论文标题
利用GPU/SIMD架构来解决线性二次MPC问题
Exploiting GPU/SIMD Architectures for Solving Linear-Quadratic MPC Problems
论文作者
论文摘要
我们通过利用图形处理单元（GPU）来报告解决约束线性季度模型预测控制（MPC）问题的数值结果。提出的方法通过消除状态变量来减少MPC问题，并应用凝结空间的内点方法来删除KKT系统中的不平等约束。最终的冷凝矩阵是正定的，可以在GPU/SIMD架构上并行分解。另外，凝结矩阵的大小仅取决于问题中的控件数量，当问题具有许多状态，但输入和中等水平的长度时，该方法特别有效。我们针对PDE约束问题的数值结果表明，该方法比标准CPU实现快的阶数。我们还提供了一个开源的朱莉娅框架，该框架促进了GPU上MPC问题的建模（DynamicnlpModels.jl）和解决方案（MADNLP.JL）。
We report numerical results on solving constrained linear-quadratic model predictive control (MPC) problems by exploiting graphics processing units (GPUs). The presented method reduces the MPC problem by eliminating the state variables and applies a condensed-space interior-point method to remove the inequality constraints in the KKT system. The final condensed matrix is positive definite and can be efficiently factorized in parallel on GPU/SIMD architectures. In addition, the size of the condensed matrix depends only on the number of controls in the problem, rendering the method particularly effective when the problem has many states but few inputs and moderate horizon length. Our numerical results for PDE-constrained problems show that the approach is an order of magnitude faster than a standard CPU implementation. We also provide an open-source Julia framework that facilitates modeling (DynamicNLPModels.jl) and solution (MadNLP.jl) of MPC problems on GPUs.
