  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.
