Interval Analysis : Methods, Applications, Contractors and Sets
Luc Jaulin, Nacim Ramdani, Nacim Meslem, Tarek Raissi, Benoît Desrochers, Michel Kieffer


  1. Welcome to IAMACS
  2. People
  3. Slides
  4. A small doc on PyIbex and Vibes
  5. Exercise 0. Install all you need
  6. Exercise 1. Contractors and separators
  7. Exercise 2. Parameter estimation
  8. Exercise 3. Localization of a robot
  9. Exercise 4. Simultaneous Localization And Mapping (SLAM)

Welcome to IAMACS

IAMACS (Interval Analysis: Methods, Applications, Contractors and Sets) is a two-days summer school that will take place July 8-9 during the IFAC Congres in Toulouse All courses and conversations will be in English.
During this school, you will have several speakers and some practices. This page is mainly related to the practice. We believe that it is better if you arrive with your own computer. If you cannot, please, let us know and we will find a solution.
Before arriving to the school, please, install Python, PyIbex, Vibes. The procedure is described in Exercise 0. The install should be easy but in case of problems, we will be here to help you, now (lucjaulin@gmail.com) or later in Toulouse.
In this school, you will also have some exercises to do. They will be taken from Exercises 8,9,10,11 in this pdf file.

More details can be found on the website of Nacim Ramdani at this link this link.

Venue : Toulouse, Pierre Baudis Congress center, Room : Ariane 2.
Day 1. Saturday 8 July 2017, 9h-17h30
9h-10h30, 11h-12h30. Luc Jaulin (Lab-STICC, France): Interval methods.
14h-15h30. Nacim Ramdani (Université d’Orléans, France) Reachability computation with hybrid dynamical systems. Application to state estimation.
16h-17h30. Nacim Meslem (Grenoble-INP, France) and Nacim Ramdani (Université d’Orléans, France): Reachability for control synthesis and validation.

Day 2. Sunday 9 July 2017, 9h-17h30
9h-10h30. Michel Kieffer (Université Paris-Sud, IUF, France) : Guaranteed characterization of confidence sets: Application to distributed localisation.
11h-12h30. Tarek Raïssi (CNAM, Paris, France) Interval observers and fault tolerant control.
14h-15h30, 16h-17h30. Luc Jaulin (ENSTA Bretagne, France) and Benoît Desrochers (DGA-TN)


Luc Jaulin

Chapter 1: Intervals
Chapter 2: Subpavings
Chapter 3: Contractors
Chapter 4: Separators
Chapter 5: Robust estimation

Michel Kieffer

Slides Part 1
Slides Part 2

Nacim Meslem


Nacim Ramdani


Tarek Raissi



Name Town Country
BALUGANI Elia Modena Italy
FERGANI SOHEIB Fergani Toulouse France
HAMMOUCHE Mounir Besancon France
LICHTENBERG Gerwald Hamburg Germany
MAHATO Nisha Rani Rourkela India
REITERER Florian Linz Linz Austria
Vencatasamy Khadimoullah Paris/Brest France
VERDIER Cees Ferdinand Delft Netherland
BHIRI Bassem Longwy France
BOUKAL Yassine Longwy France
CUNIS Torbjørn Toulouse France
DALMAS Violaine Grenoble France
GASMI Noussaiba LONGWY France
BORSALI Salima Tlemcen Algeria
TRAN Tuan Anh Toulouse France
HADJ HENNI Abderraouf Bourges France
ARKHIPOV Dmitry Toulouse France
MEYER Luc Evry France

Exercise 0. Install all you need


In the last version of PyIbex (2017), few things have changed in the Python code and the code written in the videos is not always exactly consistent with the latest version of PyIbex. Below are listed the changes.
from pyIbex import * should be replaced by from pyibex import *
SepQInterProjF should be replaced by SepQInter
Moreover, to start Vibes from your terminal, write Vibes-viewer instead of vibes.
Some other modifications are described in the PyIbex documentation. (in magenta)


The goal of Exercise 0 is to help you to install all what you need to follow IAMACS. You need Vibes for graphics.


If you already use Python and you feel confortable with the installation, you probably do not need to install all tools. It suffices to go to the PyIbex site. If Python is not installed in your computer, the best is to follow the following procedure:
1) Install Conda as described at http://conda.pydata.org/docs/install/.
2) Install pyibex

     conda install -c benensta pyibex 
3) Install Vibes
     conda install -c benensta vibes vibes-bin 
4) Install Spyder
     conda install spyder 
A video to help you for the install is available for Windows and also for Linux (Ubuntu).

Proxy problems. In your institute, you may have a proxy which blocks some access to conda packages. In this case, the install can be done from your home, or from any internet environment without any proxy.

Exercise 1. Contractors and separators

This corresponds to Exercice 8 found in this this pdf file.
A separator is a pair of two contractors: an inner contractor and an outer contractor. This exercise illustrates how Pybex (which is a Python extension of Ibex) can be used to build easily separators for sets defined as union, intersection and complements of primitive sets. You can use the second part of the following video in case of problems.

Exercise 2. Parameter estimation

This corresponds Exercice 9 found of this pdf file.
Bounded error estimation problems can now be solved very easily and efficiently with the help of PyIbex.

Exercise 3. Localization of a robot from landmarks using range and bearing measurements

This corresponds Exercice 10 found of this pdf file.
This exercise shows an important application which can be solved efficiently with interval analysis. Without any linearization, we show that it is possible to localize a robot in a guaranteed manner.

Exercise 4. Simultaneous Localization And Mapping (SLAM)

This corresponds Exercice 11 found of this pdf file.
In a SLAM problem, many variables are involved with nonlinear constraints. This problem is considered as difficult. We show here that it it possible to solve it easily and in a reliable way using intervals.