用并行时间方法加速求解复杂最优控制问题，实测提速达5倍。
Parallel Dynamic Programming for Conic Linear Quadratic Control
- 将ADMM与动态规划结合，按时间轴拆分问题并行求解
- 在多核CPU上实现最高5倍于传统方法的加速
- 适合需要实时控制的工业系统与大规模优化场景
线性二次（LQ）控制问题是线性控制理论和模型预测控制（MPC）的核心。尽管性能优越，但标准求解方法本质上是串行的，限制了其在现代多核CPU上的实时可扩展性。为解决此问题，我们提出一种基于‘分而治之’思想的并行时间方法，通过交替方向乘子法（ADMM）求解计算密集型的锥型最优控制问题。具体而言，将ADMM的内层原始更新形式化为一个LQ问题，并沿时间轴拆分重构问题。由此推导出一种变体的Riccati递推算法，可在并行环境下求解各子问题。在两个实际应用中的数值基准测试表明，在多核CPU硬件上相比现有相关方法最高可实现5倍速度提升。
原文摘要 · Abstract (English)
Linear Quadratic (LQ) control problems are at the heart of linear control theory and Model Predictive Control (MPC). While performant, standard approaches to solving such problems are inherently serial, limiting real-time scalability despite the parallel computing power available on modern multi-core CPUs. Contributing to addressing this challenge and motivated by ``divide and conquer'' strategies, we present a parallel-in-time approach that solves computationally demanding conic optimal control problems through the use of the alternating direction method of multipliers (ADMM). In particular, we formulate the inner primal update of ADMM as an LQ problem and split the reformulated problem along the time horizon. This enables us to derive a variant of the Riccati recursion using dynamic programming to solve each subproblem in parallel. Numerical benchmarks on two real-world applications demonstrate as much as a 5x speedup compared to existing related approaches on multi-core CPU hardware.
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