This paper is concerned with the problem of computing the bounded time reachable set of a polynomial discrete-time dynamical system. The problem is well-known for being difficult when nonlinear systems are considered. In this regard, we propose three reachability methods that differ in the set representation. The proposed algorithms adopt boxes, parallelotopes, and parallelotope bundles to construct flowpipes that contain the actual reachable sets. The latter is a new data structure for the symbolic representation of polytopes. Our methods exploit the Bernstein expansion of polynomials to bound the images of sets. The scalability and precision of the presented methods are analyzed on a number of dynamical systems, in comparison with other existing approaches.

Reachability computation for polynomial dynamical systems

DREOSSI, Tommaso
;
PIAZZA, Carla
2017-01-01

Abstract

This paper is concerned with the problem of computing the bounded time reachable set of a polynomial discrete-time dynamical system. The problem is well-known for being difficult when nonlinear systems are considered. In this regard, we propose three reachability methods that differ in the set representation. The proposed algorithms adopt boxes, parallelotopes, and parallelotope bundles to construct flowpipes that contain the actual reachable sets. The latter is a new data structure for the symbolic representation of polytopes. Our methods exploit the Bernstein expansion of polynomials to bound the images of sets. The scalability and precision of the presented methods are analyzed on a number of dynamical systems, in comparison with other existing approaches.
File in questo prodotto:
File Dimensione Formato  
main.pdf

accesso aperto

Descrizione: Articolo post-print
Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 1.39 MB
Formato Adobe PDF
1.39 MB Adobe PDF Visualizza/Apri
dreossi2017.pdf

non disponibili

Descrizione: editoriale
Tipologia: Versione Editoriale (PDF)
Licenza: Non pubblico
Dimensione 1.59 MB
Formato Adobe PDF
1.59 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1108075
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 13
social impact