@agustinyabo should be rather easy to test MPC (fixed / moving horizon) implementing a basic loop (see, e.g., this simple example) on the nice example you treated in the ref. below:

Yabo, A.; Caillau, J.-B., Gouzé, J.-L.
Hierarchical MPC applied to bacterial resource allocation and metabolite synthesis
IEEE Conference on Decision and Control (2021), 667-672
Proceedings of the 60th CDC, Austin, December 2021