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

A RMPC framework for unknown nonlinear systems with general nonlinear constraints based on data-driven bilinear Koopman realizations is proposed and robust satisfaction of the original nonlinear constraints is proved by the true closed-loop trajectory, recursive feasibility, and convergence to a neighborhood of the target state.

Tube MPC for Bilinear Koopman Models using Robust Control Contraction Metrics

A robust tube model predictive control framework for nonlinear systems represented by bilinear Koopman models identified from data, which establishes recursive feasibility, robust constraint satisfaction and input-to-state stability of the closed-loop system with respect to the mismatch between the Koopman model and the true dynamics.

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.