Control Strategies for Multi-Species Wasserstein Gradient Flows

Dante Kalise; Lucas M. Moschen; Grigorios A. Pavliotis

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arXiv · 2609.11422

Control Strategies for Multi-Species Wasserstein Gradient Flows

Dante Kalise·Lucas M. Moschen·Grigorios A. Pavliotis

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Abstract

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.

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Dante Kalise, Lucas M. Moschen, Grigorios A. Pavliotis. 2026-09-10. Control Strategies for Multi-Species Wasserstein Gradient Flows. https://arxiv.org/abs/2609.11422

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