Optimal Control of Continuity Equations
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Abstract (arXiv)
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.
Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Jun 2015.
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Citing papers per year: 2022: 1; 2023: 3.
4 papers.
- 2022Neural ODE Control for Trajectory Approximation of Continuity Equationcited by 8
- 2023Learning on Manifolds: Universal Approximations Properties using Geometric Controllability Conditions for Neural ODEscited by 4
- 2023Variational formulations of ODE-Net as a mean-field optimal control problem and existence resultscited by 3
- 2023PDE+: Enhancing Generalization via PDE with Adaptive Distributional Diffusioncited by 3
- 2023PDE+: Enhancing Generalization via PDE with Adaptive Distributional Diffusion25 May 2023
- 2023Learning on Manifolds: Universal Approximations Properties using Geometric Controllability Conditions for Neural ODEs15 May 2023
- 2023Variational formulations of ODE-Net as a mean-field optimal control problem and existence results9 Mar 2023
- 2022Neural ODE Control for Trajectory Approximation of Continuity Equation18 May 2022