168,736 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
Recovery of time dependent coefficients from boundary data for hyperbolic equations
We study uniqueness of the recovery of a time-dependent magnetic
vector-valued potential and an electric scalar-valued potential on a Riemannian
manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic
equation. The Cauchy data is observed on time-like parts of the space-time
boundary and uniqueness is proved up to the natural gauge for the problem. The
proof is based on Gaussian beams and inversion of the light ray transform on
Lorentzian manifolds under the assumptions that the Lorentzian manifold is a
product of a Riemannian manifold with a time interval and that the geodesic ray
transform is invertible on the Riemannian manifold.Comment: 31 page
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