Abstract
This work presents a scalable control framework based on nonlinear Model Predictive Control for high-dimensional dynamical systems. The approach addresses 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 dominant system dynamics. State estimation is achieved through an Unscented Kalman Filter, reconstructing the latent space from sparse and noisy measurements, enabling closed-loop control. 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 accurate stabilisation. This framework provides a practical approach for nonlinear control of complex, high-dimensional systems where full-state measurements are often inaccessible or infeasible.
