4,493 research outputs found
On the convergence of stochastic MPC to terminal modes of operation
The stability of stochastic Model Predictive Control (MPC) subject to
additive disturbances is often demonstrated in the literature by constructing
Lyapunov-like inequalities that guarantee closed-loop performance bounds and
boundedness of the state, but convergence to a terminal control law is
typically not shown. In this work we use results on general state space Markov
chains to find conditions that guarantee convergence of disturbed nonlinear
systems to terminal modes of operation, so that they converge in probability to
a priori known terminal linear feedback laws and achieve time-average
performance equal to that of the terminal control law. We discuss implications
for the convergence of control laws in stochastic MPC formulations, in
particular we prove convergence for two formulations of stochastic MPC
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High-Performance Integrated Window and Façade Solutions for California
The researchers developed a new generation of high-performance façade systems and supporting design and management tools to support industry in meeting California’s greenhouse gas reduction targets, reduce energy consumption, and enable an adaptable response to minimize real-time demands on the electricity grid. The project resulted in five outcomes: (1) The research team developed an R-5, 1-inch thick, triplepane, insulating glass unit with a novel low-conductance aluminum frame. This technology can help significantly reduce residential cooling and heating loads, particularly during the evening. (2) The team developed a prototype of a windowintegrated local ventilation and energy recovery device that provides clean, dry fresh air through the façade with minimal energy requirements. (3) A daylight-redirecting louver system was prototyped to redirect sunlight 15–40 feet from the window. Simulations estimated that lighting energy use could be reduced by 35–54 percent without glare. (4) A control system incorporating physics-based equations and a mathematical solver was prototyped and field tested to demonstrate feasibility. Simulations estimated that total electricity costs could be reduced by 9-28 percent on sunny summer days through adaptive control of operable shading and daylighting components and the thermostat compared to state-of-the-art automatic façade controls in commercial building perimeter zones. (5) Supporting models and tools needed by industry for technology R&D and market transformation activities were validated. Attaining California’s clean energy goals require making a fundamental shift from today’s ad-hoc assemblages of static components to turnkey, intelligent, responsive, integrated building façade systems. These systems offered significant reductions in energy use, peak demand, and operating cost in California
Reconstruction of cosmological initial conditions from galaxy redshift catalogues
We present and test a new method for the reconstruction of cosmological
initial conditions from a full-sky galaxy catalogue. This method, called
ZTRACE, is based on a self-consistent solution of the growing mode of
gravitational instabilities according to the Zel'dovich approximation and
higher order in Lagrangian perturbation theory. Given the evolved
redshift-space density field, smoothed on some scale, ZTRACE finds via an
iterative procedure, an approximation to the initial density field for any
given set of cosmological parameters; real-space densities and peculiar
velocities are also reconstructed. The method is tested by applying it to
N-body simulations of an Einstein-de Sitter and an open cold dark matter
universe. It is shown that errors in the estimate of the density contrast
dominate the noise of the reconstruction. As a consequence, the reconstruction
of real space density and peculiar velocity fields using non-linear algorithms
is little improved over those based on linear theory. The use of a
mass-preserving adaptive smoothing, equivalent to a smoothing in Lagrangian
space, allows an unbiased (although noisy) reconstruction of initial
conditions, as long as the (linearly extrapolated) density contrast does not
exceed unity. The probability distribution function of the initial conditions
is recovered to high precision, even for Gaussian smoothing scales of ~ 5
Mpc/h, except for the tail at delta >~ 1. This result is insensitive to the
assumptions of the background cosmology.Comment: 19 pages, MN style, 12 figures included, revised version. MNRAS, in
pres
Gas-Rich Companions of Isolated Galaxies
We have used the VLA to search for gaseous remnants of the galaxy formation
process around six extremely isolated galaxies. We found two distinct HI clouds
around each of two galaxies in our sample (UGC 9762 & UGC 11124). These clouds
are rotating and appear to have optical counterparts, strongly implying that
they are typical dwarf galaxies. The companions are currently weakly
interacting with the primary galaxy, but have short dynamical friction
timescales (~1 Gyr) suggesting that these triple galaxy systems will shortly
collapse into one massive galaxy. Given that the companions are consistent with
being in circular rotation about the primary galaxy, and that they have small
relative masses, the resulting merger will be a minor one. The companions do,
however, contain enough gas that the merger will represent a significant
infusion of fuel to drive future star formation, bar formation, or central
activity, while building up the mass of the disk thus making these systems
important pieces of the galaxy formation and evolution process.Comment: Corrected dynamical friction calculation error. Revised discussion &
conclusions. 7 pages, 4 tables, 6 figures, to appear in May 1999 Astronomical
Journa
Multi-contact Walking Pattern Generation based on Model Preview Control of 3D COM Accelerations
We present a multi-contact walking pattern generator based on preview-control
of the 3D acceleration of the center of mass (COM). A key point in the design
of our algorithm is the calculation of contact-stability constraints. Thanks to
a mathematical observation on the algebraic nature of the frictional wrench
cone, we show that the 3D volume of feasible COM accelerations is a always a
downward-pointing cone. We reduce its computation to a convex hull of (dual) 2D
points, for which optimal O(n log n) algorithms are readily available. This
reformulation brings a significant speedup compared to previous methods, which
allows us to compute time-varying contact-stability criteria fast enough for
the control loop. Next, we propose a conservative trajectory-wide
contact-stability criterion, which can be derived from COM-acceleration volumes
at marginal cost and directly applied in a model-predictive controller. We
finally implement this pipeline and exemplify it with the HRP-4 humanoid model
in multi-contact dynamically walking scenarios
Measuring eccentricity in binary black hole inspirals with gravitational waves
When binary black holes form in the field, it is expected that their orbits
typically circularize before coalescence. In galactic nuclei and globular
clusters, binary black holes can form dynamically. Recent results suggest that
of mergers in globular clusters result from three-body
interactions. These three-body interactions are expected to induce significant
orbital eccentricity when they enter the Advanced LIGO band at a
gravitational-wave frequency of 10 Hz. Measurements of binary black hole
eccentricity therefore provide a means for determining whether or not dynamic
formation is the primary channel for producing binary black hole mergers. We
present a framework for performing Bayesian parameter estimation on
gravitational-wave observations of black hole inspirals. Using this framework,
and employing the non-spinning, inspiral-only EccentricFD waveform approximant,
we determine the minimum detectable eccentricity for an event with masses and
distance similar to GW150914. At design sensitivity, we find that the current
generation of advanced observatories will be sensitive to orbital
eccentricities of at a gravitational-wave frequency of 10 Hz,
demonstrating that existing detectors can use eccentricity to distinguish
between circular field binaries and globular cluster triples. We compare this
result to eccentricity distributions predicted to result from three black hole
binary formation channels, showing that measurements of eccentricity could be
used to infer the population properties of binary black holes.Comment: 12 pages, 7 figures, 2 table
The signature of dark energy on the local Hubble flow
Using N-body simulations of flat, dark energy dominated cosmologies, we show
that galaxies around simulated binary systems resembling the Local Group (LG)
have low peculiar velocities, in good agreement with observational data. We
have compared results for LG-like systems selected from large, high resolution
simulations of three cosmologies: a LCDM model, a LWDM model with a 2 keV warm
dark matter candidate and a quintessence model (QCDM) with an equation of state
parameter w=-0.6.
The Hubble flow is significant colder around LGs selected in a flat, Lambda
dominated cosmology than around LGs in open or critical models, showing that a
dark energy component manifests itself on the scales of nearby galaxies,
cooling galaxy peculiar motions. Flows in the LWDM and QCDM models are
marginally colder than in the LCDM one.
The results of our simulations have been compared to existing data and a new
data set of 28 nearby galaxies with robust distance measures (Cepheids and
Surface Brightness Fluctuations). The measured line-of-sight velocity
dispersion is sigma = 88 +- 20 km/sec x (R/7 Mpc). The best agreement with
observations is found for LGs selected in the CDM cosmology in
environments with -0.1 <delta_rho/rho < 0.6 on scales of 7 Mpc, in agreement
with existing observational estimates on the local matter density.
These results provide new, independent evidence for the presence of dark
energy on scales of few Mpc, corroborating the evidence gathered from
observations of distant objects and the early Universe.Comment: 8 pages, 6 figures, minor changes to match the accepted version by
MNRA
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