NMPC in Active Subspaces: Dimensionality Reduction with Recursive Feasibility Guarantees

TL;DR

This paper introduces a framework for reducing the dimensionality of decision variables in NMPC using active subspaces, ensuring recursive feasibility and demonstrating significant computational savings with minimal performance loss.

Contribution

It presents a general feasibility-preserving dimensionality reduction method in NMPC, utilizing active subspaces and global sensitivity analysis for data-driven construction.

Findings

Achieved 20-40x reduction in decision variables for a chemical reactor.

Maintained less than 0.05% performance decay with reduced complexity.

Established recursive feasibility regardless of subspace choice.

Abstract

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 $0.05\%$.