Ensemble Neural Network‐Based Approximate Model Predictive Control With Strict Guarantees

This paper presents an approximate nonlinear model predictive control (NMPC) scheme based on supervised learning to alleviate computational burdens by using a deep neural network to approximate the NMPC laws. To ensure strict theoretical guarantees for constraint satisfaction and closed‐loop stability in the approximate NMPC, we estimate the Lipschitz constants of the deep neural network and derive an upper bound on the approximation error. Consequently, a robust NMPC approach is employed to provide strict, rather than probabilistic, guarantees for the approximate NMPC strategy. To further reduce the conservatism in the approximation error bound, this paper introduces ensemble neural networks instead of a single neural network for approximating the NMPC laws. The ensemble networks effectively reduce the estimated Lipschitz constants and the maximum training errors, thereby significantly reducing the approximation error bound. The theoretical results are validated through a numerical experiment, and the effectiveness of ensemble neural networks in reducing conservatism compared to a single neural network is extensively demonstrated through several simulations.