This paper presents a sparse solver based on the alternating direction method of multipliers algorithm for a linear model predictive control (MPC) formulation in which the terminal state is constrained to a given ellipsoid. The motivation behind this solver is to substitute the typical polyhedral invariant set used as a terminal constraint in many nominal and robust linear MPC formulations with an invariant set in the form of an ellipsoid, which is (typically) much easier to compute and results in an optimization problem with significantly fewer constraints, even for average-sized systems. However, this optimization problem is no longer the quadratic programming problem found in most linear MPC approaches, thus meriting the development of a tailored solver. The proposed solver is suitable for its use in embedded systems, since it is sparse, has a small memory footprint and requires no external libraries. We show the results of its implementation in an embedded system to control a simulated multivariable plant, comparing it against other alternatives.
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