6,055 research outputs found
A Lagrangian Policy for Optimal Energy Storage Control
This paper presents a millisecond-level look-ahead control algorithm for
energy storage with constant space complexity and worst-case linear run-time
complexity. The algorithm connects the optimal control with the Lagrangian
multiplier associated with the state-of-charge constraint. It is compared to
solving look-ahead control using a state-of-the-art convex optimization solver.
Simulation results show that both methods obtain the same control result, while
the proposed algorithm runs up to 100,000 times faster and solves most problems
within one millisecond. The theoretical results from developing this algorithm
also provide key insights into designing optimal energy storage control schemes
at the centralized system level as well as under distributed settings
PageRank Optimization by Edge Selection
The importance of a node in a directed graph can be measured by its PageRank.
The PageRank of a node is used in a number of application contexts - including
ranking websites - and can be interpreted as the average portion of time spent
at the node by an infinite random walk. We consider the problem of maximizing
the PageRank of a node by selecting some of the edges from a set of edges that
are under our control. By applying results from Markov decision theory, we show
that an optimal solution to this problem can be found in polynomial time. Our
core solution results in a linear programming formulation, but we also provide
an alternative greedy algorithm, a variant of policy iteration, which runs in
polynomial time, as well. Finally, we show that, under the slight modification
for which we are given mutually exclusive pairs of edges, the problem of
PageRank optimization becomes NP-hard.Comment: 30 pages, 3 figure
Lagrangian reconstruction of cosmic velocity fields
We discuss a Lagrangian reconstruction method of the velocity field from
galaxy redshift catalog that takes its root in the Euler equation. This results
in a ``functional'' of the velocity field which must be minimized. This is
helped by an algorithm solving the minimization of cost-flow problems. The
results obtained by applying this method to cosmological problems are shown and
boundary effects happening in real observational cases are then discussed.
Finally, a statistical model of the errors made by the reconstruction method is
proposed.Comment: 5 pages, 5 figures, contribution to the conference "Euler's
Equations: 250 Years On" (see http://www.obs-nice.fr/etc7/EE250/); to be
published in a special issue of Physica D containing the proceedings of that
conferenc
- …