619 research outputs found
Distributed Stochastic Market Clearing with High-Penetration Wind Power
Integrating renewable energy into the modern power grid requires
risk-cognizant dispatch of resources to account for the stochastic availability
of renewables. Toward this goal, day-ahead stochastic market clearing with
high-penetration wind energy is pursued in this paper based on the DC optimal
power flow (OPF). The objective is to minimize the social cost which consists
of conventional generation costs, end-user disutility, as well as a risk
measure of the system re-dispatching cost. Capitalizing on the conditional
value-at-risk (CVaR), the novel model is able to mitigate the potentially high
risk of the recourse actions to compensate wind forecast errors. The resulting
convex optimization task is tackled via a distribution-free sample average
based approximation to bypass the prohibitively complex high-dimensional
integration. Furthermore, to cope with possibly large-scale dispatchable loads,
a fast distributed solver is developed with guaranteed convergence using the
alternating direction method of multipliers (ADMM). Numerical results tested on
a modified benchmark system are reported to corroborate the merits of the novel
framework and proposed approaches.Comment: To appear in IEEE Transactions on Power Systems; 12 pages and 9
figure
Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization
Principal component analysis (PCA) is widely used for dimensionality
reduction, with well-documented merits in various applications involving
high-dimensional data, including computer vision, preference measurement, and
bioinformatics. In this context, the fresh look advocated here permeates
benefits from variable selection and compressive sampling, to robustify PCA
against outliers. A least-trimmed squares estimator of a low-rank bilinear
factor analysis model is shown closely related to that obtained from an
-(pseudo)norm-regularized criterion encouraging sparsity in a matrix
explicitly modeling the outliers. This connection suggests robust PCA schemes
based on convex relaxation, which lead naturally to a family of robust
estimators encompassing Huber's optimal M-class as a special case. Outliers are
identified by tuning a regularization parameter, which amounts to controlling
sparsity of the outlier matrix along the whole robustification path of (group)
least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its
neat ties to robust statistics, the developed outlier-aware PCA framework is
versatile to accommodate novel and scalable algorithms to: i) track the
low-rank signal subspace robustly, as new data are acquired in real time; and
ii) determine principal components robustly in (possibly) infinite-dimensional
feature spaces. Synthetic and real data tests corroborate the effectiveness of
the proposed robust PCA schemes, when used to identify aberrant responses in
personality assessment surveys, as well as unveil communities in social
networks, and intruders from video surveillance data.Comment: 30 pages, submitted to IEEE Transactions on Signal Processin
Distributed Recursive Least-Squares: Stability and Performance Analysis
The recursive least-squares (RLS) algorithm has well-documented merits for
reducing complexity and storage requirements, when it comes to online
estimation of stationary signals as well as for tracking slowly-varying
nonstationary processes. In this paper, a distributed recursive least-squares
(D-RLS) algorithm is developed for cooperative estimation using ad hoc wireless
sensor networks. Distributed iterations are obtained by minimizing a separable
reformulation of the exponentially-weighted least-squares cost, using the
alternating-minimization algorithm. Sensors carry out reduced-complexity tasks
locally, and exchange messages with one-hop neighbors to consent on the
network-wide estimates adaptively. A steady-state mean-square error (MSE)
performance analysis of D-RLS is conducted, by studying a stochastically-driven
`averaged' system that approximates the D-RLS dynamics asymptotically in time.
For sensor observations that are linearly related to the time-invariant
parameter vector sought, the simplifying independence setting assumptions
facilitate deriving accurate closed-form expressions for the MSE steady-state
values. The problems of mean- and MSE-sense stability of D-RLS are also
investigated, and easily-checkable sufficient conditions are derived under
which a steady-state is attained. Without resorting to diminishing step-sizes
which compromise the tracking ability of D-RLS, stability ensures that per
sensor estimates hover inside a ball of finite radius centered at the true
parameter vector, with high-probability, even when inter-sensor communication
links are noisy. Interestingly, computer simulations demonstrate that the
theoretical findings are accurate also in the pragmatic settings whereby
sensors acquire temporally-correlated data.Comment: 30 pages, 4 figures, submitted to IEEE Transactions on Signal
Processin
From Sparse Signals to Sparse Residuals for Robust Sensing
One of the key challenges in sensor networks is the extraction of information
by fusing data from a multitude of distinct, but possibly unreliable sensors.
Recovering information from the maximum number of dependable sensors while
specifying the unreliable ones is critical for robust sensing. This sensing
task is formulated here as that of finding the maximum number of feasible
subsystems of linear equations, and proved to be NP-hard. Useful links are
established with compressive sampling, which aims at recovering vectors that
are sparse. In contrast, the signals here are not sparse, but give rise to
sparse residuals. Capitalizing on this form of sparsity, four sensing schemes
with complementary strengths are developed. The first scheme is a convex
relaxation of the original problem expressed as a second-order cone program
(SOCP). It is shown that when the involved sensing matrices are Gaussian and
the reliable measurements are sufficiently many, the SOCP can recover the
optimal solution with overwhelming probability. The second scheme is obtained
by replacing the initial objective function with a concave one. The third and
fourth schemes are tailored for noisy sensor data. The noisy case is cast as a
combinatorial problem that is subsequently surrogated by a (weighted) SOCP.
Interestingly, the derived cost functions fall into the framework of robust
multivariate linear regression, while an efficient block-coordinate descent
algorithm is developed for their minimization. The robust sensing capabilities
of all schemes are verified by simulated tests.Comment: Under review for publication in the IEEE Transactions on Signal
Processing (revised version
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