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Mathematics > Optimization and Control

arXiv:2303.12863 (math)
[Submitted on 22 Mar 2023 (v1), last revised 5 Apr 2023 (this version, v3)]

Title:Peak Estimation of Time Delay Systems using Occupation Measures

Authors:Jared Miller, Milan Korda, Victor Magron, Mario Sznaier
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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
Comments: 34 pages, 14 figures, 3 tables
Subjects: Optimization and Control (math.OC); Systems and Control (eess.SY)
Cite as: arXiv:2303.12863 [math.OC]
  (or arXiv:2303.12863v3 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2303.12863

Submission history

From: Jared Miller [view email]
[v1] Wed, 22 Mar 2023 18:58:12 UTC (1,705 KB)
[v2] Sat, 25 Mar 2023 17:39:45 UTC (1,705 KB)
[v3] Wed, 5 Apr 2023 15:44:41 UTC (1,706 KB)
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