Computational Analysis of the Long Horizon FCS-MPC Problem for Power Converters

Long prediction horizon finite control set model predictive control (LPH-FCS-MPC) for power converters can be reformulated as a box-constrained integer-least squares (ILS) problem to find the optimal control action without requiring an exhaustive search. Instead, the solution can be found by means of a sphere decoding method that still presents several intricacies regarding its complexity and its variable computational cost. This paper provides a study of the computational behavior of this approach. Special emphasis is placed on how the generator matrix is calculated, either as a lower or an upper triangular structure. This choice decides whether the switching sequences are explored forward- or backward-in-time during the optimization process. In this work, it is explained how this selection holds a great impact on the computational burden of the algorithm. Similarly, it is also analyzed how the tuning of the FCS-MPC and system parameters also drastically impacts the computational cost.