Controlling a nonlinear Fokker-Planck equation via inputs with nonlocal action
Abstract
This paper concerns an optimal control problem (P) related to a nonlinear Fokker-Planck equation. The problem is deeply related to a stochastic optimal control problem (PS) for a McKean-Vlasov equation. The existence of an optimal control is obtained for the deterministic problem (P). The existence of an optimal control is established and necessary optimality conditions are derived for a penalized optimal control problem (Ph) related to a backward Euler approximation of the nonlinear Fokker-Planck equation (with a constant discretization step h). Passing to the limit (h→ 0) one derives the necessary optimality conditions for problem (P).
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.