44,258 research outputs found
Distributed Control of Positive Systems
A system is called positive if the set of non-negative states is left
invariant by the dynamics. Stability analysis and controller optimization are
greatly simplified for such systems. For example, linear Lyapunov functions and
storage functions can be used instead of quadratic ones. This paper shows how
such methods can be used for synthesis of distributed controllers. It also
shows that stability and performance of such control systems can be verified
with a complexity that scales linearly with the number of interconnections.
Several results regarding scalable synthesis and verfication are derived,
including a new stronger version of the Kalman-Yakubovich-Popov lemma for
positive systems. Some main results are stated for frequency domain models
using the notion of positively dominated system. The analysis is illustrated
with applications to transportation networks, vehicle formations and power
systems
Research and Education in Computational Science and Engineering
Over the past two decades the field of computational science and engineering
(CSE) has penetrated both basic and applied research in academia, industry, and
laboratories to advance discovery, optimize systems, support decision-makers,
and educate the scientific and engineering workforce. Informed by centuries of
theory and experiment, CSE performs computational experiments to answer
questions that neither theory nor experiment alone is equipped to answer. CSE
provides scientists and engineers of all persuasions with algorithmic
inventions and software systems that transcend disciplines and scales. Carried
on a wave of digital technology, CSE brings the power of parallelism to bear on
troves of data. Mathematics-based advanced computing has become a prevalent
means of discovery and innovation in essentially all areas of science,
engineering, technology, and society; and the CSE community is at the core of
this transformation. However, a combination of disruptive
developments---including the architectural complexity of extreme-scale
computing, the data revolution that engulfs the planet, and the specialization
required to follow the applications to new frontiers---is redefining the scope
and reach of the CSE endeavor. This report describes the rapid expansion of CSE
and the challenges to sustaining its bold advances. The report also presents
strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie
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Preparing sparse solvers for exascale computing.
Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'
On Optimal Frame Conditioners
A (unit norm) frame is scalable if its vectors can be rescaled so as to
result into a tight frame. Tight frames can be considered optimally conditioned
because the condition number of their frame operators is unity. In this paper
we reformulate the scalability problem as a convex optimization question. In
particular, we present examples of various formulations of the problem along
with numerical results obtained by using our methods on randomly generated
frames.Comment: 11 page
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