The general form of the mixed input/output constraints is:
Eu(k +
j) +
Fy(k +
j) + Sv(k +
j) ≤ G +
εV
Here, j = 0,...,p, and:
p is the prediction horizon.
k is the current time index.
u is a column vector manipulated variables.
y is a column vector of all plant output variables.
v is a column vector of measured disturbance variables.
ε is a scalar slack variable used for constraint softening (as in Standard Cost Function).
E, F, G, V, and S are constant matrices.
Since the MPC controller does not optimize
u(k+p),
getconstraint
calculates the last constraint at time
k+p
assuming that u(k+p) =
u(k+p-1).