Using SOS and Sublevel Set Volume Minimization for Estimation of Forward Reachable Sets
Dynamical Systems
2019-02-01 v1
Abstract
In this paper we propose a convex Sum-of-Squares optimization problem for finding outer approximations of forward reachable sets for nonlinear uncertain Ordinary Differential Equations (ODE's) with either (or both) L2 or point-wise bounded input disturbances. To make our approximations tight we seek to minimize the volume of our approximation set. Our approach to volume minimization is based on the use of a convex determinant-like objective function. We provide several numerical examples including the Lorenz system and the Van der Pol oscillator.
Cite
@article{arxiv.1901.11174,
title = {Using SOS and Sublevel Set Volume Minimization for Estimation of Forward Reachable Sets},
author = {Morgan Jones and Matthew M. Peet},
journal= {arXiv preprint arXiv:1901.11174},
year = {2019}
}