  Harmonic model predictive control (HMPC) is a model predictive control (MPC)
formulation which displays several benefits over other MPC formulations,
especially when using a small prediction horizon. These benefits, however, come
at the expense of an optimization problem that is no longer the typical
quadratic programming problem derived from most linear MPC formulations due to
the inclusion of a particular class of second order cone constraints. This
article presents a method for efficiently dealing with these constraints in
operator splitting methods, leading to a computation time for solving HMPC in
line with state of the art solvers for linear MPC. We show how to apply this
result to the alternating direction method of multipliers algorithm, presenting
a solver which we compare against other solvers from the literature, including
solvers for other linear MPC formulations. The results show that the proposed
solver, and by extension the HMPC formulation, is suitable for its
implementation in embedded systems.
