在GPU上利用两级并行直接求解加速分支模型预测控制

中文摘要 AI 辅助

分支模型预测控制在优化多个通过共享决策耦合的未来轨迹时，其计算需求随着场景数量和预测时域的增长而增加。我们提出了一种针对分支模型预测控制公式的GPU加速直接线性求解器，其中所有轨迹共享单个根决策节点，并在此之后独立演化。通过在线性代数层面操作，该求解器为多种优化算法提供了可复用的后端，这些算法的简化系统具有所需的对称正定结构。该求解器利用了两级并行性：跨场景并行和沿每个预测时域并行。定制的变量排序使得能够进行时域并行的Cholesky分解，同时在因子中为每个场景保留单个根-尾耦合块。数值实验表明，与最先进的稀疏直接求解器相比，实现了显著的加速，分解加速比相对于cuDSS高达6.0倍，相对于八线程PARDISO高达27.6倍，三角求解加速比分别高达3.5倍和15.8倍。

英文摘要

Branch model predictive control optimizes multiple future trajectories coupled through shared decisions, with computational demands increasing as the number of scenarios and prediction horizon grow. We present a GPU-accelerated direct linear solver for branch MPC formulations in which all trajectories share a single root decision node and evolve independently thereafter. By operating at the linear-algebra level, the solver provides a reusable backend for multiple optimization algorithms whose reduced systems have the required symmetric positive-definite structure. The solver exploits two levels of parallelism: across scenarios and along each prediction horizon. A tailored variable ordering enables horizon-parallel Cholesky factorization while preserving a single root-tail coupling block per scenario in the factor. Numerical experiments demonstrate substantial speedups over state-of-the-art sparse direct solvers, achieving factorization speedups of up to 6.0$\times$ over cuDSS and 27.6$\times$ over eight-thread PARDISO, with triangular solve speedups of up to 3.5$\times$ and 15.8$\times$, respectively.

发表机构

• École polytechnique fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
• Delft University of Technology（代尔夫特理工大学）
• Johns Hopkins University（约翰斯·霍普金斯大学）

机构由 AI 辅助整理，请以论文原文为准。