Toward Grassmannian Dimensionality Reduction in MPC

Model predictive control presents remarkable potential for the optimal control of dynamic systems. However, the necessity for an online solution to an optimal control problem often renders it impractical for control systems with limited computational capabilities. To address this issue, specialized dimensionality reduction techniques designed for optimal control problems have been proposed. In this letter, we introduce a methodology for designing a low-dimensional subspace that provides an ideal representation for a predefined finite set of high-dimensional optimizers. By characterizing the subspace as an element of a specific Riemannian manifold, we leverage the unique geometric structure of the subspace. Subsequently, the optimal subspace is identified through optimization on the Riemannian manifold. The dimensionality reduction for the model predictive control scheme is achieved by confining the search space to the optimized low-dimensional subspace, enhancing both efficiency and applicability.