论文标题
控制Fokker-Planck方程的一阶和二阶最佳条件
First and Second Order Optimality Conditions for the Control of Fokker-Planck Equations
论文作者
论文摘要
在本文中，我们研究了一个受Fokker-Planck方程的最佳控制问题\ [\ partial_tρ-ρ-νδρ-{\ rm div} \ big（ρb[U] \ big）= 0。\ \]控制变量$ u $是时间依赖的，并且可能是多数级的，并且函数$ b $ b $ b $ b $ b。成本功能是跟踪类型，并在控件上包含一个二次正则化项。对于这个问题，我们证明存在最佳控制和一阶必要条件。主要重点是必要和充分的条件。
In this article we study an optimal control problem subject to the Fokker-Planck equation \[ \partial_t ρ- νΔρ- {\rm div } \big(ρB[u]\big) = 0. \] The control variable $u$ is time-dependent and possibly multidimensional, and the function $B$ depends on the space variable and the control. The cost functional is of tracking type and includes a quadratic regularization term on the control. For this problem, we prove existence of optimal controls and first order necessary conditions. Main emphasis is placed on second order necessary and sufficient conditions.
