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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{kalise2026control,
  title = {{Control Strategies for Multi-Species Wasserstein Gradient Flows}},
  author = {Dante Kalise and Lucas M. Moschen and Grigorios A. Pavliotis},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11422},
  eprint = {2609.11422},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11422},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Control Strategies for Multi-Species Wasserstein Gradient Flows
AU  - Dante Kalise
AU  - Lucas M. Moschen
AU  - Grigorios A. Pavliotis
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11422
UR  - https://arxiv.org/abs/2609.11422
AB  - 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.
ER  -