On the choice of norm in finite control set model predictive control

In power electronics, the ℓ1-norm (instead of the squared 2-norm) is often used in the objective function of model predictive controllers (MPCs) with reference tracking. Although the ℓ1-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 ℓ2-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 ℓ2-norm.