I have a discrete state space model: $$x(k+1) = Ax(k) + Bu(k)$$ $$y(k) = Cx(k)$$ And I'm trying to compute the predicted inputs. The first thing I do is that I fist create the extended observability matrix $\Phi$ $$\Phi = \begin{bmatrix} CA\\ CA^2\\ CA^3\\ \vdots \\ CA^{n-1} \end{bmatrix}$$ Th...

I have a few confusions about Model Predictive Control (MPC). Since they are all minor questions related to the same category, I ask them under one topic. In an article, the cost function is defined as: $$J(t)=\sum_{j=1}^{N_p}\delta(j) ( y(t+j|t) -ref(t+j) )^2 + \sum_{j=0}^{N_c-1}\lambda(j) u(t+...

As I know, the Generalized Predictive Control(GPC) is older than Model Predictive Control(MPC). But what is the real difference between them? I know that GPC contains some kind of system identification, which make GPC as an adaptive controller. But what if MPC has system identification too? Woul...

As I understand Model Predictive Control (MPC) in practice takes the form of a convex QP something like $$\min_{u_1,...,u_T,x_1,...,x_T} \sum_{t=1}^{T}(x_t-r_t)^{T}Q_t(x_t-r_t) + u_t^{T}R_tu_t$$ $$s.t. \ Ax_t+Bu_t=x_{t+1} \ \forall t \in \{1,...,T-1\} $$ and there can be additional constraints on...

Lately I've been reading numerous papers regarding Energy Hub optimization, and often the authors talk about rolling horizon optimization for taking into account uncertainty. For instance: "A rolling horizon optimization framework for the simultaneous energy supply and demand planning in micr...

If you read "Nonlinear Model Predictive Control" by L. Grune and J. Pannek (and anywhere else), everyone says that the prediction horizon size $N$ must be larger or equal to $2$,$ N\geq2$. Why?