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 khi giai bang cac thuat giai thdng thirdn
Trang 1Tr^n Thj Ngan va Org Tap chi KHOA HOC & CfJNG NGHE 90(02): 9 3 - 9 9
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 L O A I BAI T O A N
D I E l K H I E N C H I A T I C H P H A N 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^n
1(')M l A l
Bai loan dieu khien dii dugc nhieu tac gia trong va ngoai nudc quan tam giai quyet biing nhieu
phuong phap khac nhau 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 khi 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 - ' ; ( " ) : = Z C ' ^ ' + " - " - ' * ' ^ ' )
pluin kiru han va vccto h = (h^ h^^)eR" , -r ~\
vdi Ciic thanh pluin nluin die gia tri cd the la + | \-a^^-~-^ ^ | —> inf (/e U
vd kiin Lien quan tcii ckung la liinh hop inir
|a.b) cac thdi diem / „ T s R vit ldp U cac
hiim kang uing kkuc tren [/„ T] xac dink lan
liipl dudi diiim:
Q,Uc
(1.2)
z,(t) = p.(i)'i,il) i,<i<T:z,{IJ^z,
da cko \/i = ]^ i!-\
|.Y:=(.V, v„) e / ? " : - z : < (/ I ^ , ,
\a.h):=\ ^ ' " r „ ( n = C)(i^, ,;/,,,;0-"„(/),
< V, < h < +'Z' V; = I ^ ; ; ^ , da eho
; , , , , / „ < / < r ; - , ( / „ ) = r„
f • = i n u u ; 7 ;=max/i l , ( i ) ^
l s , - - « I , - , ' ' • ( I J )
I khiveV , , " , Trong dd:
: U:=®U, , ^
0 khiyi) -' pyx):=\, \p{x, v, vj^o-.v,
U,
„,(.) = »,( (7):=l|_,,|(.):[/„.ri|
-^{0.1(1 a, <0, </i, J
V; = I ^;;
V.v, 6 | ; T] \<i<ir
f I " \
(.JUi ;;„ ,;.v„):=| j/l(.v)fli;,(.v,;^,)c/v,
( I T ) _ ,_
Xci biii loan dieu khien tal dink Lagrange vdi |' | 75( v i[~[ (/.v, :=cj{0y,xj
kiim dieu kkien ii = {ii, ii„)e I dugc ••, •- '
tham sd kda tkeo cic tkam sd
0 =(()^,.()Je(ii.h)
U(u, i„ |);= I (Jill, ;;„ i;.v„)c/.v„
' ' ' = ( ^ ^,,-1 ) e ( X ) : , ( ' ' , ^ ) ^ a vdi tkdi J ^ I \piy)dx„ clx„ = '\qiO„:x„)dx„:=i,AO)
gian dicu khidn (r„.7") cd tke ki vd han sau; i ».,.'
/,./ ii'tS'J II4II 4.-4 t'.mall ttngan a icllt edu rn
(1.4)
\'di cac aia thiet sau dugc thda man;
93
Trang 2Tran Thi Ngan i a Dig Tap chi KHOA HOC & CONG NGHE 90(02): 93-99
( \ ) - Ham da cho p\R' ->R la duong
hen tue vii kha uch (theo nghia Lebcsgucl
tren [a.b):
/ 2 ( \ - ) > l ) -ixela.by p&C[a.b)\
j /'(-v)J.v -:\\p ,^
( 1 5 )
(B)- ( ac tham sd a := ( a , cc, )thoa man:
0 < a < | | 7 r | | :=^ \\p~\\,
1 1 ' II I I ' 11 / I ,; /I I
V / = l ^ / ; - l 0 < a < 1
(1.6) Khi dung phuang phap true liep de giai biii
,in dieu khien i 1,2) ( 1 1 ) ta cd the chuven
no vc biii loan quy koack
Jill ^ ( / , ( ( M - a
0 e (a.h): I (I) ) - - /,((-', ) I < ; < ;;
(!.'')
I (II I I I f j " I /'"(-'' >''-'' •
V (^ e ( i/ /) ) 1 < / < ;?
(1.8)
\if(U :.v k/.v
/
(0)'.'-iTlO I
I \]nx)dx •'(? e.(u.h)
(1.9)
\'iee giai sd bai toan quy koack (I.") tkeo eac
pkirong pkap tiit dink gap khd khiin a chd can
phai tmh (n -1) tick pkiin bdi 1 {0 ) trong
( I S ) va die tich phan bdi trong (1.9)
(/, ((A, ) trong (1.4) tki mdi xac dink dugc mdt
gia trj eko luim miic lieu 1(6 )
Wo rpng cac kel qua da co va su diiiig ket qua
cua cong trink ['^j biii toan dieu khien
(1.2)-(1 t) duoc giai trong dang tdng quat \ di v
ngkia dd pkuong phap Monte Carlo, lao iroc Iupng kkdng chech cua cac tich pluin bdi si-dup'c sir dung (trong muc 11.2) de thiet kip ciic phirong trinh hdi quy urong ung vd'i biii toiin quy hoach (l.")-(1.9) Tren co so nay phirong pkap Robins Monro (Robins Monro's Procedure RMP) dugc xay dung di- giai so biii loiiii ban diiu Nkimg img dung vao ly tliuyel
dp tin Ciiy sc dupe trinh bay trong muc 11 3
112 X A i D I N G MCi H I N H XAP \|
NG.\L NHIFN Nham ckuyen biii toan dicu khien (l.2)-( I li
ve bai loan quy koiicli (L7)-(l.9l ta xel kcl qua sau:
Bd de 2.1: \'eu cdc dii'ii kicn t.li (Bi dugc thoa man liit:
I-Bdi lodn quy hogch (I.'I co Idi giai dm nhdi:
0" 0 : lO\' ()') (().',.()')
6 (a.h );(;„ : - (0, 0„ , )
t2 h ('ho boi nghiem diiy nhdt:
0 • ()'* e Ul h ).i -~ 1 n cua it ph" mg Irinh phi lit\ en:
/ Co]) = a,, i - 1 -:- n I t„(0 ) a„
i2 2i
2- He ddng lice (1.3)-( 1.3 i Id dii'it khii'ii dugc hoi ldp hdm L vd Idp hdm niiy cimg lit lap hop cdc dieu khien chdp nitdii dmrc cuu bill todn dii'it khien (1.2i-i 1.3"!
3- Bdi lodn dieu khien fl.2i-i 1.3"! cd dieu khii'n ldi ini dm nhdi ii* ^ ii *( (>'*) e i' \iic dinh lir Idi giai i2 U cua hdt loim quy hogch
11 ") theo cimg thitc
u {.:()' ) :^ (;/, ;;„).;; (/); =;/ (1:0 )
:^- 1^_ ,, U) 'it c [ 0 7 ' ] / 1 ; H
i2 ll
Bd dc tren day dira v iec giai bai loiin dicu khicn ( 1 2 i - i l 3 " ) vc vice lim nghiem
0=0 elci.h) cua ke plurang trink phi
tuyen (2 2) Nham thiet kip luge dd tinh loan theo RMP tkuc kien dicu niiv ta dita
V ao ham v ccto ')4
Trang 31 rin Thi Ngim ru Dig Lap chi KHOA HOC & C ONG NGI 11 9 0 ( 0 2 ) , 9 3 - 9 9
, C ' ( » ) : - ( g , ( " A g„{ii„))e (a.h)
V » :=- (u, "„ ) e ^"
(2,1)
cd cac thiink pluin tkoa man dicu kien (C)
dudi diiy:
(C)- Vdi mdi ;' / ,;, kam
g : R ' >(cf.h^) \'A mgt song ank kka v i
lien luc tren R '
g,(t)^ 0 ( V / G R ' )
Gan voi cac luim g,(li, ) / = 1 n ndi ti'cn
0 < f (0)<\\p\\ VO <E R ' / = U « - 1 :
0 < / „ ( 6 ' ) < 1 \/0e R
la ky kieu:
ivn /C.',(;;,) ,!,'„(;(„l|[ |,e(;;) \'ii In ;;„)> /?'
/'(;;):= \ \iAi(.-l(.:.ii„)\\dn^ Vii,eR' i = \+n
'/("•",) f- j / t " ^ - " " J I l''",- Vi;„e«'
/' (;' P ,k R"
I (in - I,(0,) : \ p.[l)d
V (I c R ' ; 1 ;; 1
I r/ (C; „ ; ;; ) ; / 1 ;
(2.6*)
Trong dd
/ ( ) ; / ? ' >(0.|j/3||) / - I /7-^I
I'd / (0 ) : / ? ' >(0.1) Vi-',, e R" ' tiong do Id cdc hdm lii'll Inc lliirc su ldng rdi i I
;;-/ I'd thgc sir giant vdi i it 2-Hc n /thtnmg irinh phi luyen:
I (0 ) a I -A : It 1 /„((^) ;/„
(2 7)
ludn cd nghieni duv nhdi:
0^0' : {0, 0 ) c R" vd h'fi giai
0 trong (2 I) cua hdi loan (l.~) dirge xiic dinh lir nghieni tidy theo cdng lliitc:
0' - (,?,((?,•) gjO;, ) ) e (a.h)
II '. (()' OJ e R"
12 Sl
3-Klii chudn hda hdm p(ll) \/it c R' Irong (2 5/ la thu dugc liiitn tiigl do
pill)
( 2 S )
l„(0 )
-j q (0 „: n „ ) (/ ;;
( i ( ( ; ) : - - - V;; e R": \il>iu)du 1
'IP\\
o{ii)>O.Vii c R"
(2 9i , V 0 I R 0 ( i y , , ( > „ ) ( R Tli ket liiiin 3 cua bd de Iren la ed the lliiel
(2 5*) lap vccio ngiiu nhien r : - ( r^ r , ) £ R" co
va kin lugl ckiing minh dupe die ket qua sau:
Bd di' 2.2: Xen cite dii'it kiin (A) (B), (C)
dirge thoa mdn thi:
l-l'iii mdi I I /; ludn ldn Igi hinn ngii-gc
liin llic If -o '(.V ) e / ^ ' V.v £ ( < ; / ' )
cua hinn v - t,' (;; ) G (i/ A, ) \Ut e R' i'<> 0: i(j 0„) c R"
la CO
T(0,) tyO ), / = I -: n I
i,(0) = !„(<>)
0 ul, 0 „ ) 0 : g idle R'
V H ( a / ' , ) ; I n
(2 6)
ham mat dd (ddng tkdi) lii (p(li).ii c R" va kip qua trink ngiiu nkien \ii(0).0 & Ri^
dudi dang:
:(0) \: (0,) : ,{u„ , ) j „ (;/))e «"
11 kht T < 0 : (0 ) 3(7 0^): ' '
• [0 khir >()
1 < ; •
: , ( 0 ) \ { T O ]
3 (z 0 ), a„ I P" (r„.l)„ )
(2 10) 9.>
Trang 4Gpi F:R >R \a ham vccto xac djnh
d u d i d a n g :
F{(n'.-^]r{i>} F iO ,).F,(0))- R
e:=iO 0 )^R
F(ii,):= p 1 [0] \<i<n-\
F ^[11 ]: (/ |-CL : ' - ' , / „
/'
•MO'.it )
/•
(/;; 0 : id d )
( 2 1 1 ) Kki dd ta tku dirpe cac ket qua sau:
Rd di' 2.3: \eu cdc dieu kien (.Ai-(Ci ihri/c
ihoa mdn llii la cd:
E\:{(i)\- FiOi-^OeR
i2 I2i
F\^'{I') Fid) , < a - ' const.-;0i R'
2.13/
l)i)tf:2 ihi'ri he phitimg irinh t2.6i tirang
diiinig rdi lui' phinnig irinh hdi quy sent ddy:
T\::{ii)[ a: u:^ ifr ( « , «,, O j e / ? '
(2 I-II
Ddi viii ham
/ ; ( ; / ) > 0 -rii-iu ;; ) e R xac dink
trong ( 2 " ) vil t k a m so u neu t r o n g gia tkiet
(B) la cdn bd s u n g t k e m gia tkiet ( D ) d u d i
diiy:
1
( l ) ) - l k a n i sd u > V il ham
pill, ): R • ( 0 - X ) phij thudc t h a m bicn
(; - ((;, 11, ) fc/?' ' lil ddi xirng qua
true ;;,, /;;:
pill ni • II ) = pill in-i) ).r'ii = (it it ) e ^
^aii c h o : (2,15)
^ ( 0 - (I ] \ p (w )du > 0,, -U'i\.\\p\
'.'He R I) - (I^
( 2 , 1 5 ' ^ )
Bd de 2.4: Sen cdc dicu kicn ch il)i dugc ihoa nidn tin viii mgi € e (0.1 ), ta ci>:
G((l)'.= {F{d) u.O 0 ]>().\''0*()'
(2.16i
^ i n f ^ ( f {0} a.O t r ) > 0 ( ) ( , )
:= \0 e R" :s < 0 0'\\< 1 / £•}
'2 PI
Trong dd: 0 -((> 0 )lit nghiem din nhdi cua hi ' 2 9/
Chdy 2.1: T.i nhgn tliax rimg: cd thi thu hep mii'n dp dung R' ' ,() | cua dii'u kii'ii i2 I4*t thiinh miin Q l f ) \gliTa Id la cd the llun diiu kien ndi tren trong gia lliiel (D) htri dieu kii'ii salt
\ (O 0 ' ) ^ p ( It )d u
> \0 0 \ \\p\\ V C; fc ^ M ^ )
(2 IS, Kilt do cd llii' dira ra mdl ddu hieu du cuu diiu kiin niiy diriri dgng:
T ( ( 9 ) : = m i n / ; (C; ) > i L O y()<.B,(0')
0& R" : 0 0 <
" f: j
i 2 / v Biiy gio ta sir d u n g p k u o n g p k a p R M P de xav
d u n g diiy n g k i e m xdp xi ngau nhien /) | , ,
cua ke p h i r a n g trinh hdi quy (2 11) theo md hinh lap sau:
IF" {()'•' .il';; ) -Jin > \:d;;
= 0;; - y„ A [:" 0" )
0"'" = 0'" - ^
1 < / < n
''-'"" ' M;
(2 I9|
t r o n a d d : v e c t o ngau nhien d b R' laliiyv
la dav sd tkoa man d i i u kien:
\/ 'c
96
Trang 5Fran Thi Ngiin vd Dig Tap chi KHOA HOC & CONG NGHE 90(02): 93 - 99
Tuana tu do 0 < a < / nen ta cdn cd;
/,„>0,V/77>l;Z/„, = +x.Z/:<+x ,'',^.c(l{Oc.ii„)dii.,
m= I /»= I 'F,.(0)\^ \
(2.20) -•- \\F\
f>(r 0" ).\(r" 0'") Xiic dink tkeo (2.10) "ru(0-.u )du,_ r /
1 / „ „, 11 ' * I ^^Fl ^ J ^ ( " ) ' ' " ^
-Vii iT - \T r )| la diiy nkirnu tke " | | P | | ,
pc:
Incn ddc lap cua vccto ngiiu nkien Ket hgp dicu nav vdi (2,21) la thu duoc
r = r, r , duoc tao biing pkuong pkap „ ^-^ , ,' , ^
; V ^ ' ( ' 9 ) = > \'''{0,)\ +\F (Ot Monte Carlo tir kam mat dp (p(ii) cko dudi " • ^ ' i i •• i
dang (2.9) (2.5) Kki dd ta cd: _ \\r-in\'l^ T T"A , w / i D"
„ , , , , , , , ,.-• , „ ^ => \\F {0)\\< \^n-v :> = consl vOeR Dinh ly 2.1: I in cac dteu kien (A/-(l)/, la dgl: » ^ '»
0"-.= {():" o"']e{Li.h) o;"-.^i^ ((F) .^ ^., ; , , J., , , , ^-, '"^"i;"''
^ ' " I ^ ' ' -'-•^ • > j a h,(., | ,ng: lu cae dieu kicn (2.2,->) (2,20)
V;' = l 4 ; 7 w > l (2 17) (2 13) (2.12) cd tke suy ra su kdi tu
lice cua dav ngkiem xap xi ngiiu nkien
;; : = ( ; ; , ' ; ; ' " ) ; ; ; " ' ( / ) : = l ,, ( / ) i , ; I ; • , • " ' , , " , , i - '
I ' " ; ' c, ll • ' p j I ve ngkiem cua he phirong Irinli koi
V/ 6 [ ^ „ 7 ' ] , / = l-f w quy (2.14):
(2.21) ^ 1 'i'Ti 0'" = iF \ = \ Trong dd ,(-''" |,„ , Id chiy iigliicyn xdp xt ngdu ^ f j jim C;'" = i^ * | = 1 V / = I H- /; nhien cna hi' (2.14) liip theo RMP (2.19) Khi
, ' (2 26)
do
l-Ddx \0'"\ , se hdi in hchi chiic chdn dice) """"s" ^o do kc pkuang trink kdi quv nay
urong duong vol lie (2 9) (Iheo bd de 2 3) nen
I'd /()'; giai 0 fc(«./i) cua hdi lodn quy ngkiem (F ndi tren cimg la ngkiem duy iiluit hogch (l.-p P\\\yy\d"' =0'\=\ eua (2.'^) Boi viiy lir (2.14K (2.2 I) va tinh
(2.22)
lien tue cua eac ham g, (theo gia thict (C))
la CO
2- D<7r {;;'"},„.I si' hdi lu theo nine liiu l'[ lini 0 = ()'] < P{ lim ,t,', (i'''")
(theo milmi him chdc chdn) ve dieu khien ldi
ini u-e I cua hdi loim diin khiin (1.2,- = ^' 1^ )l = ^ i j ' ™ / ^ ' ="i l-V/ = 1 - "
"-^*' P\UmJ,(lr) = J^li)\= 1 Kh, do tir (2 26) ta tku d u p c
''-•'' r\ lim 0;" = 0 , ' j V / = I +;7
Chimg minh Kki xet cac thiink pluin cua
vccto kam fiOi Uong (2.11) la nluin thiiy => '^' ,1',"^ ^'' ' ""'^ ' " ' '
laiu; do link diioiu; cua die luim „ ; ,, , , ,,
, " , , , , , ^ , tronu do (xem Bo dc 2,2) 0 e(a.h) la r\ii).p\it].tl[Oy.ii ) ti'onu (2 '^) nen tu , • " , , , ; , ^ , ,
' ' ' ^ ' '^ ' ' " dieu kkien loi uu dimg (2.1) cua bai toan (2,s) (2 5*) va (2.9) ta co, ( 1 2 ) , i 4) NghT;, |;\ ,2 2^2) dupe ckimg mink
, f,(0.) r f i' ) , Cudi cinm tir tinh lien tue cua die kam
0 s F, (0 ) 1,1 = -n-:^lT'''' - / - \
\\p\\ ' \\p\\ / ( ( U / = 1 + " trong (1,8) (1.9) la suv ra
< I Oiii ^du = 1 I < ;' < n, ,||,|T |j^.„ ^^^ ciia iia^ j{p] tropg (23) Kki
(224) ^I'^-laeo
Trang 6Tran Thi Ncan va Di'Z Tap chi KHOA HOC & CONG NGHE 90(02): 93-99
] = PW'm 0 =e']<P[ lim j[()' ) = /(6'')}
= P[ lim ;, ( ; ; ' ) = J , (;;');
Nghia lil i2.23) dugc chirng mink.l
Chd y 2.2: Do Idi giai 0 e(ci.h) cua bai
loan quy hoack (L~) cung la ngkiem duy nkat
cua he phirong trinh (2 2) (theo Bd de 2.1)
nen ta ciing ed the su dung cac cdng thirc
(2.19) (2.21) de lap day ii?'"), , cac nghieni
xdp XI eua he (2.2) voi sir kdi tu tkeo nghia
cua cdng thirc (2 22)
11.3 L ng dung vao ly thuyet do tin ciiv
Ciia su V " := ,.S , ^ la mdt ke thdng ma
mdi bd phan S', / = 1-:-n giin vdi hien chi
thi irgiig ihdi hogt ddng [ 10] co dang:
khi r > 0"'
.V = ,V (O ); =
0 khi r < 0
(-1 1)
Frong do I la ky kieu ke thdng hoat ddng 0
la ky hicu he thdng bj le liet
trong dd r, la mdi thg cua bd phan (ca the
|4]) V v a i ' lii mirc ldi ihieu cua ludi dig
dc cho bp pkan nay cdn koat ddng dugc Fa
xem riing lie 5 "' := |.S' }" ^ tku dirge lir sir bd
sung bp phiin N vao he V " ' ' ; |.S' |
trong do gpi / ' ' 1 < / ' < « - 1 \a do tin cc'n
hoal dong eua mdi bd pkan V trpng ke
.V " theo ngkia:
' ' := \ - a
P \r > 0] I
i-l ^ 11 < \ i - \ ^ n - \
(3.2)
COI O ' (.V, V J k=n'\.n lahiinchi
ihi trang thdi hoal ddng cua hi S ' *':
' , I,,,,- l"
•I'' \; ,.\
( 3 3 )
va xem riing ca 2 ke V'" k = n-\.n ddu
koat cicsn'i tkeo cdu true song song, nokia la
(xem [6]) cac hdm can triic cua chinig co
dang;
O " (.V, V ) = n"uix|.Vi k=n-\.n
(3 4)
Bai toan ngirgc cua ddnh gid do tin ea'i
(DGDTC) mdt he tkdng dugc dat ra (xem [1])
la de xac dink cac mirc tdi tkieu
0 \ < i < n cua tudi tko eac bd pkan trona
he S'"" vd'i gia tkiet rang da cko cic dp tin cay hpat ddng / ' ' = 1 - o r cua mdi bd phan .S' I < / < H - 1 trong ke V " '' ban dau va
cko xac siuit (/ dc hd phgn hd irg (hd sung)
.S'„ se lam cko he mdi S"" hoat ddng khi he
eu S""^" bi te liet:
p]o'"'(.\; v,) = i | o " ''(,v, v,_i)=o;
= a —<a < I
2
(3 5) Trong viec giai bai loan tren diiv ta gia thiei
(xem [2]) riing tudi tko cua mdi bd pkan S
la mdt dai Iupng ngau nkic-n (dinn)
f G[0.-f-x) \<i<n six xem riing da cho
ham mat dp (ddng thdi)
/i(,V| X,,) > 0 V.v > 0 i ~\^n cua
vecto ngau nhien r — (r, f )
Dc cd tke su dung md kink tinh toiin trong Muc 2.2 vao viec giai bai loan ngugc cua DGDTC ndi tren trud'c het ta km y rang: trpng trudng kgp nay kien nkien la dieu kien (.A) dugc tkoa man vdi:
a, = 0 , 6, = -F X V / = 1 -^ n:
{a,b) = R : '.= ( O i - x )' ; 11/7^11 = J p( x)dx = 1
(3.61
Do |75| = 1 nen tu (3.2) va (3 5) ta tku diroc dieu kien (B) N^^oai ra cae ham;
*)S
Trang 7friin Fhi Ngiin vd Dig Tap chi KHOA HOC & CONG NGHE 90(02): 9 3 - 9 9
/'(A):- j j
/K.v, • - V , )
•' f'l^'.v, I (0)- j/i(.v )dx
,(3.-) lan lugl la kam mat dp va kam phan bd cua
dInn r 1 < ; ' < / ? Kki dd tir (3.2) ta cd:
{o-)-i 1 I
f < i y \ = a, V/'="l M - 1
(3.8)
Chd y 3.1: Khi p(x) Id hdm mdl do cua
redo ngdu nhiin f, hdm / [0 j Irong (1.9)
cd dgng:
,- /'I 6^>f 1<;'<;7-1 i? < r '
' P[ 0,>f, \<i<n~\\
\iO:r {o^ i;,Jc r
/ , ( i / j - r/„ V i ; ' := [0[
(3.10)
Chd y 3.2: Dira trin (3 Si r('; (3.10) la nhdn
thdy (xem Bd di 2.1) riing: ldi giai
0 -(0\ Oil) trong hdi loan iigirtrc cua
IXrDTC' chinh Id nghiim diiy nhdi cna he
pliinnig Irinh (2 2l Bai niy, cd the sir dung
md hinh linh loan nin Irong Chu i 2.2 di I hiit
lap ildy p " (,„,| nliinig ldi giai xd/> xt cho Idi
giai 0 ndi Iren
(3.9)
0„ )e R"
KFf IT \N Kki giai cac bai toiiii dicu kkien viec ckira cae tick pkan bdi ludn gap khd khiin C ac phirong phap true tiep dupc su dting nhtmg co
dp pkirc tap cao \ d i pkuong phap xap xi ngau nhien cac bai toiin chira tich phiin bdi dugc giai quyet vcii dp pkirc tap nkp hon L'ng dung cu the trong bai toiin danh giii dp tin cay Idi giai cua bai loan tim dupc bang qua trinh thiet lap diiy cac kii giai xiip xi,
TAI L I F L T H A M KH \ ( ) [1] Nguyen \"an Ho Nguyen Viln Hiiu Nguyen
Quy 1 Iv 1 'c mdl bdi lodn ngircrc cuu ddnh gid dd tin c d\ mdl he thdng Irong nghien ciru lining qiiun dong chay giira sdng Dd Ddng \ui Ky yen Fldi
nghj Ung dung loan hpc Toan qudc lan thii 1 r.2
N \ B D H Q G H N 2000 (Tr 191-206)
|2] Nguven Qii.v Hy Nguven Dinh Hoa The popululton und tl rene\rul luncttoii \ ict J Math
\ o l 2 1 N.l 1996 (Ir 198-224) [3] Nguyen Ouv Hy Nguven Van lluu Nguven
\ an Ho Tong Dinh Quv Mai Van Duoc The
\liniie Carlo method in theory o) reliubililr und its applnaff'in to hydroelectric srsiem Proc,
ISl \l M llongKong2001 (85-88),
(4| Nguyen Quv' Hv Phirang phdp md phtmg sii Miiiifc Carlo N.\B Dl IQGIIN 2004
|5| Revcs/ P I note on the Rohhins-Monro method Stuchia Sci, Math Hung, N 7, 1972
(3.N^-3ii2)
[6] Barlow R F Proschan F, Stulisticul Theor\
ol Reliubiliiy und fife 'Testing Neu York 1975,
ABSTR,\C I
TIIF STOCHASTIC APPOROXIMATION METHOD FOR SOLMNG A KIND
OF ( O N I R O L PROBLEM INC Ll DING M l l.TIPLR INlLCiUALS AND APPl.IC ATION
Tran Thi Ngan , Tran Manh Tuan
i'ollegi of hilormulion Technology and( oiiiiiiih ,inoii I XI
Control problems have been solved by many authors in dilTerenl methods 1 here are some problems that contain multiple integrals These problems always get high computing complexity when using normal algorithms (mathematical analysis tools) Bv applying stochastic apporoviniation method, multiple integrals are solved with much less computing complexity
Kev words: I'ontrol problems Multiple integrals Complexify Muthemulicul unulysis reliability
theory
'Tet-ii'fscj mil is 1 I mail ttngan a iclii cdu rn