Friday, July 29, 2022 1:00 pm
-
1:00 pm
EDT (GMT -04:00)
Candidate:
Craig
Joseph
Lalumiere
Title:
Supervisory
Adaptive
Control
Revisited:
Linear-like
Convolution
Bounds
Date:
July
29,
2022
Time:
1:00pm
Place:
EIT
3142
Supervisor(s):
Miller,
Daniel
Abstract:
Classical
feedback
control
for
LTI
systems
enjoys
many
desirable
properties
including
exponential
stability,
a
bounded
noise-gain,
and
tolerance
to
a
degree
of
unmodeled
dynamics.
However,
an
accurate
model
for
the
system
must
be
known.
The
field
of
adaptive
control
aims
to
allow
one
to
control
a
system
with
a
great
deal
of
parametric
uncertainty,
but
most
such
controllers
do
not
exhbit
those
nice
properties
of
a
LTI
system,
and
may
not
tolerate
a
time-varying
plant.
In
this
thesis,
it
is
shown
that
an
adaptive
controller
constructed
via
the
machinery
of
Supervisory
Control
yields
a
closed-loop
system
which
is
exponentially
stable,
and
where
the
effects
of
the
exogenous
inputs
are
bounded
above
by
a
linear
convolution
-
this
is
a
new
result
in
the
Supervisory
Control
literature.
The
consequences
of
this
are
that
the
system
enjoys
linear-like
properties:
it
has
a
bounded
noise-gain,
it
is
robust
to
a
degree
of
unmodeled
dynamics,
and
is
tolerant
of
a
degree
of
time-varying
plant
parameters.
This is demonstrated in two cases: the first is the typical application of Supervisory Control - an integral control law is used to achieve step tracking in the presence of a constant disturbance. It is shown that the tracking error exponentially goes to zero when the disturbance is constant, and is bounded above by a linear convolution when it is not. The second case is a new application of Supervisory Control: it is shown that for a minimum phase plant, the d-step-ahead control law may be used to achieve asymptotic tracking of an arbitrary reference signal; in addition to the convolution bound, a crisp bound is found on the 1-norm of the tracking error when a disturbance is absent.
This is demonstrated in two cases: the first is the typical application of Supervisory Control - an integral control law is used to achieve step tracking in the presence of a constant disturbance. It is shown that the tracking error exponentially goes to zero when the disturbance is constant, and is bounded above by a linear convolution when it is not. The second case is a new application of Supervisory Control: it is shown that for a minimum phase plant, the d-step-ahead control law may be used to achieve asymptotic tracking of an arbitrary reference signal; in addition to the convolution bound, a crisp bound is found on the 1-norm of the tracking error when a disturbance is absent.