Control and stabilisation of probability distributions
Spectral and feedback control methods for steering probability distributions towards equilibrium.
I study how feedback can steer an evolving probability distribution toward a chosen equilibrium, including when its natural dynamics converge slowly. In joint work, we developed a spectral method that targets slow modes of the Fokker–Planck equation. We then designed feedback for nonlinear McKean–Vlasov dynamics and proved local exponential stabilisation at a prescribed rate. Our later work explains this effect through the geometry of the free energy: the feedback makes it locally convex near the target in Wasserstein space.
I am now studying how to implement these controls with particles and whether faster convergence outweighs the computational cost of applying them.
Related papers:
- A Spectral Approach to Optimal Control of the Fokker–Planck Equation — IEEE Control Systems Letters, 2025.
- Linearization-Based Feedback Stabilization of McKean–Vlasov PDEs — accepted in SIAM Journal on Control and Optimization.
- Feedback Control and Local Convexification of Wasserstein Gradient Flows — preprint, 2026.