A major bottleneck in state-of-the-art algorithms for global dynamic optimization using complete methods is computing enclosures for the solutions of nonlinear parametric differential equations. This paper presents a new algorithm for computing such enclosures, which features a combination of Taylor model propagation and ellipsoidal calculus. The former enables high-order convergence to the exact reachable set as the parameter set shrinks, while the latter mitigates bound explosion compared to interval analysis. The convergence properties of the proposed bounding technique are analyzed and conditions under which higher order convergence can be achieved are given. Implementation details are also discussed and the approach is demonstrated on a numerical case study.

Enclosing the Reachable Set of Parametric ODEs using Taylor Models and Ellipsoidal Calculus

Villanueva, Mario;
2013-01-01

Abstract

A major bottleneck in state-of-the-art algorithms for global dynamic optimization using complete methods is computing enclosures for the solutions of nonlinear parametric differential equations. This paper presents a new algorithm for computing such enclosures, which features a combination of Taylor model propagation and ellipsoidal calculus. The former enables high-order convergence to the exact reachable set as the parameter set shrinks, while the latter mitigates bound explosion compared to interval analysis. The convergence properties of the proposed bounding technique are analyzed and conditions under which higher order convergence can be achieved are given. Implementation details are also discussed and the approach is demonstrated on a numerical case study.
9780444632340
Taylor models, Ellipsoidal calculus, Differential inequalities, Ordinary differential equations
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/20.500.11771/21500
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
social impact