SIAM Journal on Control and Optimization, Volume 59, Issue 3, Page 2011-2046, January 2021.
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.

中文翻译：

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平均场最优控制的内在 Lipschitz 规律

SIAM Journal on Control and Optimization，第 59 卷，第 3 期，第 2011-2046 页，2021
年1 月。在本文中，我们提供了充分条件，在该条件下，在连续性方程上制定的最优控制问题的受控矢量场解在空间中是 Lipschitz 正则的。我们的方法涉及无限维多智能体最优控制问题的平均场近似的新组合，以及局部最优 Lipschitz 反馈的存在结果的仔细扩展。后者基于用 Wasserstein 微积分语言重新表述的矫顽力估计，用于通过经验测量沿着近似序列获得统一的 Lipschitz 界限。