On multi-step prediction models for receding horizon control

Let us denote with p ∈ N a finite number of time steps in the future. We are interested in deriving a prediction model of the future output z(k+ p), exploiting the input and output measurements collected in the time interval [k− o+ 1,k], where o ∈ N is the chosen order of the model, and the future (planned) inputs in the interval [k,k+ p−1]. Specifically, at any instant k let us define the regressor φp(k) ∈ R2o−1+p as: φp(k) . = [ Y T o (k) U T o (k) U T p (k) ]T (2)