Convex Optimization: Model Predictive controller

I am trying to implement MPC Controller for my project where the variable used for optimization is not same as the states of plant. We take a difference of state variables with another quantity. How to implement this in MATLAB. For eg. There is a sys (A,B,C,D) with States X and another quantity R now i want to apply MPC optimization over the difference of (X-R) and want to find appropriate control input U for prediction horizon Np and control horizon Nc. Any assistance would be much appreciated. Thanks in advance Exact Alternative cost function is enclosed.