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.

翻译：模型预测控制（MPC）是动态系统最优控制的一种强大框架。然而，MPC求解器面临计算负担高的问题，这限制了其在低采样频率系统中的应用。对于需要在迭代过程中嵌套MPC求解器的非线性约束系统，这一问题进一步加剧。本文通过为约束非线性优化问题开发并行时间算法来解决这些问题，该算法利用大规模并行硬件实现规划时域上的对数级计算时间缩放。我们基于内点法和交替方向乘子法开发了时间并行二阶求解器，充分利用了快速收敛和每次迭代较低计算成本的优势。并行化基于将子问题重构为关联操作，这些操作可通过关联扫描算法实现并行化。我们在非线性约束动态系统的数值算例上验证了所提方法。