The impact of the input parameterisation on the feasibility of MPC and its parametric solution

Feasibility is an important issue in predictive control, but the influence of many important parameters such as the desired steady-state, or target, the current value of the input are rarely discussed in the literature. This paper makes two contributions. First it gives visibility to the issue that including core parameters such as the target and the current input vastly increases the dimension of the parametric space, with possible consequences on the complexity of any parametric solutions. Secondly, it is shown that a simple re-parameterisation of the d.o.f. to take advantage of reference governor concepts can lead to large increases in feasible volumes, with no increases in the dimension of the required optimisation variables.