发表机构
Imperial College London（帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过反馈控制稳定多物种McKean-Vlasov方程的稳态，扩展谱方法至多物种情形，给出单物种驱动下的稳定条件及最少控制数，并用两个模型验证。
AI 中文摘要
我们通过反馈控制来稳定耦合多物种McKean--Vlasov方程的稳态，将基于Wasserstein Hessian和Riccati方程的谱方法从单一密度扩展到Wasserstein空间的乘积。我们给出了当仅驱动一个物种时，以指定速率实现局部指数稳定的必要和充分条件，以及所需的最少控制输入数量。对于两个物种，该条件简化为对未驱动物种线性化动力学的特征空间上交叉相互作用核的傅里叶系数的秩条件。一个双社区噪声Kuramoto模型和一个细胞分选模型验证了这些结果。
英文摘要
We stabilize stationary states of coupled multi-species McKean--Vlasov equations by feedback control, extending a spectral approach based on the Wasserstein Hessian and a Riccati equation from a single density to a product of Wasserstein spaces. We give necessary and sufficient conditions for local exponential stabilization at a prescribed rate when only one species is actuated, together with the minimum number of control inputs required. For two species, the condition reduces to a rank condition on the Fourier coefficients of the cross-interaction kernel over the eigenspaces of the unactuated species' linearized dynamics. A two-community noisy Kuramoto model and a cell-sorting model illustrate the results.
Comments6 pages, 2 figures. Submitted to IEEE L-CSS
