这篇论文用学习加速ADMM让场景模型预测控制跑得更快，在微电网问题上比IPOPT和MadNLP快很多，适合做实时控制的人看看。
论文提出了基于学习加速的ADMM算法，用于高效求解场景模型预测控制（SBMPC）问题。该方法将SBMPC重写为共识形式，通过ADMM分解实现场景和时间步的并行更新，并引入Moreau envelope学习加速原始更新。在微电网能量管理问题上，与IPOPT和MadNLP求解器相比，该方法在保持可靠闭环性能的同时实现显著计算加速。
Learning-enabled Acceleration of Scenario-based Model Predictive Control
Scenario-based model predictive control (SBMPC) is a variant of model predictive control (MPC) that explicitly accounts for uncertainty by optimizing control actions over multiple predicted scenarios. However, its computational complexity increases rapidly with the number of scenarios and prediction horizon, limiting is applicability to real-time planning and control. This paper presents a learning-accelerated Alternating Direction Method of Multipliers (ADMM) algorithm for efficiently solving SBMPC problems by leveraging parallel computing and Moreau envelope learning, while maintaining high solution accuracy. We reformulate the SBMPC problems into consensus forms that can be decomposed via ADMM, separating the scenario-dependent dynamics from non-anticipativity constraints and enabling parallel updates across scenarios and time steps. Building on this decomposition, we utilize existing learning-to-optimize schemes, which leverages Moreau envelope learning of the cost function to accelerate the primal update in ADMM, thereby reducing computation time. The proposed framework is evaluated on a microgrid energy management problem subject to load and renewable generation uncertainties. Comparisons with IPOPT and MadNLP, popular and modern nonlinear programming solvers, demonstrate substantial computational speedups while maintaining reliable closed-loop control performance.