1,862 research outputs found
R3MC: A Riemannian three-factor algorithm for low-rank matrix completion
We exploit the versatile framework of Riemannian optimization on quotient
manifolds to develop R3MC, a nonlinear conjugate-gradient method for low-rank
matrix completion. The underlying search space of fixed-rank matrices is
endowed with a novel Riemannian metric that is tailored to the least-squares
cost. Numerical comparisons suggest that R3MC robustly outperforms
state-of-the-art algorithms across different problem instances, especially
those that combine scarcely sampled and ill-conditioned data.Comment: Accepted for publication in the proceedings of the 53rd IEEE
Conference on Decision and Control, 201
Control limitations from distributed sensing: theory and Extremely Large Telescope application
We investigate performance bounds for feedback control of distributed plants
where the controller can be centralized (i.e. it has access to measurements
from the whole plant), but sensors only measure differences between neighboring
subsystem outputs. Such "distributed sensing" can be a technological necessity
in applications where system size exceeds accuracy requirements by many orders
of magnitude. We formulate how distributed sensing generally limits feedback
performance robust to measurement noise and to model uncertainty, without
assuming any controller restrictions (among others, no "distributed control"
restriction). A major practical consequence is the necessity to cut down
integral action on some modes. We particularize the results to spatially
invariant systems and finally illustrate implications of our developments for
stabilizing the segmented primary mirror of the European Extremely Large
Telescope.Comment: submitted to Automatic
Factor Analysis of Moving Average Processes
The paper considers an extension of factor analysis to moving average
processes. The problem is formulated as a rank minimization of a suitable
spectral density. It is shown that it can be adequately approximated via a
trace norm convex relaxation
Sensitivity analysis of oscillator models in the space of phase-response curves: Oscillators as open systems
Oscillator models are central to the study of system properties such as
entrainment or synchronization. Due to their nonlinear nature, few
system-theoretic tools exist to analyze those models. The paper develops a
sensitivity analysis for phase-response curves, a fundamental one-dimensional
phase reduction of oscillator models. The proposed theoretical and numerical
analysis tools are illustrated on several system-theoretic questions and models
arising in the biology of cellular rhythms
Global analysis of a continuum model for monotone pulse-coupled oscillators
We consider a continuum of phase oscillators on the circle interacting
through an impulsive instantaneous coupling. In contrast with previous studies
on related pulse-coupled models, the stability results obtained in the
continuum limit are global. For the nonlinear transport equation governing the
evolution of the oscillators, we propose (under technical assumptions) a global
Lyapunov function which is induced by a total variation distance between
quantile densities. The monotone time evolution of the Lyapunov function
completely characterizes the dichotomic behavior of the oscillators: either the
oscillators converge in finite time to a synchronous state or they
asymptotically converge to an asynchronous state uniformly spread on the
circle. The results of the present paper apply to popular phase oscillators
models (e.g. the well-known leaky integrate-and-fire model) and draw a strong
parallel between the analysis of finite and infinite populations. In addition,
they provide a novel approach for the (global) analysis of pulse-coupled
oscillators.Comment: 33 page
- …