平均场最优控制的内禀Lipschitz正则性
Intrinsic Lipschitz Regularity of Mean-Field Optimal Controls
摘要：
本文给出了连续性方程组上的最优控制问题的受控向量场解在空间上是Lipschitz正则的充分条件。我们的方法涉及一种新的组合的平均场近似的无限维多智能体最优控制问题，随着仔细扩展的存在结果的局部最优Lipschitz反馈。后者的基础上重新制定的一个adjuvity估计的语言Wasserstein演算，这是用来获得一致的Lipschitz边界沿序列的近似经验措施。
英文摘要：
In this article, we provide sufficient conditions under which the controlled vector fields solution of optimal control problems formulated on continuity equations are Lipschitz regular in space. Our approach involves a novel combination of mean-field approximations for infinite-dimensional multi-agent optimal control problems, along with a careful extension of an existence result of locally optimal Lipschitz feedbacks. The latter is based on the reformulation of a coercivity estimate in the language of Wasserstein calculus, which is used to obtain uniform Lipschitz bounds along sequences of approximations by empirical measures.
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