# Computation and Control of Unstable Steady States for Mean Field Multiagent Systems

arXiv: https://arxiv.org/abs/2406.11725 · HTML: https://mlsanity.com/paper/2406.11725/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2024.

## Built on by (most cited first, 4 of 4)

- [Nonlocal Mean Field Schr"odinger Bridge with Learned Interactions](https://mlsanity.com/paper/2606.04265/) (2026)
- [Time-optimal neural feedback control of nilpotent systems as a binary classification problem](https://mlsanity.com/paper/2503.17581/) (2025)
- [Data-driven approximation of transfer operators for mean-field stochastic differential equations](https://mlsanity.com/paper/2509.09891/) (2025)
- [Discovery of interaction and diffusion kernels in particle-to-mean-field multi-agent systems](https://mlsanity.com/paper/2603.15927/) (2026)

## Abstract (arXiv)

We study interacting particle systems driven by noise, modeling phenomena such as opinion dynamics. We are interested in systems that exhibit phase transitions i.e. non-uniqueness of stationary states for the corresponding McKean-Vlasov PDE, in the mean field limit. We develop an efficient numerical scheme for identifying all steady states (both stable and unstable) of the mean field McKean-Vlasov PDE, based on a spectral Galerkin approximation combined with a deflated Newton's method to handle the multiplicity of solutions. Having found all possible equilibra, we formulate an optimal control strategy for steering the dynamics towards a chosen unstable steady state. The control is computed using iterated open-loop solvers in a receding horizon fashion. We demonstrate the effectiveness of the proposed steady state computation and stabilization methodology on several examples, including the noisy Hegselmann-Krause model for opinion dynamics and the Haken-Kelso-Bunz model from biophysics. The numerical experiments validate the ability of the approach to capture the rich self-organization landscape of these systems and to stabilize unstable configurations of interest. The proposed computational framework opens up new possibilities for understanding and controlling the collective behavior of noise-driven interacting particle systems, with potential applications in various fields such as social dynamics, biological synchronization, and collective behavior in physical and social systems.