756 research outputs found
Convex Chance Constrained Model Predictive Control
We consider the Chance Constrained Model Predictive Control problem for
polynomial systems subject to disturbances. In this problem, we aim at finding
optimal control input for given disturbed dynamical system to minimize a given
cost function subject to probabilistic constraints, over a finite horizon. The
control laws provided have a predefined (low) risk of not reaching the desired
target set. Building on the theory of measures and moments, a sequence of
finite semidefinite programmings are provided, whose solution is shown to
converge to the optimal solution of the original problem. Numerical examples
are presented to illustrate the computational performance of the proposed
approach.Comment: This work has been submitted to the 55th IEEE Conference on Decision
and Contro
Reconstruction of Support of a Measure From Its Moments
In this paper, we address the problem of reconstruction of support of a
measure from its moments. More precisely, given a finite subset of the moments
of a measure, we develop a semidefinite program for approximating the support
of measure using level sets of polynomials. To solve this problem, a sequence
of convex relaxations is provided, whose optimal solution is shown to converge
to the support of measure of interest. Moreover, the provided approach is
modified to improve the results for uniform measures. Numerical examples are
presented to illustrate the performance of the proposed approach.Comment: This has been submitted to the 53rd IEEE Conference on Decision and
Contro
Sizes and albedos of Mars-crossing asteroids from WISE/NEOWISE data
Context. Mars-crossing asteroids (MCs) are a dynamically unstable group
between the main belt and the near-Earth populations. Characterising the
physical properties of a large sample of MCs can help to understand the
original sources of many near-Earth asteroids, some of which may produce
meteorites on Earth. Aims. Our aim is to provide diameters and albedos of MCs
with available WISE/NEOWISE data. Methods. We used the near-Earth asteroid
thermal model to find the best-fitting values of equivalent diameter and,
whenever possible, the infrared beaming parameter. With the diameter and
tabulated asteroid absolute magnitudes we also computed the visible geometric
albedos. Results. We determined the diameters and beaming parameters of 404
objects observed during the fully cryogenic phase of the WISE mission, most of
which have not been published elsewhere. We also obtained 1572 diameters from
data from the 3-Band and posterior non-cryogenic phases using a default value
of beaming parameter. The average beaming parameter is 1.2 +/- 0.2 for objects
smaller than 10 km, which constitute most of our sample. This is higher than
the typical value of 1.0 found for the whole main belt and is possibly related
to the fact that WISE is able to observe many more small objects at shorter
heliocentric distances, i.e. at higher phase angles. We argue that this is a
better default value for modelling Mars-crossing asteroids from the
WISE/NEOWISE catalogue and discuss the effects of this choice on the diameter
and albedo distributions. We find a double-peaked distribution for the visible
geometric albedos, which is expected since this population is compositionally
diverse and includes objects in the major spectral complexes. However, the
distribution of beaming parameters is homogeneous for both low- and high-albedo
objects.Comment: 8 pages, 6 figures, accepted for publication in Astronomy &
Astrophysic
Corporate taxes and the location of FDI in Europe using firm-level data
European countries are facing an ever-increasing competition for Foreign Direct Investment (FDI). This paper studies how corporate taxes affect the location of FDI in Europe. Firm-level data is used to estimate a conditional logit model. We start by analysing the impact of the level and volatility of three different tax rates on FDI. Next, we analyse how economic and monetary integration influences the effect of taxes on FDI. The interaction between taxes and the upward and downward cycles of FDI is also analysed. Finally, we focus on how the impact of taxes depends on project characteristics. We conclude that taxes play a significant role in attracting FDI, but the issues analysed imply that there are some nuances in this relation, many of them relevant for policy makers.FDI, Location, Taxes, Conditional Logit Model
Simple Approximations of Semialgebraic Sets and their Applications to Control
Many uncertainty sets encountered in control systems analysis and design can
be expressed in terms of semialgebraic sets, that is as the intersection of
sets described by means of polynomial inequalities. Important examples are for
instance the solution set of linear matrix inequalities or the Schur/Hurwitz
stability domains. These sets often have very complicated shapes (non-convex,
and even non-connected), which renders very difficult their manipulation. It is
therefore of considerable importance to find simple-enough approximations of
these sets, able to capture their main characteristics while maintaining a low
level of complexity. For these reasons, in the past years several convex
approximations, based for instance on hyperrect-angles, polytopes, or
ellipsoids have been proposed. In this work, we move a step further, and
propose possibly non-convex approximations , based on a small volume polynomial
superlevel set of a single positive polynomial of given degree. We show how
these sets can be easily approximated by minimizing the L1 norm of the
polynomial over the semialgebraic set, subject to positivity constraints.
Intuitively, this corresponds to the trace minimization heuristic commonly
encounter in minimum volume ellipsoid problems. From a computational viewpoint,
we design a hierarchy of linear matrix inequality problems to generate these
approximations, and we provide theoretically rigorous convergence results, in
the sense that the hierarchy of outer approximations converges in volume (or,
equivalently, almost everywhere and almost uniformly) to the original set. Two
main applications of the proposed approach are considered. The first one aims
at reconstruction/approximation of sets from a finite number of samples. In the
second one, we show how the concept of polynomial superlevel set can be used to
generate samples uniformly distributed on a given semialgebraic set. The
efficiency of the proposed approach is demonstrated by different numerical
examples
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