发表机构
Johns Hopkins University; Slovak University of Technology in Bratislava（约翰斯·霍普金斯大学; 布拉迪斯拉发斯洛伐克理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出混合整数非线性可微预测控制，用于地下抽水蓄能系统日前调度，通过Gumbel-Softmax和Transformer实现高效求解，仅1.6%次优性且加速五个数量级。
AI 中文摘要
本文将混合整数可微预测控制（MI-DPC）扩展到地下抽水蓄能系统（UPHES）中出现的多模态离散决策和非凸多项式动力学问题。通过Gumbel-Softmax层将问题参数映射到连续设定点和整数模式选择的神经策略，以自监督方式训练，通过对非线性动力学模型中的有限时域控制目标期望进行微分来实现。三个方法论贡献促成了这一扩展：一个保持梯度幅度的并行可微模拟器，一个捕捉长程时间依赖的Transformer编码器，以及一个正则化组合搜索的Gumbel-Softmax温度退火调度。我们在UPHES的日前调度中展示了该框架，这是一个具有非线性机组性能曲线和体积-水头耦合的大规模混合整数最优控制问题。MI-DPC相对于分段混合整数二次规划基线仅实现了1.6%的次优性，同时在在线调度时间上提供了五个数量级的加速。
英文摘要
This paper extends Mixed-Integer Differentiable Predictive Control (MI-DPC) to multi-modal discrete decisions and nonconvex polynomial dynamics arising in Underground Pumped Hydro Energy Storage Systems (UPHES). A neural policy mapping problem parameters to continuous setpoints and integer mode selections via a Gumbel-Softmax layer is trained in a self-supervised manner by differentiating the expectation of the finite horizon control objective through the nonlinear dynamics model. Three methodological contributions enable this extension: a parallel differentiable simulator that preserves gradient magnitude, a Transformer encoder that captures long-range temporal dependencies, and a Gumbel-Softmax temperature annealing schedule that regularizes the combinatorial search. We demonstrate the framework on day-ahead scheduling of a UPHES, a large-scale mixed-integer optimal control problem with nonlinear unit performance curves and volume-head coupling. MI-DPC achieves only 1.6% suboptimality relative to a piecewise mixed-integer quadratic programming baseline, while providing five orders of magnitude speedup in online scheduling time.
Comments6 pages, 5 figures. Accepted for publication in the 2026 65th IEEE Conference on Decision and Control (CDC)
