  Dimensionality reduction of decision variables is a practical and classic
method to reduce the computational burden in linear and Nonlinear Model
Predictive Control (NMPC). Available results range from early move-blocking
ideas to singular-value decomposition. For schemes more complex than
move-blocking it is seemingly not straightforward to guarantee recursive
feasibility of the receding-horizon optimization. Decomposing the space of
decision variables related to the inputs into active and inactive complements,
this paper proposes a general framework for effective feasibility-preserving
dimensionality reduction in NMPC. We show how -- independently of the actual
choice of the subspaces -- recursive feasibility can be established. Moreover,
we propose the use of global sensitivity analysis to construct the active
subspace in data-driven fashion based on user-defined criteria. Numerical
examples illustrate the efficacy of the proposed scheme. Specifically, for a
chemical reactor we obtain a significant reduction by factor $20-40$ at a
closed-loop performance decay of less than $0.05\%$.
