Kleene Algebra to Compute Invariant Sets of Dynamical Systems
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 theo...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-03-01
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| Series: | Algorithms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4893/15/3/90 |
| _version_ | 1797473310395596800 |
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| author | Thomas Le Mézo Luc Jaulin Damien Massé Benoit Zerr |
| author_facet | Thomas Le Mézo Luc Jaulin Damien Massé Benoit Zerr |
| author_sort | Thomas Le Mézo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T20:12:55Z |
| format | Article |
| id | doaj.art-c0fb360fa27248708cf87bf7c7a5e138 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-09T20:12:55Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-c0fb360fa27248708cf87bf7c7a5e1382023-11-24T00:08:58ZengMDPI AGAlgorithms1999-48932022-03-011539010.3390/a15030090Kleene Algebra to Compute Invariant Sets of Dynamical SystemsThomas Le Mézo0Luc Jaulin1Damien Massé2Benoit Zerr3ENSTA Bretagne, Robex, LabSTICC, 2 Rue François Verny, 29806 Brest, FranceENSTA Bretagne, Robex, LabSTICC, 2 Rue François Verny, 29806 Brest, FranceLab-STICC, UMR 6285, University of Brest, 29238 Brest, FranceENSTA Bretagne, Robex, LabSTICC, 2 Rue François Verny, 29806 Brest, FranceIn 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.https://www.mdpi.com/1999-4893/15/3/90invariant setsKleene algebranonlinear dynamical systemspath planning |
| spellingShingle | Thomas Le Mézo Luc Jaulin Damien Massé Benoit Zerr Kleene Algebra to Compute Invariant Sets of Dynamical Systems Algorithms invariant sets Kleene algebra nonlinear dynamical systems path planning |
| title | Kleene Algebra to Compute Invariant Sets of Dynamical Systems |
| title_full | Kleene Algebra to Compute Invariant Sets of Dynamical Systems |
| title_fullStr | Kleene Algebra to Compute Invariant Sets of Dynamical Systems |
| title_full_unstemmed | Kleene Algebra to Compute Invariant Sets of Dynamical Systems |
| title_short | Kleene Algebra to Compute Invariant Sets of Dynamical Systems |
| title_sort | kleene algebra to compute invariant sets of dynamical systems |
| topic | invariant sets Kleene algebra nonlinear dynamical systems path planning |
| url | https://www.mdpi.com/1999-4893/15/3/90 |
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