Latent-Space Non-Linear Model Predictive Control for Partially-Observable Systems

TL;DR

This paper introduces a scalable nonlinear Model Predictive Control framework that uses data-driven reduced order modeling and latent space control to effectively manage high-dimensional, partially observable dynamical systems.

Contribution

It integrates Operator Inference, Proper Orthogonal Decomposition, and Unscented Kalman Filtering into a unified control approach for complex systems.

Findings

Achieves accurate stabilization of chaotic systems

Reduces computational complexity in control calculations

Effective in systems with sparse and noisy measurements

Abstract

This work presents a scalable control framework based on nonlinear Model Predictive Control for high-dimensional dynamical systems. The proposed approach addresses the key challenges of model scalability and partial observability by integrating data-driven reduced order modelling, control in a latent space, and state estimation within a unified formulation. A predictive model is constructed via Operator Inference on a Proper Orthogonal Decomposition basis, yielding a compact latent representation that captures the dominant system dynamics. State estimation is achieved through an Unscented Kalman Filter, which reconstructs the latent space from sparse and noisy measurements, enabling closed-loop control. The input signals are computed directly in the reduced-order latent space, improving computational efficiency with negligible impact on predictive capability. The methodology is validated on the one- and two-dimensional Kuramoto--Sivashinsky equations, serving as benchmarks for chaotic and spatially-extended systems. Numerical experiments demonstrate that the proposed framework achieves accurate stabilisation. Overall, the framework provides a practical approach for nonlinear control of complex, high-dimensional systems where full-state measurements are often inaccessible or infeasible.