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Article Dans Une Revue Mathematics Année : 2022

Set-Based B-Series

Résumé

B-series were defined to unify the formalism of solutions for ordinary differential equations defined by series. Runge–Kutta schemes can be seen as truncated B-series, similar to Taylor series. In the prolific domain of reachability analysis, i.e., the process of computing the set of reachable states for a system, many techniques have been proposed without obvious links. In the particular case of uncertain initial conditions and/or parameters in the definition of differential equations, set-based approaches are a natural and elegant method to compute reachable sets. In this paper, an extension to B-series is proposed to merge these techniques in a common formalism—named set-based B-series. We show that the main properties of B-series are preserved. A validated technique, based on Runge–Kutta methods, able to compute such series, is presented. Experiments are provided in order to illustrate the proposed approach.

Dates et versions

hal-03842058 , version 1 (07-11-2022)

Identifiants

Citer

Julien Alexandre Dit Sandretto. Set-Based B-Series. Mathematics , 2022, 10 (17), pp.3165. ⟨10.3390/math10173165⟩. ⟨hal-03842058⟩
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