Ellipsoidal Enclosure Techniques for a Verified Simulation of Initial Value Problems for Ordinary Differential Equations

Andreas Rauh (1, 2) , Auguste Bourgois (1, 2) , Luc Jaulin (1, 2) , Julia Kersten (3)

1 Lab-STICC_ROBEX - Equipe ROBotics for EXploration
2 ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées Bretagne
3 Universität Rostock

The verified simulation of initial value problems (IVPs) for ordinary differential equations (ODEs) with uncertain parameters is an up-to-date research topic and a basic building block for predictor-corrector type state estimators. Such state estimators are based on a two-stage procedure: First, the continuous-time state equations are evaluated up to the discrete time instant at which new measured data become available. Second, the forecasted state enclosures need to be refined by accounting for the information provided by the available sensors. In this paper, we focus on the first stage by presenting a novel ellipsoidal enclosure technique for continuous-time processes. It is based on thick ellipsoids and temporal Taylor series for a verified integration of ODEs that in combination allow for determining inner and outer bounds for the domains of reachable states. Comparisons with other set-valued integration techniques conclude this paper.

Mots clés: Ellipsoidal enclosure techniques; Interval analysis; Robustness analysis; Uncertain systems; Verified simulation of initial value problems

Domaines: Modélisation et simulation; Systèmes et contrôle [cs.SY]; Systèmes dynamiques [math.DS]; Automatique / Robotique

Andreas Rauh, Auguste Bourgois, Luc Jaulin, Julia Kersten. Ellipsoidal Enclosure Techniques for a Verified Simulation of Initial Value Problems for Ordinary Differential Equations. 2021 International Conference on Control, Automation and Diagnosis (ICCAD), Nov 2021, Grenoble, France. pp.1-6, ⟨10.1109/ICCAD52417.2021.9638755⟩. ⟨hal-03494430⟩