Latent-space nonlinear model predictive control for partially observable systems

Abstract This work presents a scalable control framework based on nonlinear model predictive control (MPC) 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 (ROM), control in a latent space and state estimation within a unified formulation. A predictive model is constructed via operator inference (OpInf) on a proper orthogonal decomposition (POD) basis, yielding a compact latent representation that captures the dominant system dynamics. State estimation is achieved through an unscented Kalman filter (UKF), 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 effect on predictive capability. The methodology is validated on the one- and two-dimensional (1D and 2D) Kuramoto–Sivashinsky (KS) equations, serving as benchmarks for chaotic and spatially extended systems. Numerical experiments demonstrate that the proposed framework achieves accurate stabilization. Overall, the framework provides a practical approach for nonlinear control of complex, high-dimensional systems, where full-state measurements are often inaccessible or infeasible.