  We address the challenge of dimension reduction in the discrete-time optimal
control problem which is solved repeatedly online within the framework of model
predictive control. Our study demonstrates that a reduced-order approach, aimed
at identifying a suboptimal solution within a low-dimensional subspace, retains
the stability and recursive feasibility characteristics of the original
problem. We present a necessary and sufficient condition for ensuring initial
feasibility, which is seamlessly integrated into the subspace design process.
Additionally, we employ techniques from optimization on Riemannian manifolds to
develop a subspace that efficiently represents a collection of pre-specified
high-dimensional data points, all while adhering to the initial admissibility
constraint.
