SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 903-923, April 2024.
Abstract. An optimal control problem in the space of probability measures and the viscosity solutions of the corresponding dynamic programming equations defined using the intrinsic linear derivative are studied. The value function is shown to be Lipschitz continuous with respect to a smooth Fourier–Wasserstein metric. A comparison result between the Lipschitz viscosity sub- and supersolutions of the dynamic programming equation is proved using this metric, characterizing the value function as the unique Lipschitz viscosity solution.

中文翻译：

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圆环上 McKean-Vlasov 控制的粘度解决方案

SIAM 控制与优化杂志，第 62 卷，第 2 期，第 903-923 页，2024 年 4 月。
摘要。研究了概率测度空间中的最优控制问题以及使用固有线性导数定义的相应动态规划方程的粘度解。值函数相对于平滑的 Fourier-Wasserstein 度量是 Lipschitz 连续的。使用该度量证明了动态规划方程的 Lipschitz 粘度子解和超解之间的比较结果，将值函数表征为唯一的 Lipschitz 粘度解。