arXiv:2607.12775math.OCcs.LG2026-07

用学习加速场景预测控制,实时求解更高效。

Learning-enabled Acceleration of Scenario-based Model Predictive Control

  • 将场景预测控制转为可并行的ADMM框架,分离动态与约束
  • 通过莫雷包络学习加速迭代,计算速度提升显著
  • 适合需实时决策的能源管理等不确定性系统

基于场景的模型预测控制(SBMPC)通过在多个预测场景上优化控制动作来显式处理不确定性,但其计算复杂度随场景数和预测时长迅速增加,限制了实时规划与控制的应用。本文提出一种基于学习加速的交替方向乘子法(ADMM)算法,结合并行计算与莫雷包络学习,高效求解SBMPC问题,同时保持高精度。将SBMPC重构为可分解的共识形式,利用ADMM分离场景相关动力学与非提前性约束,实现跨场景和时间步的并行更新。在此基础上,采用现有的学习优化方法,通过学习目标函数的莫雷包络加速ADMM中的原始变量更新,显著降低计算时间。在考虑负荷与可再生能源不确定性的微电网能量管理问题上进行了评估。与IPOPT和MadNLP等主流非线性规划求解器相比,该方法实现了显著的计算加速,同时保持可靠的闭环控制性能。

原文摘要 · Abstract (English)

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.

模型预测控制学习优化并行计算微电网

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