关于平均场最优控制问题
On a Mean Field Optimal Control Problem
摘要：
在本文中，我们考虑一个平均场最优控制问题的聚集扩散约束，代理人通过潜在的相互作用，在高斯噪声项的存在。我们的分析集中在耦合Hamilton-Jacobi和Fokker-Planck方程的PDE系统上，分别描述了问题的最优控制方面和代理群体的演化。本文的主要贡献是对上述系统的解的存在性的结果。我们注意到这个模型与平均场博弈系统理论有着密切的联系。然而，一个显着的特点涉及的相互作用的非局部性;它影响的漂移项在福克-普朗克方程以及系统的哈密顿量，导致新的困难要解决。
英文摘要：
In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a Hamilton-Jacobi and a Fokker-Planck equation, describing the optimal control aspect of the problem and the evolution of the population of agents, respectively. The main contribution of the paper is a result on the existence of solutions for the aforementioned system. We notice this model is in close connection with the theory of mean-field games systems. However, a distinctive feature concerns the nonlocal character of the interaction; it affects the drift term in the Fokker-Planck equation as well as the Hamiltonian of the system, leading to new difficulties to be addressed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
