Search results for "Mathematic"
showing 10 items of 24974 documents
Adaptive-Gain Observers and Applications
2007
We distinguish two kinds of observers for nonlinear systems which are used by scientists and engineers: empirical observers and converging observers.
Субфинслерова задача на группе Картана
2019
Изучается задача субфинслеровой геометрии на свободной нильпотентной группе ранга $2$ глубины $3$. Такая группа также называется группой Картана, она имеет естественную структуру группы Карно, на которой вводится метрика с помощью $\ell _\infty $-нормы на ее первом слое. Используются методы теории оптимального управления. С помощью принципа максимума Понтрягина охарактеризованы экстремальные кривые. Описаны анормальные и особые дуги, построен релейный поток.
Modified F-transform Based on B-splines
2018
The aim of this paper is to improve the F-transform technique based on B-splines. A modification of the F-transform of higher degree with respect to fuzzy partitions based on B-splines is done to extend the good approximation properties from the interval where the Ruspini condition is fulfilled to the whole interval under consideration. The effect of the proposed modification is characterized theoretically and illustrated numerically.
Metric Rectifiability of ℍ-regular Surfaces with Hölder Continuous Horizontal Normal
2021
Abstract Two definitions for the rectifiability of hypersurfaces in Heisenberg groups $\mathbb{H}^n$ have been proposed: one based on ${\mathbb{H}}$-regular surfaces and the other on Lipschitz images of subsets of codimension-$1$ vertical subgroups. The equivalence between these notions remains an open problem. Recent partial results are due to Cole–Pauls, Bigolin–Vittone, and Antonelli–Le Donne. This paper makes progress in one direction: the metric Lipschitz rectifiability of ${\mathbb{H}}$-regular surfaces. We prove that ${\mathbb{H}}$-regular surfaces in $\mathbb{H}^{n}$ with $\alpha $-Hölder continuous horizontal normal, $\alpha> 0$, are metric bilipschitz rectifiable. This impr…
A Novel Intelligent Technique of Invariant Statistical Embedding and Averaging via Pivotal Quantities for Optimization or Improvement of Statistical …
2020
In the present paper, for intelligent constructing efficient (optimal, uniformly non-dominated, unbiased, improved) statistical decisions under parametric uncertainty, a new technique of invariant embedding of sample statistics in a decision criterion and averaging this criterion over pivots’ probability distributions is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, the technique of invariant statistical embedding and averaging via pivotal quantities (ISE&APQ) is independent of the choice of priors and represents a novelty i…
Large multiple neighborhood search for the soft-clustered vehicle-routing problem
2021
Abstract The soft-clustered vehicle-routing problem (SoftCluVRP) is a variant of the classical capacitated vehicle-routing problem. Customers are partitioned into clusters and all customers of the same cluster must be served by the same vehicle. In this paper, we present a large multiple neighborhood search for the SoftCluVRP. We design and analyze multiple cluster destroy and repair operators as well as two post-optimization components, which are both based on variable neighborhood descent. The first allows inter-route exchanges of complete clusters, while the second searches for intra-route improvements by combining classical neighborhoods (2-opt, Or-opt, double-bridge) and the Balas-Simo…
LMI-based 2D-3D Registration: from Uncalibrated Images to Euclidean Scene
2015
International audience; This paper investigates the problem of registering a scanned scene, represented by 3D Euclidean point coordinates , and two or more uncalibrated cameras. An unknown subset of the scanned points have their image projections detected and matched across images. The proposed approach assumes the cameras only known in some arbitrary projective frame and no calibration or autocalibration is required. The devised solution is based on a Linear Matrix Inequality (LMI) framework that allows simultaneously estimating the projective transformation relating the cameras to the scene and establishing 2D-3D correspondences without triangulating image points. The proposed LMI framewo…
Convergence of direct recursive algorithm for identification of Preisach hysteresis model with stochastic input
2015
We consider a recursive iterative algorithm for identification of parameters of the Preisach model, one of the most commonly used models of hysteretic input-output relationships. The classical identification algorithm due to Mayergoyz defines explicitly a series of test inputs that allow one to find parameters of the Preisach model with any desired precision provided that (a) such input time series can be implemented and applied; and, (b) the corresponding output data can be accurately measured and recorded. Recursive iterative identification schemes suitable for a number of engineering applications have been recently proposed as an alternative to the classical algorithm. These recursive sc…
Adaptive-gain extended Kalman filter: Extension to the continuous-discrete case
2009
In the present article we propose a nonlinear observer that merges the behaviors 1) of an extended Kalman filter, mainly designed to smooth off noise , and 2) of high-gain observers devoted to handle large perturbations in the state estimation. We specifically aim at continuous-discrete systems. The strategy consists in letting the high-gain self adapt according to the innovation. We define innovation computed over a time window and justify its usage via an important lemma. We prove the general convergence of the resulting observer.
Consistent Clustering of Elements in Large Pairwise Comparison Matrices
2018
[EN] In multi-attribute decision making the number of decision elements under consideration may be huge, especially for complex, real-world problems. Typically these elements are clustered and then the clusters organized hierarchically to reduce the number of elements to be simultaneously handled. These decomposition methodologies are intended to bring the problem within the cognitive ability of decision makers. However, such methodologies have disadvantages, and it may happen that such a priori clustering is not clear, and/or the problem has previously been addressed without any grouping action. This is the situation for the case study we address, in which a panel of experts gives opinions…