426
IEEE TRANSACTIONS ON AUTOMATIC CONTROL. VOL.
AC27. NO. 2. APRIL 1982
must sample
to reconstruct the original continuous time signal. It
appears.
however. that stability can
be awmd provided only that samples are
taken in manner which assures that
temporary instabilities are obsenable
in the error sequence
cA. k
2
0.
Practicallv speaking. however. if the
sampling
rate is too slow and the system is initially
unstable. signals may
quickly reach saturation levels.
Remark 4:
Although we have proven that the identification error
e(
I)
converges to zero we have not shown that the parameter estimates
O(
r)
converge to one of the optimal vectors
8:.
In general this \vi11 only
be the
case if the external
input is persistently exciting so that the conditiona of
proposition I are met. Furthermore xve ha\e not guaranteed
that the plant
output converges to
that of the model. Houever.
simulation
studies sce~n
to indicate that this
is the case.
Remurk
i:
We have proposed the use of two alternative
adJu>tnlent
schemes of a prqection type. and a leastsquares type. Although our
simulations
studies
indicate considerably improved comergencs using the
leastsquares algorithm. it should be
pointed
out that care must be taken
when implementing ths algorithm since
PA
must be assured to remain
positive definite.
VI.
CONCLUDING
REMARKS
This
report studied an alternative approach
to
the
problem of applying
discrete
adaptation
techniques for the control of continuous time
proceseeb.
For this approach stability results were derived which are
independent of
the average sampling
rate.
One
important
advantage of this approach over
those proposed for continuous
adaptive
control of continuous processes is
that this approach allows for use of the rapidly converging sequential
leastsquares
estimation
procedure. To control the rate of parameter
convergence in continuous time adaptation
prncedures
one must resort to
multiple equation
error
estimators
[7].
[8].
These require implementation
of considerably lugher order
input
and
output filters. and lead
tn
conhid
erably more complex control
structures.
The
use of sequential least
squares is also of great importance in extending these mults to the
multivariable case. since as discussed in (51. there are many more parame
ters to adjust.
Decentralized Control of Finite State Markov
Processes
K.41 HSU.
MEllBER. IEEE. ASD
STEVEN
1.
MARCUS.
MEMBER. IEEE
A hsrracr
\Ye
are concerned
with the control of a
particular class of
d:nan~ic qstemsfinite
state Markov chainx
The
information
pattern
a\ailable
is
the
socalled
one step dela! sharing
information
pattern. Using
this information
pattern.
the
d!namic
programming
algorithm
can
be
elplicitl! carried
out
to
obtain
the
optimal
polic).
The
problems
are
discussed
under
three different
cost
criteriafinite
horiLon
problem
with
expected
total
cost.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 R.Srikant
 optimal control policy, ﬁnite state Markov, centralized case, stationary optimal policy

Click to edit the document details