论文标题
一类随机的颈控制问题的平均场限制
Mean-field limit for a class of stochastic ergodic control problems
论文作者
论文摘要
我们研究了McKean-Vlasov（平均场）类型的Ergodic最佳控制问题，并具有线性控制的最佳控制问题，以及对成本函数控制的二次依赖。对于这类问题，我们确定了最佳控制的存在和独特性。我们提出了一个$ n $ - 粒子马尔可夫最佳控制问题，该问题近似于McKean-Vlasov One，我们证明了相对熵，总变化和Wasserstein在$ n $时，前者法律对后者法律的距离。还建立了一些麦克基·维拉索夫（McKean-Vlasov）的最佳控制问题，以及这些问题与玻色 - 因斯坦凝结的数学理论的关系。
We study a family of McKean-Vlasov (mean-field) type ergodic optimal control problems with linear control, and quadratic dependence on control of the cost function. For this class of problems we establish existence and uniqueness of an optimal control. We propose an $N$-particles Markovian optimal control problem approximating the McKean-Vlasov one and we prove the convergence in relative entropy, total variation and Wasserstein distance of the law of the former to the law of the latter when $N$ goes to infinity. Some McKean-Vlasov optimal control problems with singular cost function and the relation of these problems with the mathematical theory of Bose-Einstein condensation is also established.
