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