Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This article proposes a primal active‐set strategy, called PRESAS, for the efficient solution of such block‐sparse QPs, based on a preconditioned iterative solver to compute the search direction in each iteration. Rank‐one factorization updates of the preconditioner result in a per‐iteration computational complexity of , where m denotes the number of state and control variables and N the number of control intervals. Three different block‐structured preconditioning techniques are presented and their numerical properties are studied further. In addition, an augmented Lagrangian based implementation is proposed to avoid a costly initialization procedure to find a primal feasible starting point. Based on a standalone C code implementation, we illustrate the computational performance of PRESAS against current state of the art QP solvers for multiple linear and nonlinear MPC case studies. We also show that the solver is real‐time feasible on a dSPACE MicroAutoBox‐II rapid prototyping unit for vehicle control applications, and numerical reliability is illustrated based on experimental results from a testbench of small‐scale autonomous vehicles.

中文翻译：

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PRESAS：用于快速模型预测控制的原始主动集方法内的迭代求解器的块结构预处理

线性动力学系统的模型预测控制（MPC）需要在每个采样时刻求解最优控制结构的二次程序（QP）。本文提出了一种原始的主动集策略，称为 PRESAS，用于基于预先确定的迭代求解器来计算每次迭代的搜索方向，从而有效地解决了此类块稀疏QP。预条件器的秩一因子分解更新导致迭代计算复杂度为，其中m表示状态和控制变量的数量，N表示控制间隔的数量。提出了三种不同的块结构预处理技术，并对它们的数值特性进行了进一步研究。另外，提出了一种基于增强拉格朗日的实现方式，以避免寻找原始可行起点的昂贵初始化过程。基于独立的C代码实现，我们针对多个线性和非线性MPC案例研究，说明了PRESAS针对最新QP求解器的计算性能。我们还表明，该求解器在用于车辆控制应用的dSPACE MicroAutoBox-II快速原型制作单元上是实时可行的，并且基于小型自动驾驶汽车测试台的实验结果说明了数值可靠性。