HAL Id: pastel-00001822
https://pastel.archives-ouvertes.fr/pastel-00001822
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Méthodes d’optimisation de contrôleurs de logique floue
pour le paramétrage automatique des réseaux mobiles
UMTS
Hervé Dubreil
To cite this version:
Hervé Dubreil. Méthodes d’optimisation de contrôleurs de logique floue pour le paramétrage automa-tique des réseaux mobiles UMTS. domain_other. Télécom ParisTech, 2005. English. �pastel-00001822�
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)
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(
) (
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∈ ∈ × + = & " U Uπ π γ π M> =<N ' 9 " S M> =AN + I#" π * M> =>N & :( )
∑
(
) (
[
)
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∈ + × = & " U )π γ π M> =AN 56 # 56 # , M> =FN M> =<N M> =AN " U " ) π ) * / π " =π( )
-+ M> =FN M> =AN O( )
)(
( )
)
Uπ = π π M> =CN / π + M> =<N M> =AN O( )
( ) ( )
( )∑
∈ = ) Uπ π π M> BDN 3 & ' " "" ( , O / g g4 ( M N ', g4 g M gN O ∈ ∀ Uπ( )
≥Uπ( )
, g- ( g 9 g- M # N • '5 +5 6 #4 ( 6 ( 7 g- g4 O ∈ ∀ UπT( )
≥Uπ( )
M> B;N " ".. • &+5 < #4 7 #4 ( 6 #5 ( ( ( ' ' P2 D>Q 5 " " " D≤ γ <; ( - M> =FN M> =AN M> =CN M π N + " " U- " )-O
( )
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+ × =∑
∈ ∈ & " U UT ( γ T M> B=N -( )
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∈ ∈ + × = & " ) )T γ ( T M> BBN " U- )- " g- # 9 M> B;N • A # #4 * + # #4 ( 6 #5 ( . # ', " & " " % . g- O M;N . g; M N ∀ ∈( )
( )((
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)
; π π ∈ + = # #4 e j / ∀ ∈ π +;( )
=π( )
M> B>N ∀ ∈( )
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) (
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)
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× + =∑
∈ ∈ + + U " & Uπ ; ( γ π ; M> BEN - g- G g^ " + M> B=N " U g-" 6 j * " & "?) ( ( " 4 ( ( M ( RN 8 > & > $!" ' $(( $" * # 5 " & " . (.2 O M "" N M ) *N 3 3 ) & " ' $2 $γγγγ%% ' P2 D>Q "" g 5 M;N 8 UDM N=D ∈ M=N α ∈
[ ]
D; γ ∈[ [
D; MBN * M>N % O MEN ' gO π( )
→ MFN % 4 " M" > EN M<N U+;( ) (
← ;−α) ( )
×U +α ×(
+γ ×U( )
)
M> BFN MAN / 4 MCN / ← M;DN $ ) ( ( "" ( -"" @ * $ @ ) * • &+5 < # $ * "" " Ug g ;N =N BN F ( +< j 5 " g ;N * ', " " =N D≤ γ <; BN∑
=∞ ∞ =D α∑
∞ <∞ =D = α j " U " Ug g X U M> BFN M<N "" , " "" ' 9 g "" "" ( " 3 3 & & " ' 7 " ' P2 C<Q P CAQ ) * * @ , 52; * " ! @ ! " . # "" ) * O M;N 8 )DM N=D ∈ ∈ M=N α ∈
[ ]
D; γ ∈[ [
D; MBN * M>N % O MEN ' ( K ( --,$8%O 33(
))
→ MFN % 4 " M<N MTTN( ) (
) ( )
( )( )
+ × + × − ← ∈ +; ; ) () ) α α γ M> B<N MAN / 4 MCN / ← M;DN $ MTN(
)
) 33 ( K ( εMk ;? N R εT ( " )M N * ( ( "" MTTN / Y M> B<N M<N O( )
( )(( )
; ) ) ∈ + ← +γ M> BAN ' ( M X M> B<NN ! @ H 5 , ', ! " " B 8 ) * /8$ M > = EN - " "" " " "" Z M # N • &+5 < # $ * ) * " )- g- ;N =N BN F ( +< j 5 " ;N # R K T ', " " =N D≤ γ <; BN∑
=∞ ∞ =D α∑
∞ <∞ =D = α2 j " ) --, ( K ( " )- g- X ) M> B<N M<N ) * • '5 # ( 6 ( g-) * --, " ) M> BBN ! g- M N g-R T ( " )-R K T O
( )
( )() T( )
T ∈ = π M> BCN - g- " ( + M- M> B=N M> BBNN( )
( ))( )
U T ( T ∈ = π M> >DN • 6 6 #437( 37( 33 7 -( K -( P2 C<Q P CAQ M > * # N " O[ ]
D; ∈ ε ∈ ( )()( )
∈ ← ← >( ) { }
R >T(
))
33 → ) * " "" ', " * @ ( @ ( M "" +RN , " ) * ! " " " B ', " M ( "" N - " ( , "" " " "" Z ' " ) * "" ( " " ' ( "" ! > & A $( $ ?1! $ " $ * 8 5 )# )! ' ) * ! " " ( * ) * ! " " (-2
""
5 M > = =N
3 9 & ( ! & & " ' 7 "
B ; ; ! " " M/8$N . /8$ /" " O " O / @ R / @/ 1 / 1/ "" " /8$ O " ! G R K KSK /T M/ N @J M " N J " " J @ µ " @J Y / R K KSK / T 1J M " N J " * # " ! " " @ # 0 ! 7 / ' ( ) * /8$ " '5 #5 5 #4 A8 # ( 5 ) * ( D #4 # B B B $G+* @ " " ! / " > F " ! M "" N O $ > F O /! @ . ( # " $G+* ! " " ) * ( ! " ' " " M ( ( N M DN O $ # ( !$ $ $! $ # ( ! 2 $ $" #"$ !$ $ $! 2 2 2
2 G R ;K #;T× R K # T × ×R /K #/T M> >;N X / " W;K XY× W;K XY × × W;K XY ' " " ) ( " ( J ( #J O " " ' " " " ( ( " " ! " ( ( ( ! 9 ( M ) *N $ > < O $ ( ( ' " O " 1 5 M @ N . " O O ( # # + " O , ( 9 O ;? ; ^;? ' " " . /8$ " ;F " M_ => > ! = " N M N B " "" , /8$ * 9 ( O ( ' ; V ( 8 8 V D BE ; ( ' ; V ( 8 8 V D = ;
2 -( O / , K ' K , U ? ' U ? # ' O G ;? ; -( O / , " K ' " K , U ? " ' U ? ( D # ' # # O O G ;? ; 1; M N O G ;?; 1= M N O G ; 1B M( # # N . ( > = F " > A /8$ " @ $ > A O / /8$ " @ ) * ( " ' " M ( N /8$ " > A 3 9 & ' !" : / * P2 C<Q /8$ " →α
( )
" M N * " " " ( "" P CAQ O , 8 8 ' * 5 #4 (( 7 " " O k ; O ] ; O G ; U # $5 5 ( # 5 <* ' 8 8 , U ? 8 8 ' U ? 8 8 " " " 1 1 1 3 52
( )
(
@( ) ( )
@ @( )
/)
" & / µ µ µ α ; = = ; = M> >=N )X & 9 " M N O( )
∏
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= = / J J @ " J ; µ α M> >BN O( )
( )
@( )
J / J " µ J α ; = = M> >>N ' " ! " # " ! " '5 O ! " " O( )
( )
J J " " ≠ = = D ; α α M> >EN 56 $ # # A8 /8$ 9 ( " /8$ * " & ! * * MP2 C<QN{
; /}
∈ ∀( )
( )
( )
∑
∑
= × = / " " " ; α α M> >FN - ( " @ ! " " 3 9 : / 2 ; " : " ' & ! * * Pd D;Q " !( )
/ ; = T O( )
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= = × = / " / " ; ; α α M> ><N " " ( O -/ /8$2
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= = × = / " / " 6 ) ; ; α α M> >AN X6 R K T " ' ) * " # ( # 4 * + # ) * l A8 " H " * > = > = -( K -( M--,N M N / --, ( O ( )(
6( )
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1 ( ( ∈ = M> >CN X1 R T M> >AN ( " " O( )
( )
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= = × = / " / " 6 ) ; ; α α M> EDN ) 9 ( U " M> >AN M> >CN O( )
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= = × = / " / 7 " 6 U ; ; α α M> E;N ( ) * ! " " M;N 8 " 6 M N=D " 1 ∈ ∀ ∈ ∀ M=N γ ∈[ [
D; ∈[ ]
D; ε∈[ ]
D; MBN * M>N % O MEN , "O ( K ( --, MFN * " R T )R K T M<N % 4 "2 MAN * UR 4T MCN " " )R K T UR 4T M;DN / M;;N / ← M;=N $ * ( P2 C<Q P CAQ "" " c; )^ R K T ) R K T 9 " O
( ) ( )
) U )= + × − ∆ γ M> E=N . ∆) " MCN ) * " , ( ( " P2 C<Q O[
]
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= × ∆ × = ∆ / " " ) 6 ; α α M> EBN X ( 8 ) * " "" " MCN ) * 3 9 3 / & / : . " ( /8$ 9 G O( )
9( )
( )
9 " 7 " α α ∈ = ( M> E>N 7 " α G ( ! . " ! /8$ M X α N 9 G O( )
(
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∈ > ∈ × > = 9 " 9 " " " 9 α α α α α α ; ; M> EEN " α G ! ! " α " G ) * /8$ " O( )
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= × = /" " " 9 9 ; α α M> EFN2. / " " H ( O ! " " " ) -"" ( > & B C 2 ?1! $ " $ ! $ ! ( $ 6 ' J ) * @ " %% + 3 < ' & * " ( * ( " ) * " , " ) " "
{
7}
" " ' /8$ " " ( ! ) " ( B O O * ' - " " 1J J " ( 5 ' ( " " * " M" N ' ( "" ( " > A 1; 1= 1B ! " ( 5 ' " ( * ! 9 " ( ( " ' ( ( ! " (22 ' ) * ( , ( @ # 0 ! O # ' ! " " B ;C # ' ! " " B ;C # , " , ) * * "" /8$O ( " R / /8$ " ) * " "" ! 3 < ' ! & " ' 7 " ) # "" " " ( ) * O • h " ! O;?2 k h k ;?22 • 7 ( K ( ! # M > * # N O , " , ( " " R >T
( )
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)
$ ; ; + = M> E<N X $( )
" X Z ' ! " " . # " " • " " " " J @ µ # " @J " O( )
,( )
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,U( )
"U( )
" µ µ µ µ α = × × × M> EAN;; 3 < : ' & . /8$ " > = E ; . " ;F " " ( ) * ! " O $ > C O $ ) * M;N 8 ∀ ∈
{
; = ;F}
6 M N=D ∈ ∈1 M=N γ ∈[ [
D; ( ( ∈[ ]
D; M > = F =N ε∈[ ]
D; MBN * M>N % O MEN , " α"( )
≠D ( K ( O * ( ) 6( )
1 , ( ∈ = R >T( )
{ }
, 1 > MFN * " O( )
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= = × = / " / " ; ; α α " O( )
( )
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= = × = / " / " 6 ) ; ; α α M<N % R T 4 " MAN * O( )
( )
(
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= = × = / " / 7 " 6 U ; ; α α MCN " )R K T UR 4T O( ) ( )
) U )= + × − ∆ γ M> ECN R T 2 # 56 ( % -c; % " c; % "; , ( " " ( O
[
]
( )
( )
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= × ∆ × = ∆ / " " ) 6 ; α α M> FDN M;DN / M;;N / ← M;=N $ ( ) * # O # ( ( " "" @ O ;DDD @ ( " " " " # ! # ( K ( ! , ( " " # , ( "" ! " M ( N . " $ " /8$ " D ( " " O[
]
( )
( )
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= + = ∆ / " " $ ; α α M> F;N C ) * ( O # / G ;? ( # / " O[
]
$ ; ; + = M> F=N " " -* ( ( M N " M " N M " N , ) * @ ' " " O; # 7 ( O ( Z ( M ( E\ ( 7 /N # 7 ( O ( Z ( M ( =\ ( 7 /N # " " 9 " " M ( ( N ' " " ( M "" ( ! ! B ;DN O
(
)
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# #)
"= − + × − M> FBN !" " ! " # ( @ " ( ) * > & D . ! # * ! $!" ' ?1! $ " 3 = ) & 7 " ( ! ' /8$ > = E ; " O O W ;? K ;? X W ;? K ;? X W;? K ;? X , " , ( ( 1;; ; = 1 1B; ;? ; ^;? 7 M ( N ) * " . . ( " ! * "" ! " ( # O W ;? K ;? X W ;? K ;? X W ;? K ;? X . " H " ( ( " O ( ( , 9 " S " * * ( * * ( " "" ) * ( /8$ " 7 ) * "" @ ' 9 " S !; " ) * " ( " 3 = ' /8$ > = E ; @ " ) * " /8$ @ # 0 ! " ( O ( # 0 ! (( * 5 l 4 # # ) * # ( 5 7 A8 ) ( " # 0 ! m'@ O " " , /8$ " > A Y ' ( " " ( ( " "" 9 " * " > ;D M N M " N M ( " (N ) * ( " H M CF " ( B N $ > ;D O ' " /8$ " /8$ ) * " " 5 5 ( ( 6 ( # 4 A8 "<* # $ A8 " " " 3 5 # $ A8 - " /8$ c m'@ - " /8$ c m'@ - " /8$ c m'@ - " /8$ c m'@ " - " /8$ c m'@ - " /8$ c m'@ ' " O * * ( O * 8 " ( /8$O A 5* # ( # $ A8
; ) * ( /8$ " # ) "" ! ' " ! " " H " * @ "" " "" %% " ! # ! O ! "" ! > & E *(! $ 8 5 )# )! $2 ! ?1! $ " 8 " " ! " " @ , ( " ' M @ N " 9 ' M # N " /8$ 8 O # / /8$ O /8$ " /8$ # / /8$ O /8$ " " " /8$ ) /8$ " # / /8$ O /8$ " 7 " ( /8$ " A8 * A8 ' " /8$ H M # " N 7 " @ H M N " + + /8$ * /8$ : /8$ , ) * X " " /8$ " (( * ( < $ # 5 ) " "" " M " N - 9 /8$ M N M " N " "" " * ! " ( @ N , 9 ( 9 "
;
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;
A 6
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6
' ( ! ? Y " @ ( 9 ? O • ' ? " ? @ ? ( " " # ! %% • ' ? " ? " @ # %% + + " M m " N * B " ? @ " M* $N * " ? ! @ %% # 0 ! @ " 9 K # " " ( " " ! @ " * @ S ! %% ) ( " %% O N " N " " M N ' ! " M *N # " " " M " P+ DE QN ( ! " ? Z M # N Z M +N %% - "" ? ? # ! ! 7 / ? " %% "" " H M N ) " "" "" S " M RN , " %% ( ! " * M N ( %% ! + + * ( M N ( M " RN ' @ " " " Z L L , M ( N @ " ) * > 7 @ ! ) * ";. %% ( M # # N ' " L L ) * ( /8$ + " M N " ( "" + * @ - " " " ( 9 "" O " " 9 " # " %% " R
7%&%
!
6
A $ ! # $ 6 ( 7 / ! " " 9 " " : 9 -" "" ) " " M N 9 " + " ' ( 7 / @ ! " 3 M "" # N -" @ "" ' ! ( " "" "" - "" L L " , 9 # " O 9 M " # N 9 ( 8 3 " M N Y ( + . " " . * M "" N O 9 " ";2 . M N " M8/ Y N 9 & 8 " ( 7 / M # # " W#*' " N " " O ( " " . " " 7 / '5 # #4 5 RP+ D>Q P+ DE Q P+ DE QT / 7 / / " 9 /_/ 9J ! J " " " ( ) " " 7 ' O # 7 9J S 7 J # ' 9J ! S J " 7 ' ! ) " 9n ! O
(
)
= n J J J 9 9 9 = + ME ;N * 9n " #R KJT " ( O # # 9 O #( )
=D # O J #( ) ( )
J =# J - - "" ( " ( J " " ! ' O( ) ( ) ( )
J # ! # ! J # > + ME =N '5 #4 # . " ( J ' " ( + M ( BDD +N J 9n ) " ( " " ( 9n ( " O;
( )
= = 9 J J # J n; D ME BN ' " ( # 9 , ( ( O 3 # + O # 3 # " " 9 M ^& " S N O( )
(
)(
)
; = J J # J = − − # + " " 9 & & # ! ! O( )
(
)
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)
; J J # J = − − − 9 ' " * M N 9 " ( "" M N ' ( " '5 #4 # * ( " " ( ( / , , " , ^ , , 9 "" " O # * M N O(
)
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# , = # # , * " " 8 L L ( M " E ; E =N # * M ( N O(
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, # , = # + # , + * " "5 + # # # # ( * + 5 + 6 . / / . # "" * M N O ;N 8 / ( / ( =N / ( " BN / ( =N >N % =N =N BN " " ( ) " >N ( " , ( " * " 6 O ( Y M ( *N ' 9 -( * 7 / ;<E " 9n 7 / " # * $ E ; O * " " E ; * ;E * # " * " E =
$ E = O % / " E = 3 @ ( ' " * " , ( * 9 $ E B O * " ( " E B * ;E ' ( ( " ;C M " N ( ;> M N ;= ;D / 9 * * # " * " E > / " 3 ( @ M N , * O "" " (
$ E > O % A & ((! $ ! "# $ $ % -' ( O # " M N O + *+( * @ O + *#%% %.* * : " # " M ( G,8 ) *N " * ( @ 9 H - " ( ! " ( " O " ( @ M ) *N ! ( @ O MP2 eDEQ P/ DEQN < # 4 *5 # 6 ' 9 " ( * 9 9 ( ( ( O # 5 # O " * # & # O " "" " " "" # & ( # O " @ * $ " %% 7 / " " "" " ( 9
# < D 5 * 5 # # O " ! ( " ! # / $ #4 # # # # D # 5 O " " " @ X @ O + %.* ) *R # # 5 # # 5 O ( @ ( " 9 @ ! # # #4 ( #4 ( 5 O " 9 ) * %.* " " * ! @ A 4 * (! ,! ($ $ 5 6 " E E @ ! ##E0 " ' # 0 ! ' ' ##E0 M #N ! @ " # "T # ; < D E ; ; # $ F 7 G 3 H F ; F F < F D F F E F F G F H F ; F $ $ E E O 4 ' M N ( M N ( ' M N ##E0 M N " E E ! ##E0 CD ! ' ' @ " 9 ' = B + CD ' ( * T *" > ; B = 2! , + % , +
##E0 " - ' * " ' ED\ <D\ , ' @ " ##E0 = E + ;;D , "" @ ! E ; ! . @ " # "T # , , " * $ * c ' TT . ;ECADD ;FDBDD . BCDA> % " B>C=D > ?@ A = B . O *[ %2-`' BECCC BD>;= . O *[ %2-`7 =D<F B>AB . O *)74`' FFA >CB . O *)74`7 D D . O ,8 ) - D D C=3 3 CC 2 " " 3 B 9 B . O *)74`' =AB BEA . O *)74`7 D D . O *[ %2-`' D D . O *[ %2-`7 EA ;<> 3 9 2 " A B A B E ; O ! TTT @ ! # , " @ ! M N -# * $ ( 7 ( D B\ =\ ( # ( $ 413 J " E F ( # " " U Z " U / " )-, # " M "" ( >N 9 ' ( # " " ( )-, # " # " Z " Z "" " U " U * F > B T *" > ; B = TT *c ' O * @ # TTT , " O ' _D < ##E0 _B E +
D E G ; ; ; < D 6 @ .! $" 6 @ ( - + 4 / ' 1 * - 9 4 / ' 1 * 2'?D $ E F O * # " M N ( # " M N U # U
7%$%
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
. ; ; < < D D ; ;; ; <; D; ; E; ; G; H; ; ; # $ $ $ 5 ! ! 8 9 G 3 H $ E A O [ ##E0 = M;DC N A & & 2 ! ( $ ($ $ ($ ! + + %% 7 / B @ " @ S M ( N " S ! @ " ! " > B " @ ! $ % & ' " " ( : " E C " ' ! ( ( @ O # ( > " @ 8 S " U " " ( - " " " * $ ! # @ * $ ! M )-,N " ( , @ ! %% ) 5 " 5 " ( %% + M ( ! %% 5 N " " ( 9 " U "
2 $ E C O , " )-, * $ ! S " U " ( M " N * $ ! " " " " ( , @ ( M" " > = ;N - " " E C 9 9 @ A & 4 2 ! $(( $" ($ ) * # /8$ " M > = FN . + + %% 7 / ) * K O ( @ H & 0 $ # ! $ & ! 0 &
