80,140 research outputs found
Error Correcting Codes for Distributed Control
The problem of stabilizing an unstable plant over a noisy communication link
is an increasingly important one that arises in applications of networked
control systems. Although the work of Schulman and Sahai over the past two
decades, and their development of the notions of "tree codes"\phantom{} 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 decoding delay, which is what tree codes
guarantee. We prove that linear tree codes occur with high probability and, for
erasure channels, give an explicit construction with an expected decoding
complexity that is constant per time instant. We give novel sufficient
conditions on the rate and reliability required of the tree codes to stabilize
vector plants and argue that they are asymptotically tight. This work takes an
important step towards controlling plants over noisy channels, and we
demonstrate the efficacy of the method through several examples.Comment: 39 page
Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Non-stationary/Unstable Linear Systems
Stabilization of non-stationary linear systems over noisy communication
channels is considered. Stochastically stable sources, and unstable but
noise-free or bounded-noise systems have been extensively studied in
information theory and control theory literature since 1970s, with a renewed
interest in the past decade. There have also been studies on non-causal and
causal coding of unstable/non-stationary linear Gaussian sources. In this
paper, tight necessary and sufficient conditions for stochastic stabilizability
of unstable (non-stationary) possibly multi-dimensional linear systems driven
by Gaussian noise over discrete channels (possibly with memory and feedback)
are presented. Stochastic stability notions include recurrence, asymptotic mean
stationarity and sample path ergodicity, and the existence of finite second
moments. Our constructive proof uses random-time state-dependent stochastic
drift criteria for stabilization of Markov chains. For asymptotic mean
stationarity (and thus sample path ergodicity), it is sufficient that the
capacity of a channel is (strictly) greater than the sum of the logarithms of
the unstable pole magnitudes for memoryless channels and a class of channels
with memory. This condition is also necessary under a mild technical condition.
Sufficient conditions for the existence of finite average second moments for
such systems driven by unbounded noise are provided.Comment: To appear in IEEE Transactions on Information Theor
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