Inexact-Uzawa Primal-Dual Solver for Embedded Model Predictive Control

In this letter, we propose an inexact-Uzawa solver for embedded linear model predictive control (MPC). The inexact-Uzawa algorithm falls into the general framework of first-order primal-dual methods but employs both proximal-point and matrix splitting schemes to derive a numerically robust algorithm with <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}$ </tex-math></inline-formula>(<inline-formula> <tex-math notation="LaTeX">$1/k$ </tex-math></inline-formula>) convergence rate in the primal-dual gap to some saddle-point solution where <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> is the iteration count. Numerical MPC example shows the efficiency and the ease of implementation of the algorithm as compared to other related methods in the literature.