# NMPC in Active Subspaces: Dimensionality Reduction with Recursive Feasibility Guarantees

arXiv: https://arxiv.org/abs/2209.10915 · HTML: https://mlsanity.com/paper/2209.10915/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2022.

## Built on by (most cited first, 1 of 1)

- [Safe and High-Performance Learning of Model Predicitve Control using Kernel-Based Interpolation](https://mlsanity.com/paper/2410.06771/) (2024)

## Abstract (arXiv)

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%.