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Optimal Graphon Control of Collective Dynamics

  • Joseph K. Miller
  • Brandon Su
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Abstract

We study optimal control of non-linear graphon dynamics in which the interaction kernel itself is the control. Motivated by opinion formation in social networks, we ask how changing who influences whom can steer a population toward a desired outcome. We develop a framework using interaction kernels with bounded variation in the receiver label, providing compactness while accommodating finite networks. We prove existence of an optimal pair and show that finite-agent approximations recover the continuum optimal value under successive refinement of the network and initial data, with subsequential convergence of suitably chosen discrete optimizers. Numerical experiments use neural networks to approximate optimal controls for bounded-confidence and graphon Kuramoto dynamics, illustrating how changes in interactions can prevent fragmentation and promote synchronization.

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Cite

BibTeXRIS
BibTeX
@misc{miller2026optimal,
  title = {{Optimal Graphon Control of Collective Dynamics}},
  author = {Joseph K. Miller and Brandon Su},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31975},
  eprint = {2610.31975},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31975},
}
RIS
TY  - UNPB
TI  - Optimal Graphon Control of Collective Dynamics
AU  - Joseph K. Miller
AU  - Brandon Su
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31975
UR  - https://arxiv.org/abs/2610.31975
AB  - We study optimal control of non-linear graphon dynamics in which the interaction kernel itself is the control. Motivated by opinion formation in social networks, we ask how changing who influences whom can steer a population toward a desired outcome. We develop a framework using interaction kernels with bounded variation in the receiver label, providing compactness while accommodating finite networks. We prove existence of an optimal pair and show that finite-agent approximations recover the continuum optimal value under successive refinement of the network and initial data, with subsequential convergence of suitably chosen discrete optimizers. Numerical experiments use neural networks to approximate optimal controls for bounded-confidence and graphon Kuramoto dynamics, illustrating how changes in interactions can prevent fragmentation and promote synchronization.
ER  -