MPC strategies for density profile control with pellet fueling in nuclear fusion tokamaks under uncertainty

Control of the density profile based on pellet fueling for the ITER nuclear fusion tokamak involves a multi-rate nonlinear system with safety-critical constraints, input delays, and discrete actuators with parametric uncertainty. To address this challenging problem, we propose a multi-stage MPC (msMPC) approach to handle uncertainty in the presence of mixed-integer inputs. While the scenario tree of msMPC accounts for uncertainty, it also adds complexity to an already computationally intensive mixed-integer MPC (MI-MPC) problem. To achieve real-time density profile controller with discrete pellets and uncertainty handling, we systematically reduce the problem complexity by (1) reducing the identified prediction model size through dynamic mode decomposition with control, (2) applying principal component analysis to reduce the number of scenarios needed to capture the parametric uncertainty in msMPC, and (3) utilizing the penalty term homotopy for MPC (PTH-MPC) algorithm to reduce the computational burden caused by the presence of mixed-integer inputs. We compare the performance and safety of the msMPC strategy against a nominal MI-MPC in plant simulations, demonstrating the first predictive density control strategy with uncertainty handling, viable for real-time pellet fueling in ITER.