SHORT
PAPERS
443
ACKNO\.YLEDGMEN~
The
authors wish
to
thank
J.
AUemong for providing the generator
model and his helpful discussions
concerning
th
model.
REFERNCES
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Abstmcr-A
counterexample is given
to a
conjectured
separation
result
for delayed
sharing
patterns
when
the delay is
at
lest
two units.
The
conjecture is proved to be true
for
a unit
delay.
I.
IWRODUCIION
We
use the formal
setup
and, with minor modification, the notation
developed by Witsenhausen [l].
The equations
for
the dynamics and the
observations of a system are given by
Xf=f,(xf-I,u:,.
..,u~,ur),
t=l;.- ,T
(1)
y:=g:(if-],w:),
k=l,.
.-,K
r=I;.
.,T
(2)
where at time
I
X,
is the state,
u:
and
y:
are, respectively, the control
input
and observed output
at
the
kth
“station”.
The
primitive random
variables
R. Sandell, Jr., Past
Chairman of the Large Scale Systems, Differential
Games
Com-
Manuscript received June
3,
1977; revised October 19,
1977. Paper recommended by N.
mittee.
This
work was supported in part by the National Science Foundation
under Grant
Eh’G76-16816.