215 research outputs found
Synchronization in Networks of Identical Systems via Pinning: Application to Distributed Secondary Control of Microgrids
Motivated by the need for fast synchronized operation of power microgrids, we
analyze the problem of single and multiple pinning in networked systems. We
derive lower and upper bounds on the algebraic connectivity of the network with
respect to the reference signal. These bounds are utilized to devise a
suboptimal algorithm with polynomial complexity to find a suitable set of nodes
to pin the network effectively and efficiently. The results are applied to
secondary voltage pinning control design for a microgrid in islanded operation
mode. Comparisons with existing single and multiple pinning strategies clearly
demonstrates the efficacy of the obtained results.Comment: 11 pages, 9 figures, submitted to Transactions on Control Systems
Technolog
Perturbation bounds on the extremal singular values of a matrix after appending a column
In this paper, we study the perturbation of the extreme singular values of a
matrix in the particular case where it is obtained after appending an arbitrary
column vector. Such results have many applications in bifurcation theory,
signal processing, control theory and many other fields. In the first part of
this paper, we review and compare various bounds from recent research papers on
this subject. We also present a new lower bound and a new upper bound on the
perturbation of the operator norm is provided. Simple proofs are provided,
based on the study of the characteristic polynomial rather than on variational
methods, as e.g. in \cite{Li-Li}. In a second part of the paper, we present
applications to signal processing and control theory
Topological Phases: An Expedition off Lattice
Motivated by the goal to give the simplest possible microscopic foundation
for a broad class of topological phases, we study quantum mechanical lattice
models where the topology of the lattice is one of the dynamical variables.
However, a fluctuating geometry can remove the separation between the system
size and the range of local interactions, which is important for topological
protection and ultimately the stability of a topological phase. In particular,
it can open the door to a pathology, which has been studied in the context of
quantum gravity and goes by the name of `baby universe', Here we discuss three
distinct approaches to suppressing these pathological fluctuations. We
complement this discussion by applying Cheeger's theory relating the geometry
of manifolds to their vibrational modes to study the spectra of Hamiltonians.
In particular, we present a detailed study of the statistical properties of
loop gas and string net models on fluctuating lattices, both analytically and
numerically.Comment: 38 pages, 22 figure
Quantum Tutte Embeddings
Using the framework of Tutte embeddings, we begin an exploration of
\emph{quantum graph drawing}, which uses quantum computers to visualize graphs.
The main contributions of this paper include formulating a model for quantum
graph drawing, describing how to create a graph-drawing quantum circuit from a
given graph, and showing how a Tutte embedding can be calculated as a quantum
state in this circuit that can then be sampled to extract the embedding. To
evaluate the complexity of our quantum Tutte embedding circuits, we compare
them to theoretical bounds established in the classical computing setting
derived from a well-known classical algorithm for solving the types of linear
systems that arise from Tutte embeddings. We also present empirical results
obtained from experimental quantum simulations.Comment: 19 pages, 6 figure
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