Model Predictive Control (MPC) is increasing in popularity in industry as more efficient algorithms for solving the related optimization problem are developed. The main computational bottle-neck in on-line MPC is often the computation of the search step direction, i.e. the Newton step, which is often done using generic sparsity exploiting algorithms or Riccati recursions. However, as parallel hardware is becoming increasingly popular the demand for efficient parallel algorithms for solving the Newton step is increasing. In this paper a tailored, non-iterative parallel algorithm for computing the Riccati factorization is presented. The algorithm exploits the special structure in the MPC problem, and when sufficiently many processing units are available, the complexity of the algorithm scales logarithmically in the prediction horizon. Computing the Newton step is the main computational bottle-neck in many MPC algorithms and the algorithm can significantly reduce the computation cost for popular state-of-the-art MPC algorithms.
Riccati-ZORO: An efficient algorithm for heuristic online optimization of internal feedback laws in robust and stochastic model predictive control
Department of Microsystems Engineering (IMTEK), University of Freiburg（弗赖堡大学微系统工程学院（IMTEK））；Department of Mathematics, University of Freiburg（弗赖堡大学数学系）
Mean-Square Stability of Continuous-Time Stochastic Model Predictive Control
School of Mathematics, Sichuan University（四川大学数学学院）；School of Mathematical Sciences, Chengdu University of Technology（成都理工大学数学科学学院）；Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)（埃尔朗根-纽伦堡大学（FAU）数学系）；Departamento de Matemáticas, Universidad Autónoma de Madrid（马德里自治大学数学系）；Chair of Computational Mathematics, Universidad de Deusto（德乌斯托大学计算数学讲席）
$\mathcal{N}$IPM-MPC: An Efficient Null-Space Method Based Interior-Point Method for Model Predictive Control
线性模型预测控制（Linear Model Predictive Control，MPC）是一种广泛应用于线性动态控制系统的控制方法。已经提出了有效的内点方法，该方法利用了由滚动时域控制公式产生的二次规划（QP）的块对角结构。然而，他们需要两个矩阵分解每个内点法迭代，一个用于计算对偶和原始。最近，一种基于零空间方法的内点方法被提出，该方法每次迭代只需要一次分解。虽然然后使用的零空间基础导致密集的零空间投影，在这项工作中，我们提出了一个稀疏的零空间基础，保留块对角结构的MPC矩阵。由于它是基于传递矩阵的逆，我们引入了所谓的虚拟控制的概念，它使可逆性。一个组合的减少数量的因式分解和省略的评估的双重让我们的求解器优于别人在计算速度方面的增加幅度取决于状态和控制变量的数量。
WarpMPC: Large-Batch MPC on GPU via ADMM with Unrolled $LDL^\top$ Factorization
Institute for Data Science in Mechanical Engineering (DSME), RWTH Aachen University（亚琛工业大学机械工程数据科学研究所）；Department of Mechanical Engineering, Massachusetts Institute of Technology（麻省理工学院机械工程系）
