2,546 research outputs found
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
The Binary Energy Harvesting Channel with a Unit-Sized Battery
We consider a binary energy harvesting communication channel with a
finite-sized battery at the transmitter. In this model, the channel input is
constrained by the available energy at each channel use, which is driven by an
external energy harvesting process, the size of the battery, and the previous
channel inputs. We consider an abstraction where energy is harvested in binary
units and stored in a battery with the capacity of a single unit, and the
channel inputs are binary. Viewing the available energy in the battery as a
state, this is a state-dependent channel with input-dependent states, memory in
the states, and causal state information available at the transmitter only. We
find an equivalent representation for this channel based on the timings of the
symbols, and determine the capacity of the resulting equivalent timing channel
via an auxiliary random variable. We give achievable rates based on certain
selections of this auxiliary random variable which resemble lattice coding for
the timing channel. We develop upper bounds for the capacity by using a
genie-aided method, and also by quantifying the leakage of the state
information to the receiver. We show that the proposed achievable rates are
asymptotically capacity achieving for small energy harvesting rates. We extend
the results to the case of ternary channel inputs. Our achievable rates give
the capacity of the binary channel within 0.03 bits/channel use, the ternary
channel within 0.05 bits/channel use, and outperform basic Shannon strategies
that only consider instantaneous battery states, for all parameter values.Comment: Submitted to IEEE Transactions on Information Theory, August 201
Time-triggering versus event-triggering control over communication channels
Time-triggered and event-triggered control strategies for stabilization of an
unstable plant over a rate-limited communication channel subject to unknown,
bounded delay are studied and compared. Event triggering carries implicit
information, revealing the state of the plant. However, the delay in the
communication channel causes information loss, as it makes the state
information out of date. There is a critical delay value, when the loss of
information due to the communication delay perfectly compensates the implicit
information carried by the triggering events. This occurs when the maximum
delay equals the inverse of the entropy rate of the plant. In this context,
extensions of our previous results for event triggering strategies are
presented for vector systems and are compared with the data-rate theorem for
time-triggered control, that is extended here to a setting with unknown delay.Comment: To appear in the 56th IEEE Conference on Decision and Control (CDC),
Melbourne, Australia. arXiv admin note: text overlap with arXiv:1609.0959
A Nonstochastic Information Theory for Communication and State Estimation
In communications, unknown variables are usually modelled as random
variables, and concepts such as independence, entropy and information are
defined in terms of the underlying probability distributions. In contrast,
control theory often treats uncertainties and disturbances as bounded unknowns
having no statistical structure. The area of networked control combines both
fields, raising the question of whether it is possible to construct meaningful
analogues of stochastic concepts such as independence, Markovness, entropy and
information without assuming a probability space. This paper introduces a
framework for doing so, leading to the construction of a maximin information
functional for nonstochastic variables. It is shown that the largest maximin
information rate through a memoryless, error-prone channel in this framework
coincides with the block-coding zero-error capacity of the channel. Maximin
information is then used to derive tight conditions for uniformly estimating
the state of a linear time-invariant system over such a channel, paralleling
recent results of Matveev and Savkin
Coded Kalman Filtering Over Gaussian Channels with Feedback
This paper investigates the problem of zero-delay joint source-channel coding
of a vector Gauss-Markov source over a multiple-input multiple-output (MIMO)
additive white Gaussian noise (AWGN) channel with feedback. In contrast to the
classical problem of causal estimation using noisy observations, we examine a
system where the source can be encoded before transmission. An encoder,
equipped with feedback of past channel outputs, observes the source state and
encodes the information in a causal manner as inputs to the channel while
adhering to a power constraint. The objective of the code is to estimate the
source state with minimum mean square error at the infinite horizon. This work
shows a fundamental theorem for two scenarios: for the transmission of an
unstable vector Gauss-Markov source over either a multiple-input single-output
(MISO) or a single-input multiple-output (SIMO) AWGN channel, finite estimation
error is achievable if and only if the sum of logs of the unstable eigenvalues
of the state gain matrix is less than the Shannon channel capacity. We prove
these results by showing an optimal linear innovations encoder that can be
applied to sources and channels of any dimension and analyzing it together with
the corresponding Kalman filter decoder.Comment: Presented at 59th Allerton Conference on Communication, Control, and
Computin
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