2023/03/22 by Jared Miller, Miller, Jared, Milan Korda +5
Business, Management and Accounting · Engineering · #Advanced Control Systems Optimization #Advanced Queuing Theory Analysis #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2303.12863
openalex publication_date 2023/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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