Model Predictive Path Integral Control of Tokamak Plasma Boundary Evolution Using a Physics-Informed Neural Equilibrium Surrogate

F. Galfrascoli, E. Schuster

34th Symposium on Fusion Technology (SOFT)

Aix-en-Provence, France, September 21-25, 2026

Accurate control of plasma boundary shape is essential for reliable tokamak operation and advanced plasma scenario development. The plasma boundary is regulated through the currents in external poloidal-field (PF) coils, which must be adjusted to drive the plasma boundary toward a desired target shape. A plasma-shape controller is proposed in this work based on Model Predictive Path Integral (MPPI) control, a stochastic nonlinear predictive control method that optimizes sequences of coil-control actions over a finite prediction horizon. Because MPPI relies on Monte Carlo trajectory sampling rather than standard iterative optimization, it requires the rapid evaluation of the plasma equilibrium along a large number of candidate control trajectories at every control step, rendering conventional Grad-Shafranov solvers computationally prohibitive. To address this limitation, a physics-informed neural-network (PINN) equilibrium surrogate is introduced to approximate the mapping from PF coil currents to the poloidal flux distribution while enforcing consistency with the Grad-Shafranov equation. By evaluating equilibria two orders of magnitude faster than the original free-boundary solver, the PINN surrogate serves as a critical enabler for real-time trajectory optimization. To ensure the controller accounts for physical hardware constraints, PF coil actuation is modeled using simplified circuit dynamics. Each coil is represented by a first-order RL circuit model, enabling direct voltage-driven actuation. By explicitly incorporating these dynamics into the prediction horizon, the controller directly optimizes the applied voltages rather than relying on idealized lower-level current tracking. The resulting coil currents are used by the surrogate equilibrium model to predict the plasma boundary, which is parameterized by the major radius, minor radius, elongation, and triangularity. By combining stochastic predictive control, a physics-informed equilibrium surrogate, and actuator-consistent PF-coil circuit dynamics, the proposed framework enables computationally efficient and physically consistent predictive control of the tokamak plasma boundary evolution. Importantly, this approach functions as a real-time feedforward control optimization, which reduces the required feedback action and inherently supports graceful degradation of shape control when one or more coil currents or voltages approach their limits. Simulation results demonstrate that the MPPI controller successfully optimizes coil actuation in real time, driving the plasma boundary accurately to its desired target shapes.

*Supported by the U.S. DOE under Award DE-SC0010661.