Peak Estimation of Time Delay Systems using Occupation Measures
Abstract
This work proposes a method to compute the maximum value obtained by a state function along trajectories of a Delay Differential Equation (DDE). An example of this task is finding the maximum number of infected people in an epidemic model with a nonzero incubation period. The variables of this peak estimation problem include the stopping time and the original history (restricted to a class of admissible histories). The original nonconvex DDE peak estimation problem is approximated by an infinite-dimensional Linear Program (LP) in occupation measures, inspired by existing measure-based methods in peak estimation and optimal control. This LP is approximated from above by a sequence of Semidefinite Programs (SDPs) through the moment-Sum of Squares (SOS) hierarchy. Effectiveness of this scheme in providing peak estimates for DDEs is demonstrated with provided examples
Cite
@article{arxiv.2303.12863,
title = {Peak Estimation of Time Delay Systems using Occupation Measures},
author = {Jared Miller and Milan Korda and Victor Magron and Mario Sznaier},
journal= {arXiv preprint arXiv:2303.12863},
year = {2023}
}
Comments
34 pages, 14 figures, 3 tables