2015/06/30 by Nikolay Pogodaev, Pogodaev, Nikolay
Computer Science · Mathematics · #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.OC
paper · pdf · doi:10.48550/arxiv.1506.08932
arxiv created 2015/06/30 · openalex publication_date 2015/06/30 · arxiv updated 2015/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular case of the problem, where an initial distribution is absolutely continuous with smooth density and the target set has certain regularity properties, a necessary optimality condition is derived. It is shown that for the general problem one may construct a perturbed problem that satisfies all the assumptions of the necessary optimality condition, and any optimal control for the perturbed problem, is nearly optimal for the original one.