Closed-loop Analysis of ADMM-based Suboptimal Linear Model Predictive Control

Many practical applications of optimal control are subject to real-time computational constraints. When applying model predictive control (MPC) in these settings, respecting timing constraints is achieved by limiting the number of iterations of the optimization algorithm used to compute control actions at each time step, resulting in so-called suboptimal MPC. This paper proposes a suboptimal MPC scheme based on the alternating direction method of multipliers (ADMM). With a focus on the linear quadratic regulator problem with state and input constraints, we show how ADMM can be used to split the MPC problem into iterative updates of an unconstrained optimal control problem (with an analytical solution), and a dynamics-free feasibility step. We show that using a warm-start approach combined with enough iterations per time-step, yields an ADMM-based suboptimal MPC scheme which asymptotically stabilizes the system and maintains recursive feasibility.