On the micciancio-voulgaris algorithm to solve the long-horizon direct MPC optimization problem

It is widely accepted that model predictive control (MPC) with long prediction horizons yields, in general, a better performance than with short horizons. In the context of power electronic systems, the main advantages include improved closed-loop stability and lower current distortion per switching frequency. A shortcoming of MPC with long prediction horizons is the computational burden associated with solving the optimization problem in real time, which limits the minimum possible sampling interval. The solution to the MPC optimization problem is a polyhedral partition of the state-space. Pre-processing of the state-space and storing representative information thereof offline assists in reducing the online computational burden. The problem structure is a special case in the form of a truncated lattice. Exploiting this characteristic enables representation of the partitioned space to be is stored as a minimal set of Voronoi relevant vectors describing the basic Voronoi cell of a lattice. We evaluate the algorithm proposed by Micciancio and Voulgaris known as the MV-algorithm to solve the closest vector problem with pre-processing (CVPP). The performance of the algorithm is evaluated in a simulated three-level neutral point clamped (NPC) voltage source inverter with an RL load.