A challenge of running a model predictive control (MPC) algorithm in a production-embedded platform is to provide the certificate of worst-case computation complexity, that is, its maximum execution time needs to always be smaller than the sampling time. This article proposes for the first time a \textit{direct} optimization algorithm for input-constrained MPC: the number of iterations is data-independent and dependent on the problem dimension $n$, with exact value $\left\lceil\frac{\log(\frac{2n}{\epsilon})}{-2\log(\frac{\sqrt{2n}}{\sqrt{2n}+\sqrt{2}-1})}\right\rceil + 1$, where $\epsilon$ denotes a given stopping accuracy.

翻译：在嵌入式生产平台上运行模型预测控制（MPC）算法时，一个关键挑战是提供最坏情况计算复杂度的保证，即其最大执行时间必须始终小于采样时间。本文首次提出了一种针对输入约束MPC的直接优化算法：算法迭代次数与数据无关，仅取决于问题维度$n$，其精确值为$\left\lceil\frac{\log(\frac{2n}{\epsilon})}{-2\log(\frac{\sqrt{2n}}{\sqrt{2n}+\sqrt{2}-1})}\right\rceil + 1$，其中$\epsilon$表示给定的停止精度。