Controlling a nonlinear Fokker-Planck equation via inputs with nonlocal action

Stefana-Lucia Anita

Controlling a nonlinear Fokker-Planck equation via inputs with nonlocal action

Optimization and Control 2022-07-22 v1

Authors: Stefana-Lucia Anita

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 $(P_S)$ 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 $(P_h)$ related to a backward Euler approximation of the nonlinear Fokker-Planck equation (with a constant discretization step $h$ ). Passing to the limit ( $h\rightarrow 0$ ) one derives the necessary optimality conditions for problem $(P)$ .

Keywords

optimal control nonlinear fokker-planck equation mckean-vlasov equation penalized problem backward euler necessary conditions

Cite

@article{arxiv.2207.10126,
  title  = {Controlling a nonlinear Fokker-Planck equation via inputs with nonlocal action},
  author = {Stefana-Lucia Anita},
  journal= {arXiv preprint arXiv:2207.10126},
  year   = {2022}
}

Comments

21 pages

Related papers

View all related →