用并行时间算法加速非线性模型预测控制求解，大幅降低计算耗时。
A Parallel-in-Time Newton's Method for Nonlinear Model Predictive Control
- 将时间维度并行化，通过关联扫描实现快速求解
- 在非线性约束系统上实现对数级计算时间缩减
- 适合高采样频率、实时性要求高的控制场景
模型预测控制（MPC）是动态系统最优控制的强大框架，但其求解器存在高计算负担，限制了在低采样频率系统中的应用。这一问题在非线性与约束系统中尤为突出，因需嵌套迭代求解。本文提出一种基于内点法与交替方向乘子法的并行时间二阶求解器，利用大规模并行硬件实现规划周期上的对数级计算时间复杂度。该方法通过将子问题重构成可并行的关联运算，借助关联扫描算法实现高效并行。我们在多个非线性与约束动力系统数值实验中验证了该方法的有效性。
原文摘要 · Abstract (English)
Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This issue is further amplified in nonlinear and constrained systems that require nesting MPC solvers within iterative procedures. In this paper, we address these issues by developing parallel-in-time algorithms for constrained nonlinear optimization problems that take advantage of massively parallel hardware to achieve logarithmic computational time scaling over the planning horizon. We develop time-parallel second-order solvers based on interior point methods and the alternating direction method of multipliers, leveraging fast convergence and lower computational cost per iteration. The parallelization is based on a reformulation of the subproblems in terms of associative operations that can be parallelized using the associative scan algorithm. We validate our approach on numerical examples of nonlinear and constrained dynamical systems.
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