U OF M COLLEGE OF ENGINEERING
CONTROL SEMINAR SERIES
WINTER TERM 1998
Professor A. Stephen Morse
morse@sysc.eng.yale.edu
Friday, January 23, 1998
4:00  5:00 pm
1200 EECS
Certainty Equivalence, Detectability, and the Control of Uncertain
Systems

Abstract

"Certainty equivalence" is a
well known heuristic idea which advocates that in
an adaptive context, the feedback control
to an imprecisely modeled
process
should, at each instant of time, be designed on the basis of
a current estimate of what the process model is, with the
understanding that each such estimate is to be viewed as correct
even though it may not be. On the surface justification for
certainty equivalence seems selfevident: if process model
estimates converge to the "true" process model, then a certainty
equivalence based controller ought to converge to the nonadaptive
controller which would have been implemented had there been no plant
uncertainty. The problem with this justification is
that because of noise and
unmodelled dynamics,
process model
estimates
don't typically converge to the true process model
 even in those instances where
certainty equivalence controls can be shown to perform in
a satisfactory manner. A more plausible justification
stems from the fact that any {stabilizing} certainty
equivalence control
causes the familiar interconnection of a controlled
process and
associated output estimator to be
detectable
through the estimator's output error
ep,
for every frozen
value of the index or parameter vector
p
upon which both the estimator
and controller dynamics depend. Detectability is key
because adaptive controller tuning/switching algorithms
are invariably designed to make
ep
small  and so with detectability, smallness of
ep
ensures smallness of
the state of the controlled process and estimator interconnection.
The fact that certainty equivalence implies detectability
has been known for some time  this has been shown to be so
whenever the process model is linear and the controller and estimator
models are also linear for every frozen value of
p.
In this talk we will make use of
recently introduced concepts of inputtostate
stability and detectability for nonlinear systems,
to explain why the same implication is valid in a more
general, nonlinear setting. We will describe several hybrid control
architectures suggested by this implication
and will present theoretical
results and simulations to validate and demonstrate their
utility.

Biosketch

Not available at this time, please check again
[UM Control
Group Homepage 
Control Seminars
Homepage  College of Engineering
Homepage]
© UofM College of Engineering Control Research Group 
December 1997
bethi@umich.edu