Peak Estimation of Time Delay Systems using Occupation Measures - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Peak Estimation of Time Delay Systems using Occupation Measures

Résumé

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

Dates et versions

hal-04047493 , version 1 (27-03-2023)

Identifiants

Citer

Jared Miller, Milan Korda, Victor Magron, Mario Sznaier. Peak Estimation of Time Delay Systems using Occupation Measures. 2023. ⟨hal-04047493⟩
31 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More