On the Choice of Norm in Finite Control Set Model Predictive Control

In power electronics, the ℓ 1 -norm (instead of the squared ℓ 2 -norm) is often used in the objective function of model predictive controllers (MPCs) with reference tracking. Although the ℓ 1 -norm is preferred for its computational simplicity, it might lead to a performance deterioration and closed-loop instability. This paper analyzes the root cause for this and discusses the benefits of using the ℓ 2 -norm instead. Given the theoretical nature of this paper, a power electronics-oriented case study is employed to visualize and exemplify-through examples and simulations-the mathematical concepts and arguments presented. To this end, a variable speed drive system with a three-level voltage-source inverter serves as an illustrative example to clearly demonstrate the effectiveness of using the ℓ 2 -norm.