Data-Driven Identification and MPC of Coupled Tank System using Bilinear Koopman Realizations and Physics-Informed Neural Networks

Data-Driven Koopman-Based Model Predictive Control for a Three-Tank Hydraulic System

This paper presents an applied study of data-driven Model Predictive Control (MPC) based on the Koopman operator framework for a three-tank hydraulic benchmark. The central contribution is a compact, physics-informed lifting strategy: observable functions are chosen directly from Torricelli’s law governing turbulent orifice flow, yielding a seven-dimensional Extended Dynamic Mode Decomposition (EDMD) model that captures the dominant nonlinearities with fewer basis functions than generic dictionaries. The resulting Koopman-MPC replaces the nonconvex optimization of nonlinear MPC (NMPC) with a convex quadratic program, achieving comparable tracking accuracy (0.65 cm vs. 0.64 cm mean error) while reducing the average per-step computation time by 36.7× (50 ms vs. 1807 ms in Python/SciPy). A Moving Horizon Estimator (MHE) operating on the full nonlinear model reconstructs the unmeasured tank level with accuracy comparable to the 2 mm measurement noise floor. These results provide a quantitative benchmark for Koopman-based predictive control on a nonlinear hydraulic system with bidirectional inter-tank coupling and regime-dependent flow transitions.

Bilinear Koopman-Based Robust Model Predictive Control for Unknown Nonlinear Systems via Contraction Metrics

Data-driven model predictive control (MPC) using Koopman operator theory is a promising approach for constrained control of unknown nonlinear systems. While linear Koopman realizations are commonly used due to their simplicity, bilinear Koopman realizations can provide significantly higher approximation accuracy for nonlinear control systems. However, robust MPC (RMPC) formulations that account for modeling errors in bilinear Koopman realizations remain limited. This paper proposes a RMPC framework for unknown nonlinear systems with general nonlinear constraints based on data-driven bilinear Koopman realizations. A central difficulty is that finite-dimensional Koopman predictors need not preserve the manifold of valid lifted states, so multi-step prediction in lifted coordinates may leave the region where one-step error certificates apply. We address this issue by reprojecting each predicted lifted state back onto the manifold, thereby obtaining an error-aware discrete-time control-affine predictor in the original state space without impractical assumptions. For this predictor, we develop a discrete-time robust control contraction metric based homothetic tube construction, and then formulate a tube-based RMPC problem with terminal ingredients. Under the proposed formulation, we prove robust satisfaction of the original nonlinear constraints by the true closed-loop trajectory, recursive feasibility, and convergence to a neighborhood of the target state. Numerical experiments demonstrate robust stabilization of nonlinear systems and the advantages of the proposed method over existing Koopman-based RMPC approaches in terms of performance.

Tube MPC for Bilinear Koopman Models using Robust Control Contraction Metrics

This paper presents a robust tube model predictive control (MPC) framework for nonlinear systems represented by bilinear Koopman models identified from data. We derive discrete-time robust control contraction metrics (RCCMs) for bilinear Koopman models, which certify a contraction property that explicitly accounts for the mismatch between the Koopman model and the true dynamics. To synthesize such certificates for the typically high-dimensional lifted state, we propose a scalable learning approach that trains neural network parameterizations of the metric and of an associated feedback controller over a sparsely sampled subset of the lifted state space. The resulting certificates are used to construct a robust tube MPC scheme with tightened constraints, for which we establish recursive feasibility, robust constraint satisfaction and input-to-state stability (ISS) of the closed-loop system with respect to the mismatch between the Koopman model and the true dynamics. By exploiting the linear parameter-varying structure of bilinear Koopman models, the MPC problem becomes convex for a fixed scheduling sequence, while the geodesic computation underlying the contractive feedback is reformulated, via a Chebyshev pseudospectral discretization, as a sequence of quadratic programs. The complete framework is validated on a nonlinear pendulum benchmark with a state-dependent input gain.

Scalable Predictive Control for District Heating Networks: A Physics-Guided Koopman Operator Approach

This article addresses the control of large-scale district heating networks (DHNs). Traditional nonlinear model predictive control (MPC) suffers from computational intractability due to the nonconvex optimization of complex thermal-hydraulic dynamics. We present scalable predictive control strategies based on the Koopman operator framework, developing a physics-guided methodology to construct meaningful Koopman observables by integrating the network’s graph topology and thermodynamic conservation laws. This ensures that critical nonlinear interactions and energy transport phenomena are accurately captured in physically interpretable lifted representations. The resulting linear model enables a Koopman-based receding horizon formulation in which each iteration reduces to a convex quadratic program (QP), guaranteeing global optimality of the QP surrogate at each step. Extensive numerical validation on benchmark DHNs demonstrates computational speedups exceeding one order of magnitude over state-of-the-art nonlinear MPC while maintaining comparable control performance. We further extend the methodology to DHNs with bidirectional-flow pipes, providing a tractable optimization framework with superior performance compared to nonlinear MPC.

Koopman-based model predictive control for nonlinear systems with bounded model uncertainty

Data-driven predictive control of nonlinear systems using weighted regularization

This work proposes a data-driven predictive control framework for nonlinear systems that incorporates data column preferences according to their proximity to the current operating point through a weighted norm regularization, thereby localizing the predictor without discarding any data.