A direct optimization algorithm for input-constrained MPC

One 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 has to always be smaller than sampling time. This paper 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 $\left\lceil\frac{\log\left(\frac{2n}{\epsilon}\right)}{-2\log(1-\frac{1}{4\sqrt{2n}})}\right\rceil+1$, where $\epsilon$ denotes a given stopping accuracy.