Just In Time Control of Timed Event Graphs: Update of Reference Input, Presence of Uncontrollable Input

HAL Id: hal-00844944

https://hal.archives-ouvertes.fr/hal-00844944

Submitted on 16 Jul 2013

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Just In Time Control of Timed Event Graphs: Update of Reference Input, Presence of Uncontrollable Input

Eric Menguy, Jean-Louis Boimond, Laurent Hardouin, Jean-Louis Ferrier

To cite this version:

Eric Menguy, Jean-Louis Boimond, Laurent Hardouin, Jean-Louis Ferrier. Just In Time Control of

Timed Event Graphs: Update of Reference Input, Presence of Uncontrollable Input. IEEE Transac-

tions on Automatic Control, Institute of Electrical and Electronics Engineers, 2000, 45 (11), pp.2155-

2159. �hal-00844944�

I n i t i a l m a r k i n g o f a p l a c e ( t o k e n )

1 H o l d i n g t i m e o f

t o k e n s i n a p l a c e ( i n t i m e u n i t s )

UY 2

1 22

4

O u t p u t s g r e a t e r t h a n d e s i r e d o u t p u t s

z '

y

t i m e

e v e n t s

0 5 1 0 1 5

5

1 0 1 5 2 0

t ' = 6

K = 4

F i g u r e 1 : A t i m e d e v e n t g r a p h

K = 4

r4

(

t ' = 6

r 4 ( u _{o p t} u '_{o p t})

t i m e

e v e n t s

0 5 1 0 1 5

05

1 0 1 5 2 0

u 'o p t

u o p t

) =

F i g u r e 3 : C o n t r o l s ( t h i n l i n e ) , ( t h i c k l i n e ) ^u

u '

a n d ( d o t t e d l i n e ) ^{r -}

^{( u}

⁾

F i g u r e 4 : O u t p u t ( t h i n l i n e ) a n d r e f e r e n c e y

F i g u r e 2 : R e f e r e n c e i n p u t ( t h i n l i n e ) , ' ( t h i c k z z

z i n p u t ' ( d o t t e d l i n e )

0 5 1 0 1 5

5

1 0 1 5 2 0

z '

z 4

z(k ) = z '(k ) k = 0 , . . . , 4

r- u

g ^Ä ( o p t )

t i m e

e v e n t s

t ' = 6

K = 4

l i n e ) a n d ( d o t t e d l i n e ) ^{g Ä r -}

^{( u}

⁾