A construction-free coordinate-descent augmented-Lagrangian method for embedded linear MPC based on ARX models

This paper proposes a construction-free algorithm for solving linear MPC problems based on autoregressive with exogenous terms (ARX) input-output models. The solution algorithm relies on a coordinate-descent augmented Lagrangian (CDAL) method previously proposed by the authors, which we adapt here to exploit the special structure of ARX-based MPC. The CDAL-ARX algorithm enjoys the construction-free feature, in that it avoids explicitly constructing the quadratic programming (QP) problem associated with MPC, which would eliminate construction cost when the ARX model changes/adapts online. For example, the ARX model parameters are dependent on linear parameter-varying (LPV) scheduling signals, or recursively adapted from streaming input-output data with cheap computation cost, which make the ARX model widely used in adaptive control. Moreover, the implementation of the resulting CDAL-ARX algorithm is matrix-free and library-free, and hence amenable for deployment in industrial embedded platforms. We show the efficiency of CDAL-ARX in two numerical examples, also in comparison with MPC implementations based on other general-purpose quadratic programming solvers.