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While I think one could set up an MPC algorithm with the BCVTB, it has not been developed for this purpose. You may rather want to look at https://github.com/lbl-srg/MPCPy

Whether you need to do a model reduction is somewhat a separate question, and opinions differ on this and highly depend on the model you have. We typically use simplified reduced order models for MPC, as they simplify the state and parameter estimation, and the solution of the optimization problem.