Invariant sets for assume-guarantee contracts

A Girard, A Iovine, S Benberkane - 2022 IEEE 61st Conference …, 2022 - ieeexplore.ieee.org
Contract theory is a powerful tool to reason on systems that are interacting with an external
environment, possibly made of other systems. Formally, a contract is usually given by …

Computational tractable guaranteed numerical method to study the stability of n-dimensional time-independent nonlinear systems with bounded perturbation

M Louedec, L Jaulin, C Viel - Automatica, 2023 - Elsevier
The stability analysis of nonlinear continuous systems often requires manual calculation,
which can become time-consuming when dealing with complex systems. Some works use …

Computation of controlled invariant sets for discrete-time switched nonlinear systems with time-delay

R Chen, Y Li, J Liu - Journal of the Franklin Institute, 2021 - Elsevier
We consider the concept of set invariance for discrete-time switched nonlinear systems with
time-delays, referred to here as D-invariance. Specifically, the existence of controlled …

Bracketing the solutions of an ordinary differential equation with uncertain initial conditions

T Le Mézo, L Jaulin, B Zerr - Applied Mathematics and Computation, 2018 - Elsevier
In this paper, we present a new method for bracketing (ie, characterizing from inside and
from outside) all solutions of an ordinary differential equation in the case where the initial …

On positively invariant polyhedrons for continuous-time positive linear systems

B Du, S Xu, Z Shu, Y Chen - Journal of the Franklin Institute, 2020 - Elsevier
This paper is concerned with the determination of positively invariant polyhedron for positive
linear systems subject to external disturbances whose (∞, 1)-norm or (∞,∞)-norm are …

Design and control of a low-cost autonomous profiling float

T Le Mézo, G Le Maillot, T Ropert… - Mechanics & …, 2020 - mechanics-industry.org
This paper presents the development made around the SeaBot, a new low-cost profiling
float design for shallow water. We introduce a simplified dynamical model of the float and …

[PDF][PDF] Automating Geometric Proofs of Collision Avoidance with Active Corners

N Kheterpal, E Tang, JB Jeannin - CONFERENCE ON FORMAL …, 2022 - library.oapen.org
Avoiding collisions between obstacles and vehicles such as cars, robots, or aircraft is
essential to the development of autonomy. To simplify the problem, many collision …

Kleene Algebra to Compute Invariant Sets of Dynamical Systems

T Le Mézo, L Jaulin, D Massé, B Zerr - Algorithms, 2022 - mdpi.com
In this paper, we show that a basic fixed point method used to enclose the greatest fixed
point in a Kleene algebra will allow us to compute inner and outer approximations of …

Proving the stability of the rolling navigation

A Bourgois, A Chaabouni, A Rauh… - Acta Cybernetica, 2023 - cyber.bibl.u-szeged.hu
In this paper, we propose to study the stability of a navigation method that allows a robot to
move in an unstructured environment without compass by measuring a scalar function ϕ …

Safe & collaborative autonomous underwater docking: interval methods for proving the feasibility of an underwater docking problem

A Bourgois - 2021 - hal.science
The increasing number of offshore facilities triggers the need for reliable autonomous robots
to perform inspection and maintenance missions, while minimising operational expenses. In …