28,436 research outputs found
The Consistency of Partial Observability for PDEs
In this paper, a new definition of observability is introduced for PDEs. It
is a quantitative measure of partial observability. The quantity is proved to
be consistent if approximated using well posed approximation schemes. A first
order approximation of an unobservability index using empirical gramian is
introduced. For linear systems with full state observability, the empirical
gramian is equivalent to the observability gramian in control theory. The
consistency of the defined observability is exemplified using a Burgers'
equation.Comment: 28 pages, 3 figure
On the Rate of Convergence for the Pseudospectral Optimal Control of Feedback Linearizable Systems
In this paper, we prove a theorem on the rate of convergence for the optimal
cost computed using PS methods. It is a first proved convergence rate in the
literature of PS optimal control. In addition to the high-order convergence
rate, two theorems are proved for the existence and convergence of the
approximate solutions. This paper contains several essential differences from
existing papers on PS optimal control as well as some other direct
computational methods. The proofs do not use necessary conditions of optimal
control. Furthermore, we do not make coercivity type of assumptions. As a
result, the theory does not require the local uniqueness of optimal solutions.
In addition, a restrictive assumption on the cluster points of discrete
solutions made in existing convergence theorems are removed.Comment: 28 pages, 3 figures, 1 tabl
Secret Key Generation from Correlated Sources and Secure Link
In this paper, we study the problem of secret key generation from both
correlated sources and a secure channel. We obtain the optimal secret key rate
in this problem and show that the optimal scheme is to conduct secret key
generation and key distribution jointly, where every bit in the secret channel
will yield more than one bit of secret key rate. This joint scheme is better
than the separation-based scheme, where the secure channel is used for key
distribution, and as a result, every bit in the secure channel can only provide
one bit of secret key rate.Comment: 5 pages, 1 figur
Sparsity-Based Kalman Filters for Data Assimilation
Several variations of the Kalman filter algorithm, such as the extended
Kalman filter (EKF) and the unscented Kalman filter (UKF), are widely used in
science and engineering applications. In this paper, we introduce two
algorithms of sparsity-based Kalman filters, namely the sparse UKF and the
progressive EKF. The filters are designed specifically for problems with very
high dimensions. Different from various types of ensemble Kalman filters
(EnKFs) in which the error covariance is approximated using a set of dense
ensemble vectors, the algorithms developed in this paper are based on sparse
matrix approximations of error covariance. The new algorithms enjoy several
advantages. The error covariance has full rank without being limited by a set
of ensembles. In addition to the estimated states, the algorithms provide
updated error covariance for the next assimilation cycle. The sparsity of error
covariance significantly reduces the required memory size for the numerical
computation. In addition, the granularity of the sparse error covariance can be
adjusted to optimize the parallelization of the algorithms
How Good Are Embodied And Disembodied Idea Flows In Bridging Income Gaps And Idea Gaps?
This paper empirically evaluates the relative importance of embodied versus disembodied idea flows in explaining income gaps and idea gaps. Trade is used as a measure of embodied idea flows and telephone call traffic a measure of disembodied flows. Since both trade and telephone traffic may be endogenous, this paper uses the geographic, linguistic, and colonial components of trade and telephone traffic as instruments to identify their effects on income and total factor productivity (TFP). The results provide little support for the embodied object models when both trade and telephone traffic are included in the regressions. Telephone traffic has a quantitatively much large effect on income per worker and TFP than trade.
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