Introduction aux contraintes d'intervalles; application à l'estimation à erreurs bornées

à Biarritz (France) du 15/11 au 16/11/2001Journées S3P "Simulation de Produits, de Procédés et de Processus industriels"Dans cet article, nous allons décrire le formalisme des contraintes d'intervalles appliquées au problème de l'estimation d'une somme de trois exponentielles dans un contexte à erreurs bornées. Les outils dédiés aux contraintes constituent une alternative aux méthodes d'optimisation classiques. Ils accélèrent la convergence, et garantissent des solutions fiables

Inner and outer approximation of capture basins using interval analysis

Abstract: This paper proposes a new approach to solve the problem of computing the capture basin C of a target T. The capture basin corresponds to the set of initial states such that the target is reached in finite time before possibly leaving of constrained set. We present an algorithm, based on interval analysis, able to characterize an inner and an outer approximation C − ⊂ C ⊂ C+ of the capture basin. The resulting algorithm is illustrated on the Zermelo problem

Capture basin approximation using interval analysis

This paper proposes a new approach for computing the capture basin C of a target T. The capture basin corresponds to the set of initial state vectors such that the target could be reached in finite time via an appropriate control input, before possibly leaving the target. Whereas classical capture basin characterization does not provide any guarantee on the set of state vectors that belong to the capture basin, interval analysis and guaranteed numerical integration allow us to avoid any indetermination. We present an algorithm that is able to provide guaranteed approximation of the inner C− and the outer C+ of the capture basin, such that C−⊆C⊂C+. In order to illustrate the principle and the efficiency of the approach, a testcase on the ‘car on the hill’ problem is provided. Copyright © 2010 John Wiley & Sons, Ltd

Guaranteeing the homotopy type of a set defined by non-linear inequalities

This paper provides an effective method to create an abstract simplicial complex homotopy equivalent to a given set S described by non-linear inequalities (polynomial or not). To our knowledge, no other numerical algorithm is able to deal with this type of problem. The proposed approach divides S into subsets that have been proven to be contractible using interval arithmetic. The method is close to Čech cohomology and uses the nerve theorem. Some examples illustrate the principle of the approach. This algorithm has been implemented

On Sufficient Conditions of the Injectivity: Development of a Numerical Test Algorithm via Interval Analysis

This paper presents a new numerical algorithm based on interval analysis able to verify that a continuously differentiable function is injective. The efficiency of the method is demonstrated by illustrative examples. These examples have been treated by a C++ solver which is made available

High speed partial Stokes imaging using a ferroelectric liquid crystal modulator

This paper describes the implementation of an imaging polarimeter using a single ferroelectric liquid crystal light modulator. It provides partial imaging Stokes information at 234 Hz, much faster than polarimeters using nematic light modulators. This information is obtained for dynamic scenes in reflection or transmission. Partial Stokes information contains the first three Stokes parameters. With this information, imaging of the linear degree of polarization and of the angle of polarization can be obtained and imaging linear depolarization can be quantified

State estimation of a dehydration process by interval analysis

This article presents a general methodology of state estimation by interval analysis in a dynamic system modeled by difference equations. The methodology is applied to a pineapple osmotic dehydration process, in order to predict the behavior of the process within a range of allowed perturbation. The paper presents simulations and validations