Parabolic set simulation for reachability analysis of linear time-invariant systems with integral quadratic constraint

Abstract

This paper describes the computation of reachable sets and tubes for linear time-invariant systems with an unknown input bounded by integral quadratic constraints, modeling e.g. delay, rate limiter, or energy bounds. We define a family of paraboloidal overapproximations. These paraboloids are supported by the reachable tube on touching trajectories. Parameters of each paraboloid are expressed as a solution to an initial value problem. Compared to previous methods based on the classical linear quadratic regulator, our approach can be applied to unstable systems as well. We tested our approach on large scale systems.

Publication
European Journal of Control
Paul Rousse
Paul Rousse
Engineer at Airbus UpNext
Didier Henrion
Didier Henrion
Senior Researcher (Directeur de Recherche) at LAAS-CNRS and Professor at Prague University