Search results for " Mathematics"
showing 10 items of 10797 documents
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…
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…
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…
Decoupled nonlinear adaptive control of position and stiffness for pneumatic soft robots
2020
This article addresses the problem of simultaneous and robust closed-loop control of joint stiffness and position, for a class of antagonistically actuated pneumatic soft robots with rigid links and compliant joints. By introducing a first-order dynamic equation for the stiffness variable and using the additional control degree of freedom, embedded in the null space of the pneumatic actuator matrix, an innovative control approach is introduced comprising an adaptive compensator and a dynamic decoupler. The proposed solution builds upon existing adaptive control theory and provides a technique for closing the loop on joint stiffness in pneumatic variable stiffness actuators. Under a very mi…
Traffic data acquirement by unmanned aerial vehicle
2017
This paper presents a methodology aimed to acquire traffic flow data through the employment of unmanned aerial vehicles (UAVs). The study is focused on the determination of driving behavior parameters of road users and on the reconstruction of traffic flow Origin/Destination matrix. The methodology integrates UAV flights with video image processing technique, and the capability of geographic information systems, to represent spatiotemporal phenomena. In particular, analyzing different intersections, the attention of the authors is focused on users’ gap acceptance in a naturalistic drivers’ behavior condition (drivers are not influenced by the presence of instruments and operators on the roa…
Optimality Conditions for Non-Qualified Parabolic Control Problems
1994
We consider parabolic state constrained optimal control problems where the usual Slater condition is not necessarily satisfied. Instead, a weaker interiority property is assumed. Optimality conditions with a Lagrange multiplier are given. As an application we present an augmented Lagrangian algorithm. Numerical test results are included.
Rotation estimation and vanishing point extraction by omnidirectional vision in urban environment
2012
International audience; Rotation estimation is a fundamental step for various robotic applications such as automatic control of ground/aerial vehicles, motion estimation and 3D reconstruction. However it is now well established that traditional navigation equipments, such as global positioning systems (GPSs) or inertial measurement units (IMUs), suffer from several disadvantages. Hence, some vision-based works have been proposed recently. Whereas interesting results can be obtained, the existing methods have non-negligible limitations such as a difficult feature matching (e.g. repeated textures, blur or illumination changes) and a high computational cost (e.g. analyze in the frequency domai…