When using convex probability sets (or, equivalently, lower previsions) as uncertainty models, identifying extreme points can help simplifying various computations or the use of some algorithms. In general, sets induced by specific models such as possibility distributions, linear vacuous mixtures or 2-monotone measures may have extreme points easier to compute than generic convex sets. In this ...

In this work we present the uncertainty transformation and its properties and apply these in a frequently encountered problem in computer vision: the alignment problem. A convex polytope is used to captivate the uncertainty of transformations that arises when the position of image points is not exactly known. The uncertainty polytope is used to compute the correspondences between points on the ...

In this paper a new method is introduced for path planning of an autonomous vehicle. In this method, the environment is considered cluttered and with some uncertainty sources. Thus, the state of detected object should be estimated using an optimal filter. To do so, the state distribution is assumed Gaussian. Thus the state vector is estimated by a Kalman filter at each time step. The estimation...

An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k ≥ 1, let g(k) be the smallest integer such that every planar point set in general position with at least g(k) interior points has a convex subset of points with exactly k interior points of P . In this article, we prove that g(3)= 9.

We prove sharp regularity results for the convex envelope of a continuous function inside a convex domain.

This paper studies the composition operator for credal sets introduced at the last ISIPTA conference in more detail. Our main attention is devoted to the relationship between a special type of compositional model, so-called perfect sequences of credal sets, and those of (precise) probability distributions, with the goal of finding the relationship between credal compositional models and credal ...

Electric power grids regularly experience uncertain fluctuations from load demands and renewables, which poses a risk of violating operational limits designed to safeguard the system. In this paper, we consider robust AC OPF problem that minimizes generation cost while requiring certain level system security in presence uncertainty. The requires satisfy for all uncertainty realizations within s...

A new method for robust fixed-order H∞ controller design for uncertain time-delayed MIMO systems is presented. It is shown that the H∞ robust performance condition can be represented by a set of convex constraints with respect to the parameters of a linearly parameterized primary controller in the Smith predictor structure. Therefore, the parameters of the primary controller can be obtained by ...

If X is a vector space and E is a subset of X, the convex hull of E is defined to be the intersection of all convex sets containing E, and is denoted by co(E). One checks that the convex hull of E is equal to the set of all finite convex combinations of elements of E. If X is a topological vector space, the closed convex hull of E is the intersection of all closed convex sets containing E, and ...

Let K be a smooth convex set with volume one in R. Choose n random points in K independently according to the uniform distribution. The convex hull of these points, denoted by Kn, is called a random polytope. We prove that several key functionals of Kn satisfy the central limit theorem as n tends to infinity.