| Title: |
Kleene Algebra to Compute Invariant Sets of Dynamical Systems |
| Authors: |
Le Mézo, Thomas; Jaulin, Luc; Massé, Damien; Zerr, Benoit |
| Contributors: |
École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne); Equipe ROBotics for EXploration (Lab-STICC_ROBEX); Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC); École Nationale d'Ingénieurs de Brest (ENIB); Université de Brest (UBO EPE)-Institut National Polytechnique de Bretagne (Bretagne INP)-Université de Brest (UBO EPE)-Institut National Polytechnique de Bretagne (Bretagne INP)-Université de Bretagne Sud (UBS)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom Paris (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique (IMT Atlantique); Institut Mines-Télécom Paris (IMT)-École Nationale d'Ingénieurs de Brest (ENIB); Institut Mines-Télécom Paris (IMT); Université de Brest (UBO EPE) |
| Source: |
ISSN: 1999-4893 ; Algorithms ; https://ensta.hal.science/hal-03648084 ; Algorithms, 2022, 15 (3), pp.90. ⟨10.3390/a15030090⟩. |
| Publisher Information: |
CCSD; MDPI |
| Publication Year: |
2022 |
| Collection: |
Université de Bretagne Occidentale: HAL |
| Subject Terms: |
path planning; nonlinear dynamical systems; Kleene algebra; invariant sets; [SPI.AUTO]Engineering Sciences [physics]/Automatic; [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]; [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] |
| Description: |
International audience ; 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 invariant-based sets for continuous-time nonlinear dynamical systems. Our contribution is to provide the definitions and theorems that will allow us to make the link between the theory of invariant sets and the Kleene algebra. This link has never be done before and will allow us to compute rigorously sets that can be defined as a combination of positive invariant sets. Some illustrating examples show the nice properties of the approach. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| DOI: |
10.3390/a15030090 |
| Availability: |
https://ensta.hal.science/hal-03648084; https://ensta.hal.science/hal-03648084v1/document; https://ensta.hal.science/hal-03648084v1/file/algorithms-15-00090-v2.pdf; https://doi.org/10.3390/a15030090 |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.8B3A9F4D |
| Database: |
BASE |