Regularity of the value function and quantitative propagation of chaos for mean field control problems
Regularity of the value function and quantitative propagation of chaos for mean field control problems
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DOI：
10.1007/s00030-022-00823-x
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发表时间：
2022-04
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影响因子：
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通讯作者：
P. Cardaliaguet;P. Souganidis
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文献类型：
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作者：
P. Cardaliaguet;P. Souganidis
本文研究了在具有强迫和终端数据的大粒子系统的最优控制极限下得到的平均场最优控制问题。我们证明了价值函数，这是已知的Lipschitz连续的，但不是类，在一般情况下，没有凸性，实际上是光滑的时间和概率措施的空间的一个开放的和密集的子集。因此，我们证明了一个新的量化传播的混沌型结果的粒子系统的最优解从这个开放和密集的集合。
We investigate a mean field optimal control problem obtained in the limit of the optimal control of large particle systems with forcing and terminal data which are not assumed to be convex. We prove that the value function, which is known to be Lipschitz continuous but not of class, in general, without convexity, is actually smooth in an open and dense subset of the space of times and probability measures. As a consequence, we prove a new quantitative propagation of chaos-type result for the optimal solutions of the particle system starting from this open and dense set.