Reachability of weakly nonlinear systems using Carleman linearization
Optimization and Control
2021-11-02 v2 Mathematical Software
Systems and Control
Systems and Control
Dynamical Systems
Abstract
In this article we introduce a solution method for a special class of nonlinear initial-value problems using set-based propagation techniques. The novelty of the approach is that we employ a particular embedding (Carleman linearization) to leverage recent advances of high-dimensional reachability solvers for linear ordinary differential equations based on the support function. Using a global error bound for the Carleman linearization abstraction, we are able to describe the full set of behaviors of the system for sets of initial conditions and in dense time.
Cite
@article{arxiv.2108.10390,
title = {Reachability of weakly nonlinear systems using Carleman linearization},
author = {Marcelo Forets and Christian Schilling},
journal= {arXiv preprint arXiv:2108.10390},
year = {2021}
}