Optimal control of continuity equations
By Nikolay Pogodaev. 2015
60 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1b8d9458cb91d989083878e4fa6a828c8d0ec638
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Differential inclusions in Wasserstein spaces: The Cauchy-Lipschitz framework (2020, background): “While a few results have been dealing with controllability properties of continuity equations [36, 37], the major part of the literature has been devoted to the study of optimal control problems, with contributions ranging from existence results [23, 38, 39, 40] and necessary optimality conditions [”
- A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems (2018, unknown): “We would also like to mention that in [17, 48], the authors derived first-order necessary optimality conditions for special classes of optimal control problems on continuity equations, via methods which are quite distinct from that which we already sketched.”