Solving set-valued constraint satisfaction problems

In this paper, we consider the resolution of constraint satisfaction problems in the case where the variables of the problem are subsets of ${\mathbb{R}^{n}}$ . In order to use a constraint propagation approach, we introduce set intervals (named i-sets), which are sets of subsets of ${\mathbb{R}^{n}}$ with a lower bound and an upper bound with respect to the inclusion. Then, we propose basic operations for i-sets. This makes possible to build contractors that are then used by the propagation to solve problem involving sets as unknown variables. In order to illustrate the principle and the efficiency of the approach, a testcase is provided.     

Guaranteed recursive non‐linear state bounding using interval analysis

The problem considered here is state estimation in the presence of unknown but bounded state perturbations and measurement noise. In this context, most available results are for linear models, and the purpose of the present paper is to deal with the non‐linear case. Based on interval analysis and the notion of set inversion, a new state estimator is presented, which evaluates a set estimate guaranteed to contain all values of the state that are consistent with the available observations, given the perturbation and noise bounds and a set containing the initial value of the state. To the best of our knowledge, it is the first estimator for which this claim can be made. The precision of the set estimate can be improved, at the cost of more computation. Theoretical properties of the estimator are studied, and computer implementation receives special attention. A simple illustrative example is treated. Copyright © 2002 John Wiley & Sons, Ltd.     

Contracting Optimally an Interval Matrix without Loosing Any Positive Semi-Definite Matrix Is a Tractable Problem

In this paper, we show that the problem of computing the smallest interval submatrix of a given interval matrix [A] which contains all symmetric positive semi-definite (PSD) matrices of [A], is a linear matrix inequality (LMI) problem, a convex optimization problem over the cone of positive semidefinite matrices, that can be solved in polynomial time. From a constraint viewpoint, this problem corresponds to projecting the global constraint PSD (A) over its domain [A]. Projecting such a global constraint, in a constraint propagation process, makes it possible to avoid the decomposition of the PSD constraint into primitive constraints and thus increases the efficiency and the accuracy of the resolution.D. Henrion acknowledges support of grant No. 102/02/0709 of the Grant Agency of the Czech Republic, and project No. ME 698/2003 of the Ministry of Education of the Czech Republic.     

Comparison of Interval Analysis and Standard Statistical Methods for Estimating Experimental Data with Uncertainty

Measurement Techniques - Interval analysis procedures are used to estimate the parameters of an experimental chemical process under conditions of noise and uncertainty in the probabilistic...     

Set-membership localization with probabilistic errors

Interval methods have been shown to be efficient, robust and reliable to solve difficult set-membership localization problems. However, they are unsuitable in a probabilistic context, where the approximation of an unbounded probability density function by a set cannot be accepted. This paper proposes a new probabilistic approach which makes possible to use classical set-membership localization methods which are robust with respect to outliers. The approach is illustrated on two simulated examples.     

Platooning Control for Sailboats Using a Tack Strategy

International Journal of Control, Automation and Systems - This paper addresses the problem of platooning control for a fleet of sailboats. A quadrilateral path is proposed to avoid going into the...     

Robust Autonomous Robot Localization Using Interval Analysis

This paper deals with the determination of the position and orientation of a mobile robot from distance measurements provided by a belt of onboard ultrasonic sensors. The environment is assumed to be two-dimensional, and a map of its landmarks is available to the robot. In this context, classical localization methods have three main limitations. First, each data point provided by a sensor must be associated with a given landmark. This data-association step turns out to be extremely complex and time-consuming, and its results can usually not be guaranteed. The second limitation is that these methods are based on linearization, which makes them inherently local. The third limitation is their lack of robustness to outliers due, e.g., to sensor malfunctions or outdated maps. By contrast, the method proposed here, based on interval analysis, bypasses the data-association step, handles the problem as nonlinear and in a global way and is (extraordinarily) robust to outliers.Luc Jaulin: on leave from Laboratoire d'Ingénierie des Systèmes Automatisés, Université d'Angers, 2 bd Lavoisier, 49045 Angers, FranceLuc Jaulin: on leave from Laboratoire d'Ingénierie des Systèmes Automatisés, Université d'Angers, 2 bd Lavoisier, 49045 Angers, FranceLuc Jaulin: on leave from Laboratoire d'Ingénierie des Systèmes Automatisés, Université d'Angers, 2 bd Lavoisier, 49045 Angers, France     

Estimation of Discrete-Event Systems Using Interval Computation

Discrete-event systems are driven by events and generate events. To describe their evolution, the dater approach associate to each event a sequence of dates, namely a dater, corresponding to the dates at which the event occurs.In this paper, we show that for a large class of discrete-event systems, the dater approach makes it possible to cast the characterization of the set of all parameters that are consistent with some collected dater, in a bounded-error context, into a set-inversion framework. Set inversion consists of characterizing the reciprocal image of a given set by a known function. Provided that an inclusion function is known for the function to be inverted, the characterization can be performed by the interval-based algorithm SIVIA. A short presentation of this algorithm is recalled in this paper. The approach is illustrated through three examples.