MPC surrogates based on supervised or unsupervised learning for the real-time control of nonlinear systems

While Model Predictive Control (MPC) is a widely used method for controlling constrained nonlinear systems, data-driven MPC has recently emerged as a viable alternative to explicit MPC when sufficient data is available. This work investigates two neural network-based strategies for learning control policies in nonlinear systems: supervised and unsupervised learning. The supervised strategy approximates the MPC feedback law using a neural network trained on demonstrations generated from offline MPC simulations. In contrast, the unsupervised approach directly minimizes an MPC-inspired cost function using a learned dynamical model, avoiding the need for expert-generated trajectories. Beyond empirical evaluation, the supervised approach is complemented by a generalization analysis that yields generalization guarantees for a simplified neural architecture and motivates an early-stopping strategy. To retain constraint handling when replacing the online MPC optimization with a compact neural policy, a one-step feasibility filter is introduced that projects the network output onto the admissible set through a small nonlinear program. The proposed framework is evaluated numerically on a realistic simulation of an open-die forging process with process and measurement noise, where deformation speed must be finely regulated to ensure product homogeneity. Simulation results show that both learning-based controllers achieve MPC-level tracking performance with compact networks, remain robust under disturbances, and reduce online computation time by more than an order of magnitude.