Search results for "Mathematical"
showing 10 items of 7967 documents
Partial Stabilization of Input-Output Contact Systems on a Legendre Submanifold
2017
This technical note addresses the structure preserving stabilization by output feedback of conservative input-output contact systems, a class of input-output Hamiltonian systems defined on contact manifolds. In the first instance, achievable contact forms in closed-loop and the associated Legendre submanifolds are analysed. In the second instance the stability properties of a hyperbolic equilibrium point of a strict contact vector field are analysed and it is shown that the stable and unstable manifolds are Legendre submanifolds. In the third instance the consequences for the design of stable structure preserving output feedback are derived: in closed-loop one may achieve stability only rel…
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 laplace type problem for three lattices with non-convex cell
2016
In this paper we consider three lattices with cells represented in Fig. 1, 3 and 5 and we determine the probability that a random segment of constant length intersects a side of lattice. c ⃝2016 All rights reserved.
Harsanyi Power Solutions for Cooperative Games on Voting Structures
2019
International audience; This paper deals with Harsanyi power solutions for cooperative games in which partial cooperation is based on specific union stable systems given by the winning coalitions derived from a voting game. This framework allows for analyzing new and real situations in which there exists a feedback between the economic influence of each coalition of agents and its political power. We provide an axiomatic characterization of the Harsanyi power solutions on the subclass of union stable systems arisen from the winning coalitions from a voting game when the influence is determined by a power index. In particular, we establish comparable axiomatizations, in this context, when co…
TIME-MINIMAL CONTROL OF DISSIPATIVE TWO-LEVEL QUANTUM SYSTEMS: THE INTEGRABLE CASE
2009
The objective of this article is to apply recent developments in geometric optimal control to analyze the time minimum control problem of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. We focus our analysis on the case where the extremal Hamiltonian is integrable.
Density Flow in Dynamical Networks via Mean-Field Games
2016
Current distributed routing control algorithms for dynamic networks model networks using the time evolution of density at network edges, while the routing control algorithm ensures edge density to converge to a Wardrop equilibrium, which was characterized by an equal traffic density on all used paths. We rearrange the density model to recast the problem within the framework of mean-field games. In doing that, we illustrate an extended state-space solution approach and we study the stochastic case where the density evolution is driven by a Brownian motion. Further, we investigate the case where the density evolution is perturbed by a bounded adversarial disturbance. For both the stochastic a…
A Pareto optimal design approach for simultaneous control of thinning and springback in stamping processes
2009
One of the most relevant research issues in automotive field is focused on the reduction of stamped parts weight also increasing their strength. In this way, a strong research effort is developed on high strength steels which are widely utilized and they require a proper springback control. Springback reduction in sheet metal forming is a typical goal to be pursued which is conflicting with thinning reduction for instance. Thus, such problems can be considered as multi-objective ones characterized by conflicting objectives. What is more, nowadays, a great interest would be focused on the availability of a cluster of possible optimal solutions instead of a single one, particularly in an indu…
Data-based modeling and estimation of vehicle crash processes in frontal fixed-barrier crashes
2017
Abstract As a complex process, vehicle crash is challenging to be described and estimated mathematically. Although different mathematical models are developed, it is still difficult to balance the complexity of models and the performance of estimation. The aim of this work is to propose a novel scheme to model and estimate the processes of vehicle-barrier frontal crashes. In this work, a piecewise model structure is predefined to represent the accelerations of vehicle in frontal crashes. Each segment in the model is corresponding to the energy absorbing component in the crashworthiness structure. With the help of Ensemble Empirical Mode Decomposition (EEMD), a robust scheme is proposed for …
Regenerative scheduling problem in engineer to order manufacturing: an economic assessment
2021
The dynamic production scheduling is a very complex process that may arise from the occurrence of unpredictable situations such as the arrival of new orders besides the ones already accepted. As a consequence, companies may often encounter several difficulties to make decisions about the new orders acceptance and sequencing along with the production of the existing ones. With this recognition, a mathematical programming model for the regenerative scheduling problem with deterministic processing times is formulated in the present paper to evaluate the economic advantage of accepting a new order in an engineer to order (ETO) manufacturing organization. The real case of an Italian ETO company …
George-Veeramani Fuzzy Metrics Revised
2018
In this note, we present an alternative approach to the concept of a fuzzy metric, calling it a revised fuzzy metric. In contrast to the traditional approach to the theory of fuzzy metric spaces which is based on the use of a t-norm, we proceed from a t-conorm in the definition of a revised fuzzy metric. Here, we restrict our study to the case of fuzzy metrics as they are defined by George-Veeramani, however, similar revision can be done also for some other approaches to the concept of a fuzzy metric.