# Optimal Control

For kinetic plasmas governed by the Vlasov–Maxwell system, feedback control has either taken the full phase-space perturbation as input or relied on instantaneous field cancellation, which degrades once sensing and actuation delays appear. This controller instead uses macroscopic quantities such as current densities, electromagnetic fields and their spatial gradients as feedback information, and a low-rank neural operator learns a residual correction to the delayed cancellation baseline while the control objective stays kinetic: stabilizing the full distribution toward a prescribed equilibrium. In numerical experiments on two-stream and Weibel-type current-filamentation instabilities, the controller keeps suppressing perturbation growth over long times under substantial feedback delay.

For kinetic plasmas governed by the Vlasov–Maxwell system, feedback control has either taken the full phase-space perturbation as input or relied on instantaneous field cancellation, which degrades once sensing and actuation delays appear. This controller instead uses macroscopic quantities such as current densities, electromagnetic fields and their spatial gradients as feedback information, and a low-rank neural operator learns a residual correction to the delayed cancellation baseline while the control objective stays kinetic: stabilizing the full distribution toward a prescribed equilibrium. In numerical experiments on two-stream and Weibel-type current-filamentation instabilities, the controller keeps suppressing perturbation growth over long times under substantial feedback delay.

MIT researchers introduced HardFlow, which recasts hard-constrained generation as a trajectory-optimization problem and enforces safety, physical or task requirements only on the final output rather than on every intermediate sampling step. The common alternative, projection-based sampling, repeatedly pulls intermediate samples back into the feasible region throughout generation, which can keep the model from reaching a better final solution. Across robotic manipulation, maze navigation and text-guided image editing, HardFlow achieved perfect constraint satisfaction and consistently beat baselines on solution quality, with computation time comparable to or lower than most competing methods.

MIT researchers introduced HardFlow, which recasts hard-constrained generation as a trajectory-optimization problem and enforces safety, physical or task requirements only on the final output rather than on every intermediate sampling step. The common alternative, projection-based sampling, repeatedly pulls intermediate samples back into the feasible region throughout generation, which can keep the model from reaching a better final solution. Across robotic manipulation, maze navigation and text-guided image editing, HardFlow achieved perfect constraint satisfaction and consistently beat baselines on solution quality, with computation time comparable to or lower than most competing methods.