnar funcon o hn arrary accuracy gvn suffcn numr of hddn layr nurons and nu nformaon. h nu ouu ma of h SHL NN can rssd n comac mar form as: hr h follong dfnons ar usd: n3 ( V ( V R ( v.. n R v ( n ( n 3 4 v ( z ( z ( z.. ( n zn R ( n ( θ v V v n θ n θ θ θ n n θ n n n n n n3 R R ( n n ( n n3 hr s h nu vcor s h sgmodal acvaon funcon vcor V s an nu layr o hddn layr s h NN ouu. and gh mar s a hddn layr o ouu layr gh mar and ar nu ass ha allo h hrsholds θ v and θ o ncludd n h gh mar V and. n n and n 3 rrsn h numr of nu hddn and ouu layr nods rscvly. Inu o hddn layr nuron s: v (3 (4 5 Amrcan Insu of Aronaucs and Asronaucs
5 6 h sgmodal acvaon funcon usd s: z V j z z n ( z j n R a j z j Dals on Nural Nork hory can found n rfrnc [67]. (5 (6 III. Onln Larnng NN Adav Conrol and Rank- Lmaon Nural Norks ar consdrd o clln funcon aromaors ha s hy can aroma any smooh nonlnar funcon hn a comac s o arrary accuracy gvn nough numr of nu layr nurons and ror nus. rsn a rf roof for h sandard ackroogaon mhod of NN onln gh aaon. h follong onln av la guarans h ounddnss of all sgnals 6 7 r V r Consdr a osv dfn Lyaunov candda of h form: v (7 8 L( V P r{ ( } r{ ( V V } 9 hr * and (8 * V V V hr * L( V ff and V V and L( V > ohrs furhrmor L( V as V v * and V * dno h dal ghs for h NN. No ha: Hnc h Lyaunov candda s rally unoundd. akng h m drvav of h Lyaunov candda hav 3 L V Q r( r{ ( ( } r{ ( V V } Eandng h NN modl cancllaon rror 66 hav (3 v 3 * * ' ( V ( V ( V ( V V H.O.. (3 Assumon: In h aov quaon H.O.. rrsns hghr ordr rms hch om for h sak of clary. I s ossl o oan ounds on h H.O.. hch changs h aaon la accordngly 34. hn 3 L V Q r{ ( r } r{ V ( V r } ( (3 v * (9 6 Amrcan Insu of Aronaucs and Asronaucs
By sng: 33 r 34 v r hav 35 L( V Q < 36 (33 V (34 (35 Esalshng Lyaunov saly no ha quaon 35 can rn as a src nqualy asd on assumon. Hovr f h H.O.. rms of quaon 3 ar consdrd quaon 35 dos no rsul n a src nqualy and h LaSall horm and h Barala s lmma nds o usd for ascranng Lyaunov saly. Solvng Eq. (3 and Eq(33 ylds h av las r V r v (36 Fac : Evry mar of rank on has h sml form Auv hr A s s vcor. m n m mar u s n vcor and v R r ( n3 R hn ( Usng h aov fac from lnar algra s asy o s ha snc n and ( s alays a mos a rank on mar. Smlarly V s also a mos rank on caus n v R and ( n r R. Hnc vn hough h NN gh aaon marcs hav a mar form hr rank s alays a mos on. hs may affc h rformanc of h NN la. In ordr o ovrcom h rank on lmaon s roosd o ulz onln as ll as ackground larnng y usng currn as ll as sord daa n h NN gh aaon rocss. In hs ar sho ha usng hs aroach ylds r rformanc snc maks us of all h nformaon avalal for h aaon uross. also sho ha us of currn as ll as sord da mrovs gloal larnng havor and guarans long rm larnng of h aaon. IV. Comnd Onln and Background Larnng Adav Conrol A. Choc of h ackground larnng la Any larnng ha dos no mmdaly affc h nsananous larnng (ha s dos no drcly affc has h follong form: 37 38 v (37 V (38 hr h suscr dnos h ackground larnng la. hs condon nsurs ha h ackground larnng aaon la s orhogonal o h undrlyng vcor sac of h nsananous larnng. hs ndcas ha h orhogonal rojcon of any NN larnng la can usd as a ackground larnng la. In hs ar consdr h orhogonal rojcon of h larnng la for h and h V mar ono h orhogonal susac of h san of quaon 37 and quaon 38 n h follong form I 39 (39 7 Amrcan Insu of Aronaucs and Asronaucs
4 V V V I V V V (4 4 hr h suscr dnos any sual NN larnng la. I s o nod ha quaon 39 and quaon 4 ar also h omal soluons o h Lagrang s consrand mnmzaon mhod y mnmzng V V corrsondng o h Fronus norm 4. On rasonal choc for h ranng of h ackground larnng la s o ran h NN usng sord daa along h currn daa n ordr o mrov gloal larnng havor of h NN and guaran long rm aaon. In h roosd mhod hs s achvd y usng currn daa as ll as a sord hsory sack 8. Boh daa ar usd concurrnly n h aaon rocss. h comnd conrol la hn has h form: 4 I And (4 43 V V V V I V V (43 V 44 B. Slcon of daa ons for ackground larnng Slcon of NN nus for ackground larnng s no a rval rolm snc hs nus mac h gloal larnng rors of h comnd onln and ackground larnng aroach. Dald dscusson on som mhods of slcng daa ons can found n [8] suffc hr y mnonng ha slc daa ons ha sasfy h follong crron: ( ( Hr h suscr dnos h nd of h las daa on sord. h aov mhod ascrans ha only hos daa ons ar slcd ha ar suffcnly dffrn from h las daa on sord. Onc h daa ons ar slcd h modl rror rlang o ha daa on mus osrvd and sord. achv hs y usng an onln mlmnaon of omal fd on smoohng. In h gvn framork of av conrol h modl rror for h h daa on s 45 ( ( Usng quaon 5 h aov can rssd as: > ε (44 δ f δ fˆ( δ (45 δ 46 (. (46 Onc a on s slcd for sorng h fd on smoohng algorhm s n unl a suffcnly accura sma of ẋ s oand. Usng hs sma and sord valus of an sma of h modl rror for h h daa on s oand. h rsdual sgnal ha s usd n h ackground larnng aaon s: r ( V 47. (47 8 Amrcan Insu of Aronaucs and Asronaucs
Consdrng quaon 6 s sn ha h rsdual sgnal n hs form for h ackground larnng NN ams o rduc s h dffrnc n h currn sma of h modl rror and a sord sma of h modl rror. Hnc on can say ha y usng hs mhod h ackground larnng NN ams o a h and V marcs of h NN n such a ay ha h modl rror for mull daa ons s smulanously rducd. Alrnavly h rsdual sgnal r can formd y smulang h rror dynamcs 8 y ngrang quaon 7 for h h daa on and hn usng quaon 8. C. Aroma modl nvrson av conrol usng Comnd nsananous and ackground larnng NN no rsn a novl NN gh ranng la ha uss oh currn and sord daa for a Lnar In h Paramrs (LIP NN. A LIP has h sml form gvn y: 48 V R n3 ( ( (48 hr s an arora ass funcon. h nf of usng a LIP NN s ha only h mar of quaon 4 conanng h ghs of h NN nds o und. horm : Consdr h sysm n quaon and h nvrng conrollr of quaon 5 h follong comnd onln and ackground av las for a LIP NN of quaon 48 guaran h ounddnss of all sgnals: 49 r ki I 5 h h sgmodal acvaon funcon dfnd as: hr ˆ (49 (... n ( n ( r n ( n ki I R (5 ar found from quaon 6 h z and k s a rdfnd nonzro consan. Proof: h orhogonaly of h oraors n quaon 39 can rssd as 5 Also no ha I (5 5 And * ˆ( ˆ( ki I ( k (. (5 53 * ˆ( ˆ( ki I (. (53 9 Amrcan Insu of Aronaucs and Asronaucs
Amrcan Insu of Aronaucs and Asronaucs hr * V * dno h dal NN ghs. h rror dynamcs for h h daa on can rn as: 54 [ ] ( ( δ δ B A (54 Consdr a Lyaunov candda of h form: 55 ( { } k r r P P V L ( (55 56 > as L furhrmor ohrs L and and ff L ( ( ( * (56 h las condon s h rally unoundd condon. akng m drvav of h Lyaunov candda along h rajcory of sysm dscrd y quaon 54 hav: 57 ( ( ( { } r k r r Q r Q V L.... ( (57 Usng quaon 5 and quaon 53 h aov quaon can rn as: 58 r I ki r r k k r Q Q V L ( (58 hn y sng 59 r k k (59 And 6 r I ki (6 And nong ha 6 (6 arrv a h uda la gvn n quaon 49. Furhrmor h m drvav of h Lyaunov candda rducs o: 6 ( R < Q Q V L n (6
Snc L > and L < h NN av la gvn n quaon 49 guarans ounddnss of all sgnals asd on h Lyaunov aroach for h conrol sysm of quaon 5. Rmark :. hn a daa on s dd h dscr chang n h Lyaunov funcon s zro.. hn a daa on s drod h n chang n h Lyaunov funcon s ngav. 3. Du o and h sysm sgnals ar all oundd n h sns of Lyaunov saly. Also no ha snc h nonzro consan k can arrarly chosn s ossl o choos small nough k such ha quaon 6 forms an arrarly clos aromaon of quaon 4 h h av la of quaon 59. Mhod : Consdr h sysm n quaon and h nvrng conrollr of quaon 5 h follong comnd onln and ackground av las for h SHL NN of quaon ar roosd: 63 r I ( V r (63 64 V V V V r I V r ( V V V. (64 V. Dmonsraon of conc for h av conrol of an nvrd ndulum o llusra h conc of ackground larnng augmnd av conrol rsn a sml aml h a lo dmnsonal rolm. h nvrd ndulum sysm dscrd y h follong quaon s o conrolld: 65 sn( δ. (65 hr δ h acuaor modl dscrs h oson of h ndulum h las o rms ar rgardd as unknon and rrsn a sgnfcan modl rror. assum ha a masurmn for ẋ s no avalal and ha h sysm ouus ar corrud y Gaussan h nos. Consqunly an omal fd lag smoohr s usd o sma h modl rror of quaon 6 for ons suffcnly far n h as. h rfrnc modl dsrd dynamcs ar ha of a scond ordr sysm. us a hsory sack of 5 daa ons rlacng h olds daa on as nr ons ar slcd. Background larnng on slcon s asd on quaon 44. h ackground larnng mhod usd s ha of horm. Fgur shos h rformanc of h NN asd av conrollr for h lan n Eq. 65. Squar avs ar commandd a rgular nrvals. No consdral mrovmn s sn ovr h san of h nu command. hs ndcas ha h av conrol has no long rm mmory and dos no sho r rformanc hn rsnd h a ask ha has ncounrd for. Fgur 3 shos h hsory of h NN gh aaon h forgng naur of h av la s clarly sn. Amrcan Insu of Aronaucs and Asronaucs
-r.5.5 Poson acual rf modl Do (-r/s 5 5 m (sc Angular Vlocy.5 -.5 acual rf modl - 5 5 m (sc Fgur Comarson of sas only onln aaon. -. -.4 -.6 5 5 m (sc 5-3 v V V -5-5 5 m (sc Fgur 3 NN gh aaon and V only onln aaon Amrcan Insu of Aronaucs and Asronaucs
Fgur 4 shos h sa comarson hn ackground larnng s usd hl Fgur 5 lcly shos h voluon of oh oson and angular vlocy rror. I s clarly sn ha h conrollr rformanc mrovs hrough susqunly r commands hch hs long rm larnng n h av lmn. o furhr characrz h mac of ackground larnng consdr h follong o crrons:. Comaravly quckr convrgnc of NN ghs o consan valus (Fgur 6. hs havor ndcas ha h NN s al o a o h unknon modl rror fasr hn ackground larnng s usd.. Convrgnc of quaon 47 for ach sord daa on (Fgur 7. hn ackground larnng s on h dffrnc n h sord sma of modl rror and h currn sma of modl rror rducs h m. hs ndcas ha h NN s concurrnly ang o varous daa ons hng smgloal larnng..5 Poson acual rf modl -r.5 -.5 5 5 m (sc Angular Vlocy.5 Do (-r/s -.5 acual rf modl - 5 5 m (sc Fgur 4 Comarson of sas h ackground larnng mhod 3 Amrcan Insu of Aronaucs and Asronaucs
.6 Poson Error Err (-r.4. -. 5 5 m (sc Angular Ra Error.5 DoErr (-r/s -.5 5 5 m (sc Fgur 5 Poson and angular ra rror h ackground larnng av conrollr.5 -.5-5 5 m (sc.5 v V V -.5 5 5 m (sc Fgur 6: NN aaon ghs and V h comnd onln and ackground larnng mhod 4 Amrcan Insu of Aronaucs and Asronaucs
Dffrnc n sord sma of modl rror and currn sma of modl rror.5 m.5 -.5 - -.5 5 5 -sm modl rror Fgur 7 Dffrnc n sord sma of modl rror and currn sma of modl rror h ackground larnng on VI. Imlmnaon on a hgh fdly flgh smulaor h Gorga ch UAV la manans a hgh fdly Sofar In h Loo flgh smulaor coml h snsor mulaon dald acuaor modls dsuranc smulaon and a hgh fdly dynamcal modl. Our arg laform s h Gorga ch GMAX Unmannd Aral Sysm (UAS hch s asd on h vrsal YAMAHA RMAX hlcor (Fgur 8. h follong rsuls hav n smul on h GMAX SIL smulaon. Snc hs s a hghr dmnsonal rolm hory ndcas ha h mac of ackground larnng should mor sgnfcan. Fgur 8 h Gorga ch GMAX n landng auo aroach h GMAX uss an aroma modl nvrson av conrollr characrzd quvalnly o h dscron n scon II a dald dscron can found n rfrnc and rfrnc 3. 5 Amrcan Insu of Aronaucs and Asronaucs
command four succssv forard s nus h arrary dlay n any o succssv ss. h rformanc of h nnr loo conrollr s characrzd y h rrors n h hr ody angular ras (namly roll ra ch ra q and ya ra r. As h roorcraf acclras and dclras n forard s nus h ody roll ra q domnas. Fgur 9 shos h rformanc of h nnr loo conrollr h only nsananous aaon n h NN. I s clarly sn ha hr s no consdral mrovmn n h roll ra rror as h conrollr follos succssv s nus. Error n r/s Error n q r/s Error n r r/s.5 Evoluon of nnr loo rrors for succssv forard s nus -.5 9 3 4 5 6 7.5 -.5 9 3 4 5 6 7.4. -. 9 3 4 5 6 7 m sconds Fgur 9 Evoluon of nnr loo rrors for succssv forard s nus h only nsananous aaon h forgng naur of h conrollr s furhr characrzd y h voluon of NN ghs n h and V marcs of quaon. Fgur and Fgur clarly sho ha h NN ghs do no convrg o a consan valu n fac as h roorcraf rforms h succssv s manuvrs h NN ghs osclla accordngly clarly characrzng h nsananous naur of h aaon. On h ohr hand hn oh nsananous and ackground larnng NN larnng la of Mhod s usd a clar mrovmn n rformanc s sn characrzd y h rducon n ch ra rror afr h frs o s nus. Fgur shos h rformanc of h ackground larnng augmnd conrollr. h long rm aaon naur of h ackground larnng augmnd av conrollr s furhr characrzd y h convrgnc of NN ghs n h and V marcs of quaon. Fgur 3 and Fgur 4 sho ha hn ackground larnng s usd along h nsananous larnng h NN ghs do no h oscllaons and nd o convrg o consan valus. hs ndcas ha h NN larns fasr and rans h larnng vn hn hr s a lack of rssn caon. hs ndcas ha h comnd nsananous larnng and ackground larnng conrollr ll al o rform r hn rformng a manuvr ha has rvously rformd a clar ndcaon of long rm mmory and sm-gloal larnng. 6 Amrcan Insu of Aronaucs and Asronaucs
.5 Evoluon of NN ghs mar (nsananous aaon only.4.3 NN ghs mar.. -. -. 9 3 4 5 6 7 m Fgur Evoluon of NN ghs V mar h only nsananous aaon.8 Evoluon of NN ghs V mar (nsananous aaon only.6.4 NN ghs V mar. -. -.4 -.6 -.8 9 3 4 5 6 7 m Fgur Evoluon of NN ghs mar h only nsananous aaon 7 Amrcan Insu of Aronaucs and Asronaucs
Error n r/s Error n q r/s Error n r r/s. Evoluon of nnr loo rrors for succssv forard s nus -. 9 3 4 5 6 7.5 -.5 9 3 4 5 6 7.5 -.5 9 3 4 5 6 7 m sconds Fgur voluon of nnr loo rror h comnd nsananous and ackground larnng conrollr 4 Evoluon of NN ghs V mar (h ackground larnng 3 NN ghs V mar - - -3 9 3 4 5 6 7 m Fgur 3 Evoluon of NN ghs V mar h comnd nsananous and ackground larnng 8 Amrcan Insu of Aronaucs and Asronaucs
5 Evoluon of NN ghs mar (h ackground larnng 4 3 NN ghs mar - - 9 3 4 5 6 7 m Fgur 4 Evoluon of NN ghs mar h comnd nsananous and ackground larnng VII. Concluson hav roosd and a novl aroach o h dsgn of NN asd conrollr hch ulz onln as ll as ackground daa. h n mhods hav h follong vanags:. Long rm larnng: h comnd onln and ackground larnng h av la s al o ran long rm larnng. hs allos h av la o rform r hn ncounrs a ask ha has ad o for.. Sm Gloal aaon: By carfully choosng ackground larnng daa ons and sorng hm n a hsory sack s ossl o mamz h dynamc nvlo ha h NN av lmn s ad o. 3. Incrasd Rousnss: Snc h nork aaon s dndn on mor han on daa on s lss snsv o occasonal oulyng sgnals. 4. Ovrcomng h Rank- lmaon: h roosd aaon la has hghr rank han h uny hs rsuls n r rformanc. hav rovdd a roof of ounddnss of all sgnals for a ackground larnng LIP NN larnng la. In h fuur sh o and h sco of hs ork y ndng our hory o ncomass varous ohr ranng schms and NN ys. also nnd o ncorora rousnss analyss and analyz h snsvy of h n aaon las o h slcon of h hsory sack daa ons. Acknoldgmns h auhors acknoldg h rvous ork of Sung Mn Oh 8 h h scond Auhor n hs ara. hs ork as suord n ar y NSF #ECS-38993. 9 Amrcan Insu of Aronaucs and Asronaucs
Rfrncs Soonr J.. Maggor M. OrdonzR. and Passno K..M. Sal Adav Conrol and Esmaon for Nonlnar Sysms: Nural and Fuzzy Aromaon chnqus John ly and Sons. Johnson E. Kannan S. Adav Flgh Conrol for an Auonomous Unmannd Hlcor AIAA GNC Monrry CA. 3 Kannan S. K. and Johnson E. N. Adav rajcory Basd Conrol for Auonomous Hlcors AIAA Dgal Avoncs Confrnc Oc. 4 Johnson E. N. Lmd Auhory Adav Flgh Conrol Ph.D. hss Gorga Insu of chnology. 5 Km Byoung S. Cals Anhony J. Nonlnar Flgh Conrol Usng Nural Norks AIAA-994-3646 Augus 994. 6 Km Y. H. Ls F.L. Hgh Lvl Fdack Conrol h Nural Norks orld Scnfc Srs n Roocs and Inllgn Sysms Vol. orld Scnc Pulshng Co. P. Ld. 998. 7 Ls F. L. Nonlnar Nork Srucurs for Fdack Conrol Asan Journal of Conrol Vol.. 5-8 Dcmr 999 8 Johnson Erc N Oh Sung-Mn Adav conrol Usng Comnd Onln and Background Larnng Nural Nork AIAA CDC 4 USA. 9 E. Johnson M. ur and A. u Gorga Insu of chnology Alana GA; S. Kannan Flgh Rsuls of Auonomous Fd-ng UAV ransons o and from Saonary Hov AIAA-6-6775 AIAA GNC 6 H. Chllaona V. Nonlnar Dynamcal Sysms and Conrol A Lyaunov Basd Aroach Prrn 6 coyrghd y h Auhors. Khall H. Nonlnar Sysms Prnc Hall USA 3 don Dcmr 8 Gl A. Ald Omal Esmaon MI rss 974. Amrcan Insu of Aronaucs and Asronaucs