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We consider the problem of reducing the dimension of the discrete-timeoptimal control problem that is solved repeatedly online in model predictivecontrol. We show that a reduced-order scheme, which solves the optimizationproblem in a low-dimensional subspace, inherits the stability and recursivefeasibility properties from the original formulation. We introduce a necessaryand sufficient condition for initial feasibility and incorporate that in thesubspace design. Finally, we use concepts of optimization over Riemannianmanifolds to compute a subspace that provides optimal representations for a setof pre-defined high-dimensional optimizers under the initial admissibilityconstraint.

Geometric Data-Driven Dimensionality Reduction in MPC with Guarantees