发表机构
Missouri University of Science and Technology; Eli Lilly and Company（密苏里科技大学; 礼来公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对异构平均场控制问题分析计算难、现有方法不易产生可扩展求解方法的状况，开发OM - MFC框架，在特定条件下使优化问题凸性化，推导FW方法，通过数值示例验证该框架能捕获多种效应，实现统一且易计算的轨迹优化。
AI 中文摘要
异构平均场控制（MFC）问题涉及多个具有不同动力学、控制约束和相互作用模式的相互作用群体，这使得分析和计算比同构设置困难得多。特别是，现有公式不易产生保留群体级结构的可扩展求解方法。为解决此问题，我们开发了一种异构占用测度平均场控制（OM - MFC）框架，将问题提升为对受测度线性动态约束的测度进行群体级优化。我们表明，在正半定矩阵值核条件下，所得优化问题是凸性的，该条件捕获了群体间的耦合相互作用。基于此公式，我们推导了一种弗兰克 - 沃尔夫（FW）方法，其线性最小化子问题分解为独立 的群体级最优控制问题，无需测度空间的先验离散化即可进行并行计算。无人机协调和搜索救援场景的数值示例表明，所提出的框架在统一且易于计算的轨迹优化框架中捕获了对称协调、不对称屈服和方向相互作用效应。
英文摘要
Heterogeneous mean-field control (MFC) involves multiple interacting populations with distinct dynamics, control constraints, and coupling structures. We develop a heterogeneous occupation-measure mean-field control (OM-MFC) framework that reformulates the population-distribution control problem as an optimization problem over occupation measures. In this representation, potentially nonlinear dynamics enter through linear weak Liouville constraints, while nonlocal inter-population interactions become structured bilinear functionals of the occupation-measure marginals. Exploiting this structure, we derive a Frank--Wolfe (FW) method and show that its linear minimization oracle decomposes into independent population-wise optimal control problems once the current population distributions are fixed, enabling parallel computation without an a priori discretization of the measure space. We further establish a sufficient convexity condition based on the symmetrized matrix-valued interaction kernel, under which Frank--Wolfe with an exact oracle admits the standard $O(1/k)$ convergence rate. Numerical examples on heterogeneous UAV coordination and three-dimensional search-and-rescue illustrate the framework both within the certified convex regime and for directional interactions beyond that regime.
