Hardware Reference
In-Depth Information
Chapter 13
Language Solving Using Simulation Relations
13.1
Model Matching by Simulation Relations
An important application coming from discrete control theory is the so-called model
matching problem. It asks to design a controller
M
B
so that the composition of a
plant
M
C
(see the controller's
topology in Fig. 1.1e). Versions of the problem where the closed-loop system
is required to be simulation-equivalent to the model have been studied in the
literature [12, 68].
M
A
with the controller
M
B
matches a given model
Definition 13.1.1.
S
1
S
2
is a
simulation relation
from an FSM
M
1
D
hS
1
;I;O;T
1
;r
1
i
to an FSM
M
2
DhS
2
;I;O;T
2
;r
2
i
if
1.
.r
1
;r
2
/ 2
,and
2.
.s
1
;s
2
/ 2 )
.
i=o
!
M
1
s
i=o
!
M
2
s
0
1
0
1
0
2
0
2
0
1
;s
0
2
/ 2
8i 8o 8s
s
1
)9s
s
2
^ .s
If such a
exists, we say that
M
2
simulates
M
1
,orthat
M
1
has a simulation into
M
1
sim
M
2
.
M
2
, and denote it by
Given
the
plant
M
A
DhS
A
;I;O;T
A
;r
A
i
and
the
reference
model
M
C
D
hS
C
;I;O;T
C
;r
C
i
, from [68] we define the relation
H
max
S
A
S
C
, that relates
state
s
A
in
M
A
with state
s
C
in
M
C
if and only if
s
C
“simulates”
s
A
.
Definition 13.1.2.
The relation
H
max
S
A
S
C
is defined by:
v
=o
!
M
A
s
0
A
0
A
.s
A
;s
C
/ 2 H
max
,
8i 9
v
8o 8s
s
A
)
s
C
i=o
!
M
C
s
0
C
0
C
0
A
;s
0
C
/ 2 H
max
9s
^ .s
:
(13.1)
Search WWH ::
Custom Search