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An Introduction to Data Rate Constraints in Feedback Control
u‰‰ŽÒFDr. Girish NairiUniversity
of Melbourne, uŽtj
“úŽžF2006”N3ŒŽ7“úi‰Îj13:00`15:00
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u‰‰ŽÒFDr. Girish NairiUniversity of Melbourne, uŽtj
Title: An Introduction to Data Rate Constraints in Feedback Control
Abstract:
In several emerging technologies
such as micro-electromechanical
systems and sensor networks, the
boundary between the fields of
communication and control has become
blurred. In these applications,
the basic aim is to control one
or more dynamical systems by feeding
back measurements over networks
with low data rates. The achievable
controller performance can be everely
affected by the communication resources
available, making it vital to understand
how the communication and control
objectives interact.
This two-part lecture aims to
give an introduction to several
recent, fundamental results in
the area of networked control.
Motivated by the role of Shannon
theory in communications, the emphasis
is on delineating ultimate bounds,
without restriction to specific
schemes such as memoryless A-D
conversion or linear coders and
controllers. In particular, the
focus is on characterising the
smallest feedback data rate which
permits stability to be achieved
or some control performance criterion
to be met.
In the first part, the case
of stochastic linear systems is
addressed.
Information and quantisation theory
are used to show that in order
for bounded mean square states
to be possible, the data rate must
exceed the intrincis entropy rate
of the plant. A universal lower
bound on the mean square states
is also derived, in terms of data
rate and channel delay.
Recent results on the case of bounded
states with bounded disturbances
will also be discussed, as well
as a solution to the problem of
optimal LQR under data rate constraints.
Deterministic nonlinear systems
are addressed in the second part.
It is demonstrated that the classical
notion of topological entropy can
be extended to yield an intrinsic
measure of the smallest rate at
which a controlled system can generate
information.
˜A—æF’ѺKŽ¡i03-5841-6891j
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