论文标题
通过非本地动作的输入来控制非线性的fokker-planck方程
Controlling a nonlinear Fokker-Planck equation via inputs with nonlocal action
论文作者
论文摘要
本文涉及与非线性Fokker-Planck方程相关的最佳控制问题$（P）$。该问题与McKean-Vlasov方程的随机最佳控制问题$（p_s）$密切相关。对于确定性问题$（p）$，获得了最佳控制的存在。建立了最佳控制的存在，并得出了必要的最佳条件，以供惩罚的最佳控制问题$（p_h）$（p_h）$与非线性fokker-Planck方程的向后欧拉近似有关（具有恒定的离散化步骤$ h $）。传递到限制（$ h \ rightarrow 0 $），一个问题$（p）$带来了必要的最佳条件。
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 $(P)$.
