I have written a book Process Control - Theory and Application, J.P. Corriou, Springer (2004). If you have the possibility to borrow that book from your library, MPC is explained in detail in chapter 16. It is not related to a specific Matlab program, but I think that the ideas of MPC are very well explained with e real progression and that it is easier to construct something when you know the theory rather than starting from a Matlab program or toolbox. My final advice: read carefully the theory.

see this link is very useful:

http://controleducation.group.shef.ac.uk/OER_index.htm

I suggest you to read also the MPC books from, (i) Maciejowski, (ii) Rawlings, (iii) Rossiter, (iv) Borrelli. In addition, there are several video lectures available on Youtube, for example, http://www.youtube.com/channel/UCMBXZxd-j6VqrynykO1dURw . For Matlab implementation examples, you should check the MPT 3 Toolbox, Yalmip toolbox, and the matlab MPC toolbox.

Once you have the optimal solution from the constrained problem, you take the first control value and implement it as a constant control action over one sampling time. Once you reach the end of the sampling time, you update your constrained problem and resolve the problem to find a new optimal solution.

Thank you very much