Given

Model f, initial conditions x(0), prediction horizon p, control horizon m, sampling time Δt, and weighting matrices Q and R

Step 1

At the current sampling time $t_k$ , set $x\left(t_{k-1}\right)\leftarrow \left(t_k\right)$

Step 2

Solve Equations (23)-(26) for a sequence of m optimal input variables $\left\{U\left(1\right),U\left(2\right),\cdots ,U\left(m\right)\right\}$

Step 3

Set $u\left(t_k\right)\leftarrow U\left(1\right)$ and inject the input to the plant

Step 4

At $t_{k+1}$ , obtain the plant measurement $y_m$

Step 5

Corresponding to $y_m$ , estimate the states $x^{*}\left(t_{k+1}\right)$

Step 6

set $t_k\leftarrow t_{k+1}$

Step 7

Shift the prediction horizon p forward and repeat Step 1