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Set-Based B-Series

Author

Listed:
  • Julien Alexandre dit Sandretto

    (U2IS, ENSTA Paris, Institut Polytechnique de Paris, 91120 Palaiseau, France)

Abstract

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.

Suggested Citation

  • Julien Alexandre dit Sandretto, 2022. "Set-Based B-Series," Mathematics, MDPI, vol. 10(17), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3165-:d:905473
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