Robust control systems synthesis is generally recast as a class of robust feasibility problems which is to find a solution satisfying a set of parameter-dependent convex constraints for all possible parameter values. For this class of the problems, a stochastic ellipsoid method with multiple cuts each of which corresponds to each of the constraint is proposed, where a new update rule is present...

This bound is achieved by the maximum volume ellipsoid contained in K. Ellipsoids have also been critical to the design and analysis of efficient algorithms. The most notable example is the ellipsoid algorithm (1, 2) for linear (3) and convex optimization (4), which represents a frontier of polynomial-time solvability. For the basic problems of sampling and integration in high dimension, the in...

This paper presents iris (Iterative Regional Inflation by Semidefinite programming), a new method for quickly computing large polytopic and ellipsoidal regions of obstacle-free space through a series of convex optimizations. These regions can be used, for example, to efficiently optimize an objective over collision-free positions in space for a robot manipulator. The algorithm alternates betwee...

Ellipsoid estimation is an issue of primary importance in many practical areas such as control, system identification, visual/audio tracking, experimental design, data mining, robust statistics and novelty/outlier detection. This paper presents a new method of kernel information matrix ellipsoid estimation (KIMEE) that finds an ellipsoid in a kernel defined feature space based on a centered inf...

The ellipsoid factor (EF) is a method for the local determination of the rod- or plate-like nature of porous or spongy continua. EF at a point within a 3D structure is defined as the difference in axis ratios of the greatest ellipsoid that fits inside the structure and that contains the point of interest, and ranges from -1 for strongly oblate (discus-shaped) ellipsoids, to +1 for strongly prol...

This paper introduces a new technique to detect the coronary arteries as well as other heart’s peripheral vessels. After finding the location of the myocardium through a graph theoretic segmentation method, the algorithm models the heart with a biaxial ellipsoid. For each point of this ellipsoid, we compute the collection of intensities that are normal to the surface. This collection is then fi...

The choice of suitable robots in manufacturing, to improve product quality and to increase productivity, is a complicated decision due to the increase in robot manufacturers and configurations. In this article, a novel approach is proposed to choose among alternatives, differently assessed by decision makers on different criteria, to make the final evaluation for decision-making. The approach i...

A self-calibration method was proposed to compensate the drawback generated by classic ellipsoid fitting algorithm. In this paper magnetometers and accelerometers were chosen to obtain geomagnetic field and gravitational field for TRIAD algorithm. The first step is using the classic ellipsoid fitting to calibrate the magnetic vector, which is taken as an internal reference in the second step. D...

Linear optimization (LO) is the fundamental problem of mathematical optimization. It admits an enormous number of applications in economics, engineering, science and many other fields. The three most significant classes of algorithms for solving LO problems are: Pivot, Ellipsoid and Interior Point Methods. Because Ellipsoid Methods are not efficient in practice we will concentrate on the comput...