Control strategies for the McKean-Vlasov equation

We address the accelerated convergence of the nonlinear McKean–Vlasov equation, which is the mean‐field limit of interacting particle systems. While standard convexity assumptions yield exponential convergence to a unique equilibrium, small spectral gaps can slow the dynamics. Moreover, in nonconvex settings, multiple steady states may arise, making transitions between them of practical interest. By modifying the potential with spatial and temporal controls, linearizing around the desired steady state, and employing a Riccati-based optimal feedback law, we achieve faster convergence. Numerical experiments with the Kuramoto model, implemented via a Fourier spectral discretization, support our approach.