24,112 research outputs found
On generalized terminal state constraints for model predictive control
This manuscript contains technical results related to a particular approach
for the design of Model Predictive Control (MPC) laws. The approach, named
"generalized" terminal state constraint, induces the recursive feasibility of
the underlying optimization problem and recursive satisfaction of state and
input constraints, and it can be used for both tracking MPC (i.e. when the
objective is to track a given steady state) and economic MPC (i.e. when the
objective is to minimize a cost function which does not necessarily attains its
minimum at a steady state). It is shown that the proposed technique provides,
in general, a larger feasibility set with respect to existing approaches, given
the same computational complexity. Moreover, a new receding horizon strategy is
introduced, exploiting the generalized terminal state constraint. Under mild
assumptions, the new strategy is guaranteed to converge in finite time, with
arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal
state constraint, while still enjoying a larger feasibility set. The features
of the new technique are illustrated by three examples.Comment: Part of the material in this manuscript is contained in a paper
accepted for publication on Automatica and it is subject to Elsevier
copyright. The copy of record is available on http://www.sciencedirect.com
A waiting time phenomenon for thin film equations
We prove the occurrence of a waiting time phenomenon for solutions to fourth order degenerate parabolic differential equations which model the evolution of thin films of viscous fluids. In space dimension less or equal to three, we identify a general criterion on the growth of initial data near the free boundary which guarantees that for sufficiently small times the support of strong solutions locally does not increase. It turns out that this condition only depends on the smoothness of the diffusion coefficient in its point of degeneracy. Our approach combines a new version of Stampacchia's iteration lemma with weighted energy or entropy estimates. On account of numerical experiments, we conjecture that the
aforementioned growth criterion is optimal
Compact surfaces with no Bonnet mate
This note gives sufficient conditions (isothermic or totally nonisothermic)
for an immersion of a compact surface to have no Bonnet mate.Comment: 7 pages, LaTeX2
Suppressing the impact of a high tensor-to-scalar ratio on the temperature anisotropies
The BICEP2 collaboration has reported a strong B mode signal in the CMB
polarization, which is well fit by a tensor-to-scalar ratio of r ~ 0.2. This is
greater than the upper limit r < 0.11 obtained from the temperature
anisotropies under the assumption of a constant scalar spectral index n_s. This
discrepancy can be reduced once the statistical error and the contamination
from polarized dust are accounted for. If however a large value for r will be
confirmed, it will need to be reconciled with the temperature anisotropies
data. The most advocated explanation involves a variation of n_s with scales
(denoted as running) that has a magnitude significantly greater than the
generic slow roll predictions. We instead study the possibility that the large
scale temperature anisotropies are not enhanced because of a suppression of the
scalar power at large scales. Such a situation can be achieved for instance by
a sudden change of the speed of the inflaton (by about 14 %), and we show that
it fits the temperature anisotropies and polarization data considerably better
than a constant running (its chi^2 improves by ~ 7.5 over that of the constant
running, at the cost of one more parameter). We also consider the possibility
that the large scale temperature fluctuations are suppressed by an
anti-correlation between tensor and scalar modes. Unfortunately, while such
effect does affect the temperature fluctuations at large scales, it does not
affect the temperature power spectrum and cannot, therefore, help in
reconciling a large value of r with the limits from temperature fluctuations.Comment: Published version. 14 pages, 5 figure
Backscatter Transponder Based on Frequency Selective Surface for FMCW Radar Applications
This paper describes an actively-controlled frequency selective surface (FSS) to implement a backscatter transponder. The FSS is composed by dipoles loaded with switching PIN diodes. The transponder exploits the change in the radar cross section (RCS) of the FSS with the bias of the diodes to modulate the backscattered response of the tag to the FMCW radar. The basic operation theory of the system is explained here. An experimental setup based on a commercial X-band FMCW radar working as a reader is proposed to measure the transponders. The transponder response can be distinguished from the interference of non-modulated clutter, modulating the transponder’s RCS. Some FSS with different number of dipoles are studied, as a proof of concept. Experimental results at several distances are provided
Bulk shape of brane-world black holes
We propose a method to extend into the bulk asymptotically flat static
spherically symmetric brane-world metrics. We employ the multipole (1/r)
expansion in order to allow exact integration of the relevant equations along
the (fifth) extra coordinate and make contact with the parameterized
post-Newtonian formalism. We apply our method to three families of solutions
previously appeared as candidates of black holes in the brane world and show
that the shape of the horizon is very likely a flat ``pancake'' for
astrophysical sources.Comment: 10 pages, MPLA style, 5 figures, accepted for publication in MPL
Methodological problems in solvency assessment of an insurance company
The recent wide development and changes in insurance markets highlighted the necessity to map out the solvency analysis in a more complete framework. The approach we present in the paper comes up with an integrated analysis of the risk profile of an insurance business, taking into account the actual European directives about solvency assessment. The aim of the paper is to construct a methodology apt to incorporate properly the effect of the risk sources in calculating mathematical provisions related to a portfolio of insurance policies.Life insurance, financial risk, demographic risk, capital adequacy, reserves, conditional random processes
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