 |
21st Southern California Nonlinear Control Workshop
Error
Correcting Codes for Control
Teja Sukhasavi, Caltech
Teja Sukhasavi, Caltech
Advisor: Babak Hassibi
There are
increasingly many instances of networked control systems where
measurement and
control signals are transmitted across noisy channels.
This necessitates
a need to reliably communicate the measurement and control signals by
correcting for the errors introduced by the channels. Although Shannon’s
information theory is concerned with reliable transmission of a
message from one point to another over a noisy channel,
the reliability is achieved at the price of large delays which
may lead to instability when they occur in the feedback loop
of a control system. Hence, we need practical real-time
encoding and decoding schemes with appropriate reliability
for controlling systems over lossy networks. Although the work of
Schulman and Sahai over the past two decades, and
their development of the
notions of "tree codes" and "anytime capacity", provides the
theoretical framework for studying such problems, there has been scant
practical progress in this area because explicit constructions of tree
codes with efficient encoding and decoding did not exist. To
stabilize an unstable plant driven by bounded noise over a noisy
channel one needs real-time encoding and real-time decoding and a
reliability which increases exponentially with delay, which is what tree
codes guarantee. We prove the existence of linear tree codes with high
probability and, for erasure channels, give an explicit construction
with an expected decoding complexity that is constant per
time instant. We demonstrate the efficacy of the method through
simulations.