ON THE EXISTENCE OF PETRI NET CONTROLLER FOR DISCRETE EVENT SYSTEMS UNDER PARTIAL OBSERVATION

ON THE EXISTENCE OF PETRI NET CONTROLLER FOR DISCRETE EVENT SYSTEMS UNDER PARTIAL OBSERVATION

Copyright (c) 2005 IFAC. All rights reserved 16th Triennial World Congress, Prague, Czech Republic ! "# $ ! " # $ %& !" ! $ ' (" )* & " +, # $ ...

313KB Sizes 0 Downloads 30 Views

Copyright (c) 2005 IFAC. All rights reserved 16th Triennial World Congress, Prague, Czech Republic

!

"# $

! " # $ %&

!"

! $

' (" )* & " +,

# $

%

& #

#

&- "'% . / ' $

(

, -

)

#

# *

# +

9

./*) -.

#

(

# ,668

# $

$

5

0 $ 1223

# -

/

# %

&

5

&

5 $

" < ! $

$

#

$# # 122;

0 .

$ # <

< <

# )

$

( 4 # 12227 4

5 # ,6667 #

# ,668

;

$

$

!

(

385

# 0

% 0

(

: #

122;

3

$

(

1 . .

1 /=(- =/ ).

.>>=/ =? @-.

+

#

$

!

& 5

=

!

4

#$

#

!

#

!

#

#

!

2

! &

5 5

2

% -

#$ %

$ 5

1

2

#

," " "& /# 3" "& "3 3 " ," 2 ! &< 3 ", "3 ," 2 , &! 3 & !" &<3 ( % & "& (= > "+ + $ (˛ 3 % % ( = > 6% " " 3 % "3 ," 2 (+

% /+0 123 4

% 2" "

-

-%

$

#

," " "& ?# 8% ," " ' &, &23 4 2 , &! ! &<3 3 & &% ! ," 3 ,& &63# & (¢ @;

5 5 =

$

, )

, + 5

$

-

1

(D (¢

6%" % & 3-& 3 & !" &<3 3 % 2 , &! !" &<3 ( " 2 ," 3 ," " ' % &23 4 2 3" "& ,& &6 2 &23 4 2 3" "& 3+

;

$# -;

5

-1

-3

$ -,

,

&

-1

&

5 &

2 &

3" "& 2

3" "&

5 &23 4 2

,

3" "&

1

$ 2

#

2

#

5

$ +

# $ 1

#

#

2

#

% , $ )

$ 5 # ,666

>

$

3

&, 3

+

3

&

&

9 :;

A

! %

, ,A

& (˛ 2 (D , ( F

,AB(,#

( +

(1# (;E

1



386

(¢ A

&

1

(2 A B(2E 2

!

& ," " "& 0# ( & 3 % 3 &, " "3 " ' "3% 2 3 3 6" % 3& " ! 7" ' ( - 3 3 % 3 &, 3 3 % 2 , &! ( 2 ," " ' & &23 4 2 3" "& 3+ & # 2 ‰$ s ˛ 8 C &! ( A B (¢ ˛ & (Ds ( ¢ ) 6% 8 "3 % 3 &, &23 4 2

3" "& 3+ &

0

2

,

, -

5 $

#

2

'& " %! 0# 0+ ," % " " " ! &<3 ; &9 : /+ & % (- & ! &<3 ,& % &23 4 2 3" "& ," 2 !" % ! &<3 @ &2 " , &! 2 ," " ' + ?+ , @ ("3 3 2 , &! & @A & % 6"3 % 6 ! &<3 @ " % &23 4 % 2" " ' -% 9 @: 6" % 2 + + , % ("3 3 3 & (- & ! &<3 '& & 3 - /+ 1 % 6"3 3 &-+

"

5

# $

#

>

@

! !

-3

;

5

!

-;

1

3" "& &<3 @



,# 2# 2# 2

,#

5

+

$

2

%

$

,

(, AB ,#

1#

;E

1

#

2

$

(2

1

2 AB(2E

#

2

,

(,

,

;

1

(1

+

," " "& # ! &<3 "3 3 " ,& 2" 3 & &, " 3 !" &<3 3 "3 ,& 2" + % 3 &, ,& 2" ! &<3 3+

, AB(,# (1# (;E

(;

," " "& # 3 & ,& & & 2 ' & 3 ! !" & 1 ' -%

1 ,

B @# D &G H

!

B

! !

!

&

&

0 # (

(I

! 5+

.

# !

C

!

/+/

,"

"

$

123 4 1

1

#

2

% 2" "

-%

& &

$

>

#

"3 3 " ' & 3 ", " ! &<3 2 ," " ' 3" "& 3+ D/ 2 % 3 &, &<3 3+ 8% 3 3 3 2 % ," &23 4 % 2" " +

," " "& # ! &<3 "3 3 " 2 & 7" ' ", " " 3 3 & !" &<3 % & & 2 3 & 3" % "4 2< -% 9 : &, % ," &23 4 % 2" " ' -%+ D 2 % 3 &, 2 & 7" ' ! &<3 3+ & % !3 ", ! &< 3 & " 3 2 & 7" ' !" &<3 % % ! &< 3 ", 2 & 7" ' &&+

!

!

&<3

," " "& E# 8% "4 2< -% 9 : "3 3 2< 1 ' -% &, # 2 & " " ' ! &<3 3 3 % % !" &<3 3 ( " 2 & !" &<3 - 3 " ' % " " " ! 7" '

B

5 + !

!

!

@

! 2"

(

&

!<

& >(<

!

4

>(<

#

#

!

," " "& F# 8% 3 2<' -% &, &23 4 2 1 % 2" " ' -% 9 : &2 " 2 !&4" ' ! &<3 3 & 2 & '" ' & ," & & 1 9 : "3 123 4 % 2" " -% & & 123 4 2 % 2" " -% & 1 9 :+ 2

!

+ ! % 1

#

#

2

2

1

#

)

,

2

# ! 1223

5

$

!

!

!

B

5

5

2

$

", D+ 2

1

#

#

2

;

$ (2 2

1

,

(,

(1

#

2

> D> W

(;

fi ‰ ¢

WAB ; 1

/+?

! 1

#

2

+

! #

!

,

+

!

˛ D>

Hˇ D>E =

!

#

2

,"

&

&

123 4

% 2" "

-%

; ).

$

.> > )=( /=(-<

+ 1

#

1 2

#

! < #

2

# %

+ 122;

# 2

-

5

2

&

387

- #

J

-#

#

!

-#

$

2

-

J

5

!

-#

-#

$

&&,# # 2 ¨

-

)

# $

#

) B- E ( 1 ;#

%

# 1

1

"!"

" 3

3&! 2 3"

"& 3

˝

2 1

#

¢ - =

" $

1

!

2

-

#

2

@

# =

2

$

#

% W #

-# !

#

1

$ %

, $

gDL

$

!

K

1

-+

-# G

(1

2

3

3

(;

(M

&

2

(N

;

M

3

1

(O

3" "&

O

3" "&

2

#

+

3

!

,

G ! #

!

) 3

2

2

" $ >

1

(8

!

G 1

-3

&

2

(2 (3

;

-1

5 &23 4 2

-=

(, 1

K

$

-;

,

G "& -# g D=L 2# " g ˛

˛8

3 -,

K

2

;#

-#

% )

#

2

1

A

2

,

#

$ W

#

2

-# #

¢ ˛

fi

1

$

# 3

# 4

W

+

2

-

! - +

#

1

- #

#

) =

-+

-# G

˛

‡ 2#

# % 2" "

;

1

;

&

<

" "&

+

;

1

&

& -

$

% 1

?+/

3

5

2

<

1

)

3#

1

1

$ ,

M

3

fi 1

M

O

> -

-

#

1 2

¢

fi

W

#-

$

7

! 1

#

2

"

- + fi

3 &

!

2

# (

- # G ¢˛

A

$ 1

?+0

2

B- E

+

#

- #

< 2#

3

W

$

," , "" , """ , "4

2

;

2

M

2

O

2

‡ 2 + - # + - # + - #

1

‡ 2 ‡ 2 + - #

1

<2

1 3

(

4

3 -

,4

"&

" "& +

3" 2 % 4"& " 2 " '& & & ", % ("3 3 3& "& 3 "3, " ' & " "& 3 / ? 3 "& " 3 " W +

2

-

2 1 2

3 & - # ,&

2

2 ",

M

-

+

fi 1 - #

O 3

$

$

388

? $ $

- # %

( #

- + % 4

+

#

3

‡ 2

?+? !(

&

& -

3

! $

3 =:-( = )= .+ ). -

.> > )=(

#

5

+ ¢

fi $

W #

-

!

)

>

,#

1 (

8 %

%

;

5

#

> 1

#

-;

8

; 5

8 $

H

;D8> 8

OD8>

$

H

fi

;

2

-M ;#

>

F

HH

HH >

5 1

#

2

- = "

- # G

D "

1

-

‡ #

2

1

5 -

- # #

8

-,

-3

,

3

- +

- # G

C

-

<

-N

-1

8

- #

-M

-

+

+

8

<

1

) HH 1 "

1

- #

-3

1

3

; +

-

1 ""

A,

-

- A,# - # M

3

+

3

- #

+

,

- #8 ‡ 2

! - #

+

3

- #8 < 2

( #

#

A !,#

N /#

&

&

2

3" "&

! !

5 &23 4 2

2Ds ,>

H 2Ds 1> HH

3" "&

D "

& ,

(

M

8 - G 1

C

#

) > 2#

=s

& 1

$

) # F $ , 2Ds 1>

.

fi

- #

2

> 1D > C1 +

2Ds ,> , 1

- +

F 1 ,

0# fi 1

,# /# ? ? $ ‡ 2# W

?

C

!

1

N

2

¢ N

2

%

389

H HH

1

,

"

s

&&,# )

M - #G

!

1

M

&&

- #

fi8 F ; + - #, +

< +

,2

1

%

-

;

-1

-0-E8

-;

,

+

-?- -

8

O ,

;

HH

&& -,

8

;

$

) H

, " # , "" #

2

!

A2

8

8

8

8

,

-/-EH-?-E-

8

1

3

M

8

!

? $ -#

-8

8

2

- #

8

-?- H-?-E-

2

, """ # , "4 2

-

;

2

- #

;

8

!



;

M

-;

, M - ",, -

-/- H-?- -

,

8

3 8 -0- H-0-E-

,

3

&&,# >

;

3

3" 2 % 4"& % 2 ) . < &, 2& " 2 " 2 " ' 2 "!& & 3 & & ", % 2 ", ("3 3 3& "& - # - + # <3 "3, " ' & " "& 3 / ? M 8 ,& 4 3 "& " 3 " W +

-

-0- -

2

1

2

8#

2

M

2

1

-

#

!

¢

fi

C

-+

2

- +

2

fi

- # s 1& +

+

-

- #

F ,

- # s

s

& ,

& ,

+

=s

- # & 1

( #

<2# $

#

-, ,

3

-0- -

2

;

-N

-1

-M

-/- H-?- -

M

8

3

-;

-

-8

;

8

8

8

- #

3

+

- #8 ‡ 2

- #

;

$ !

8

; "(

,

2

,

+

-

fi8 - #

F ,

+

,

- #

2

+

+

-

2

1

)

8

3 8 -0- H-0-E-

, ,

1

F

; 4"""

-3

-

- #8 < 2

=2

,

=2

!

N +

N

$ (

#+

1#

F 1

fi

,

- # s

+

-

2 F ,

& 1

- # /# ?# M W ? $ ‡ - # # - # s

- +

2

s

%

& ,

& ,

<

=s

& 1

-

<

- + # 8 # E

- # #

5 -

= ,#

- #

3

%

-#

# $

+

$

=+= = )=(

,

-0 -?

g1

M

-1

8 @2

3 1

-0-

;

1

g,

P# ) . & "3 1223#

;

,

,

g;

-0-?H-/ ,

8 @1

-;

8

@,

/

M

3

>

8 2

< O

!

% $ 8

,#

-1

$

!

; "" ; """

% +

- #

;

3

+

- #

M

,

=2

- #

,

- # - #

=2 =2

) ! ; "4

‡ 2

-

2

;4

F 2

2

-

+

- #8 ‡ 2

; 4"

,

2

-

+

- #

; 4""

1

-

+

- #

2

, 3

4 5 316!332 #

0 # I1 4

: :

1223 (

C < 3 !3# (

% I& 73%&11!13#

: : 122; > ) < # &! " # @ ;6# Q;#

0 : : 122; / 4 * # 3+ & &2& " 3 &! "& # @ ,6# ,# ,;N!,31 4 R. R 5 ,666 ( /=( $ * * # ! 66!223 4 R.# 4 > R 5 ,668 ( $ & # ? % #' #R ( < # 1222 > / ( . # & + & ,+ & & & 3 !3 3"' 9 @/ :# # ( 5 # 1O,!1O8 9 '# R 4 # 4 > 5 ,668 + 5 # &! " # @ ;1# Q,# ,M!1O > ) 8

;

8

g, g1 g;

- #8 = - ,

!

5 O

2

) ;"

= ,#

M

/

0

5 > *

- #

M ). )>*(-.

( #

-,

+

= - ,#

$

%

-

-3

1# $

$ 2

#

$

$

#

-

% 8 8

‡ 2 ‡ 2

390