Hi Angelo,
The following procedure can be used to convert the state constraints into input constraints.
Consider the discrete-time state-space system 
with 
states, where 
is the state vector and 
is the input vector. Let the state constraints be 
. If N is the prediction horizon, the predicted states can be concatenated into a single matrix given by,
with states, where is the state vector and is the input vector. Let the state constraints be . If N is the prediction horizon, the predicted states can be concatenated into a single matrix given by,
Where:
is equal to the initial state 
.- X and U are concatenated vectors,
and 
. - Φ is constructed as:
. - Γ is constructed as:
.
On concatenating the state constraint relations at each time step and substituting 
, one may obtain the following inequality:
, one may obtain the following inequality:
. Where,
The above equation can be rearranged to obtain an input constraint relation.
The above relation is in the general form of inequality constraints, 
. The equivalent matrices for 
and 
can be identified to be,
. The equivalent matrices for and can be identified to be,
You can refer to the attached MATLAB script for further assistance. To learn more about MPC matrices you can refer the following documentation page.
I hope this resolves your query!
