  This paper studies the closed-loop dynamics of linear systems under
approximate model predictive control (MPC). More precisely, we consider MPC
implementations based on a finite number of ADMM iterations per time-step. We
first show that the closed-loop dynamics can be described based on a nonlinear
augmented model. We then characterize an invariant set around the augmented
origin, where the dynamics become linear. Finally, we investigate the
performance of the approximate MPC for various choices of the ADMM parameters
based on a comprehensive numerical benchmark.
