8,283 research outputs found
Contracting Nonlinear Observers: Convex Optimization and Learning from Data
A new approach to design of nonlinear observers (state estimators) is
proposed. The main idea is to (i) construct a convex set of dynamical systems
which are contracting observers for a particular system, and (ii) optimize over
this set for one which minimizes a bound on state-estimation error on a
simulated noisy data set. We construct convex sets of continuous-time and
discrete-time observers, as well as contracting sampled-data observers for
continuous-time systems. Convex bounds for learning are constructed using
Lagrangian relaxation. The utility of the proposed methods are verified using
numerical simulation.Comment: conference submissio
Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators
We present an estimator-based control design procedure for flow control,
using reduced-order models of the governing equations, linearized about a
possibly unstable steady state. The reduced models are obtained using an
approximate balanced truncation method that retains the most controllable and
observable modes of the system. The original method is valid only for stable
linear systems, and we present an extension to unstable linear systems. The
dynamics on the unstable subspace are represented by projecting the original
equations onto the global unstable eigenmodes, assumed to be small in number. A
snapshot-based algorithm is developed, using approximate balanced truncation,
for obtaining a reduced-order model of the dynamics on the stable subspace. The
proposed algorithm is used to study feedback control of 2-D flow over a flat
plate at a low Reynolds number and at large angles of attack, where the natural
flow is vortex shedding, though there also exists an unstable steady state. For
control design, we derive reduced-order models valid in the neighborhood of
this unstable steady state. The actuation is modeled as a localized body force
near the leading edge of the flat plate, and the sensors are two velocity
measurements in the near-wake of the plate. A reduced-order Kalman filter is
developed based on these models and is shown to accurately reconstruct the flow
field from the sensor measurements, and the resulting estimator-based control
is shown to stabilize the unstable steady state. For small perturbations of the
steady state, the model accurately predicts the response of the full
simulation. Furthermore, the resulting controller is even able to suppress the
stable periodic vortex shedding, where the nonlinear effects are strong, thus
implying a large domain of attraction of the stabilized steady state.Comment: 36 pages, 17 figure
Reconstructing cosmological initial conditions from galaxy peculiar velocities. I. Reverse Zeldovich Approximation
We propose a new method to recover the cosmological initial conditions of the
presently observed galaxy distribution, which can serve to run constrained
simulations of the Local Universe. Our method, the Reverse Zeldovich
Approximation (RZA), can be applied to radial galaxy peculiar velocity data and
extends the previously used Constrained Realizations (CR) method by adding a
Lagrangian reconstruction step. The RZA method consists of applying the
Zeldovich approximation in reverse to galaxy peculiar velocities to estimate
the cosmic displacement field and the initial linear matter distribution from
which the present-day Local Universe evolved.We test our method with a mock
survey taken from a cosmological simulation. We show that the halo peculiar
velocities at z = 0 are close to the linear prediction of the Zeldovich
approximation, if a grouping is applied to the data to remove virial motions.
We find that the addition of RZA to the CR method significantly improves the
reconstruction of the initial conditions. The RZA is able to recover the
correct initial positions of the velocity tracers with a median error of only
1.36 Mpc/h in our test simulation. For realistic sparse and noisy data, this
median increases to 5 Mpc/h. This is a significant improvement over the
previous approach of neglecting the displacement field, which introduces errors
on a scale of 10 Mpc/h or even higher. Applying the RZA method to the upcoming
high-quality observational peculiar velocity catalogues will generate much more
precise constrained simulations of the Local Universe.Comment: Accepted for MNRAS 2012 December 1
L-PICOLA: A parallel code for fast dark matter simulation
Robust measurements based on current large-scale structure surveys require
precise knowledge of statistical and systematic errors. This can be obtained
from large numbers of realistic mock galaxy catalogues that mimic the observed
distribution of galaxies within the survey volume. To this end we present a
fast, distributed-memory, planar-parallel code, L-PICOLA, which can be used to
generate and evolve a set of initial conditions into a dark matter field much
faster than a full non-linear N-Body simulation. Additionally, L-PICOLA has the
ability to include primordial non-Gaussianity in the simulation and simulate
the past lightcone at run-time, with optional replication of the simulation
volume. Through comparisons to fully non-linear N-Body simulations we find that
our code can reproduce the power spectrum and reduced bispectrum of dark
matter to within 2% and 5% respectively on all scales of interest to
measurements of Baryon Acoustic Oscillations and Redshift Space Distortions,
but 3 orders of magnitude faster. The accuracy, speed and scalability of this
code, alongside the additional features we have implemented, make it extremely
useful for both current and next generation large-scale structure surveys.
L-PICOLA is publicly available at https://cullanhowlett.github.io/l-picolaComment: 22 Pages, 20 Figures. Accepted for publication in Astronomy and
Computin
Quantum Mechanics with Trajectories: Quantum Trajectories and Adaptive Grids
Although the foundations of the hydrodynamical formulation of quantum
mechanics were laid over 50 years ago, it has only been within the past few
years that viable computational implementations have been developed. One
approach to solving the hydrodynamic equations uses quantum trajectories as the
computational tool. The trajectory equations of motion are described and
methods for implementation are discussed, including fitting of the fields to
gaussian clusters.Comment: Prepared for CiSE, Computing in Science and Engineering IEEE/AIP
special issue on computational chemistr
- …