Tr^n Thj Ngan va Org Tap chi KHOA HOC & CfJNG NGHE 90(02): 93-99 P I U O N G P H A P X A P XI N G A I N H I E N GIAI M O T LOAI BAI T O A N D I E l KHIEN C H I A TICH PHAN BOI \ A L NG DLNC; Tr3n Thj Ngan Tran Manh Tuan Tnr&ng Dai hoc Cdng nghe Thdng tin c< I riiyen ihdng DH Thai Xguyi^ 1(')M l A l Bai loan dieu khien dii dugc nhieu tac gia va ngoai nudc quan tam giai quyet biing nhieu phuong phap khac Trong dd cd nhti-ng bai loan dieu khien chiia cac tich phan bpi Viec giii mpt bai loan chira tich phiin bdi ludn cd dp phirc tap tinh loan cao giai bang cac thuat giai thdng thirdng (sir dung cac cdng cu giai tich) \'oi viec ap dung phucmg phap xap \i ngiiu nhien cac lich phan bpi dupc giai vai dp phirc lap nho hon nhieu Til' khda: Bdi todn dii'it khien lich phdn bi)i dd phirc lup linh lodn, giai tich lodn hgc, ly- thuyet dd lin cdy MO DAU Chp vccto a = {ci if.)eR"c6 cac thank pluin kiru han va vccto h = (h^ h^^)eR" vdi Ciic pluin nluin die gia tri cd the la -';("):= Z C ' ^ ' + "-"-'*'^') , +| \-a^^-~-^ -r ~\ ^ | —> inf (/e U Q,Uc vd kiin Lien quan tcii ckung la liinh hop inir (1.2) |a.b) cac thdi diem / „ T s R vit ldp U cac hiim kang uing kkuc tren [/„ T] xac dink lan da cko \/i = ]^ liipl dudi diiim: |.Y:=(.V, \a.h):=\ v„) e / ? " : - z : < (/ I ^' " ; ls, « khiyi) ,, ^ , , ^ , da eho / „ < / < r ; - , ( / „ ) = r„ ^ • ( I J ) " , Trong dd: : U:=®U, , -' ^ pyx):=\, \p{x, „,(.) = »,( (7):=l|_,,|(.):[/„.ri| U, i!-\ l,(i) I , - , ' ' khiveV i,(0.|j/3||) / - I I'd / (0 ) : / ? ' Vii,eR' i = \+n (2.S) - V (I c I,(0,) R ' ; : \ ;; I r/ (C; „ ; ;; l„(0 ) ;;-/ I'd thgc sir giant vdi i I llic If -o II - (,?,((?,•) '. (()' = !„() (i((;):- );/1; pill) - - 'IP\\ o{ii)>O.Vii VH ul, (a.h) R" \/it c R' Irong V;; e R": \il>iu)du c R" V.v £ ( < ; / ' ) lap vccio ngiiu nhien r : - ( r^ I r , ) £ R" co ham mat dd (ddng tkdi) lii (p(li).ii c R" va kip qua trink ngiiu nkien dudi dang: :(0) \: (0,) : ,{u„ \ii(0).0 & Ri^ , ).j„ (;/))e «" c R" 3(7 0^): 11 [0 kht T < ' ' khir >() )lit din nhdi cua hi ' 9/ /• (2.11) Chdy 2.1: T.i nhgn tliax rimg: cd thi thu hep mii'n dp dung Kki dd ta tku dirpe cac ket qua sau: Rd di' 2.3: \eu cdc dieu kien (.Ai-(Ci ihoa mdn llii la cd: E\:{(i)\- ihri/c thiinh miin R' ' ,() | cua dii'u kii'ii i2 I4*t Qlf) \gliTa Id la cd the llun diiu kien ndi tren gia lliiel (D) htri dieu FiOi-^OeR kii'ii salt i2 I2i \ F\^'{I') Fid) , -rii-iu ;; ) e R (O xac > \0 \ pill, ): (; sd R - ((;, true ;;,, u V il ham • ( - X ) phij thudc tham bicn 11, ) fc/?' ' lil ddi )d u V C; fc ^ M ^ ) T ( ( ) : = m i n / ; (C; ) > i L O y() \:d;; /;;: = 0;; - y„ A [:" pill ni • II ) = pill in-i) ).r'ii = (it it ^aii cho: ^ ( \\p\\ neu gia tkiet > ( It dink (B) la cdn bd sung t k e m gia tkiet ( D ) dudi diiy: (l))-lkani p (2 IS, Kilt cd llii' dira mdl ddu hieu du cuu diiu kiin niiy diriri dgng: 0& (2.") vil tkam so u ' ) ^ R' - (I ] \ p (w )du (2,15) > 0,, 0" ) )e^ -U'i\.\\p\ 0"'" = 0'" < / < - ^ ''-'"" ' M; n (2 I9| '.'He R I) - (I^ t r o n a dd: vecto ngau nhien d (2,15'^) 96 \/ 'c b R' la dav sd tkoa man d i i u kien: laliiyv Fran Thi Ngiin vd Dig Tap chi KHOA HOC & CONG NGHE 90(02): 93 - 99 Tuana tu < a < / nen ta cdn cd; /,„>0,V/77>l;Z/„, = +x.Z/: \'''{0,)\ +\F (Ot " •^ ' i i •• i _ \\r-in\'l^ T T"A , w/i D" => \\F {0)\\< \^n-v :> = consl vOeR » ^ '» ^'('9) ^ ^., ; , , J., ,, ., ^-, '"^"i;"'' j a h,(., | ,ng: lu cae dieu kicn (2.2,->) (2,20) (2 17) (2 13) (2.12) cd tke suy su kdi tu lice cua dav ngkiem xap xi ngiiu nkien I ; •,.•" ' , , " , , i-' p j I ve ngkiem cua he phirong Irinli koi quy (2.14): ^ 'i'Ti 0'" = iF \ = \ ^ f j jim C;'" = i^ * | = V / = I H- /; (2 26) """"s" ^o kc pkuang trink kdi quv urong duong vol lie (2 9) (Iheo bd de 3) nen ngkiem (F ndi tren cimg la ngkiem iiluit eua (2.'^) Boi viiy lir (2.14K (2.2 I) va tinh lien tue cua eac ham g, (theo gia thict (C)) (2.22) la CO 2- D '^' ,1',"^ ^'' ' ""'^ ' " ' ' „ ; ,, , , ,, tronu (xem Bo dc 2,2) e(a.h) la ,•.",,,.; , ^, , dieu kkien loi uu dimg (2.1) cua bai toan ( ) , i 4) NghT;, |;\ ,2 2^2) dupe ckimg mink Cudi cinm tir tinh lien tue cua die kam - /-\ / ( ( U / = + " (1,8) (1.9) la suv ,||,|T |j^.„ ^^^ ciia iia^ j{p] tropg (23) Kki ^I'^-laeo Tran Thi Ncan va Di'Z ] = PW'm Tap chi KHOA HOC & CONG NGHE =e']