as I read through this topic, only linear MPC are available. Reason is that they are similar to a state feedback law and can be calculated fast. If you only look for nonlinear-MPC because your plant is nonlinear, Matlab helps by supplying a lot of awesome linearization tools. Recently, the MPC toolbox supports changing the linearization point during runtime so even though your model is linearized, it will be pretty close to the real solution. It is called multiple MPC:
If you need a nonlinear MPC because of you needing a very special cost function or other nonlinear (cool, awesome) stuff, the Toolboxes don't help. Then you need to make your own nonlinear MPC. Be aware that such things run very slow!