Notes on multi-step ahead prediction based on the principle of concatenation

A recent paper by Kaynak in this Journal proposes a more efficient application of generalized predictive control than that of Clarke et al., the most common in the literature. In this technical note, Kaynak's algorithm is compared with two other algorithms of Kouvaritakis and Rossiter already in the literature, and also with the original algorithm of Clarke et al., and it is demonstrated that they all in fact reduce to the same algorithm. Moreover, it is shown that the earlier algorithms are more efficient in the non-adaptive case and that Kaynak's algorithm is not efficient in the adaptive case.