Sep 2026· IEEE Transactions on Control Systems Technology· Vol 34, pp. 2721-2732· 0 citations· 50 references
Abstract
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.
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.
Wilder Hernandez Manosalva, H. Ramirez-Murillo, D. Tellez-Castro· International Conference on...· 0 citations
Real-time control of multivariable nonlinear processes requires models balancing high fidelity with computational tractability. This paper compares two data-driven paradigms: Bilinear Koopman Realizations and Physics-Informed Neural Networks. While standard Koopman approaches seek global linearization, we leverage a bilinear framework in the lifted functional space to preserve the natural coupling of control-affine systems. Simultaneously, PINNs ensure physical consistency by embedding conservation laws into the learning objective. To facilitate high-performance control, both surrogate models are integrated into a nonlinear model predictive control scheme using the CasADi framework, enabling efficient algorithmic differentiation for optimization. Simulation results for a quadruple tank system demonstrate that both paradigms reach mean VAF values above 99%, but the Bilinear Koopman model delivers a lower mean RMSE during step transients while doubling the computational speed of the PINN with a Real-Time Factor above 22. We conclude that despite structural scaling limitations regarding neural exploding gradients and operator instability risks, the Bilinear Koopman realization provides a more reliable, noise-resilient solution for real-time hydraulic benchmarks.
Amir Vanegas, Julio Barón-Velandia, Nelson Leonardo Díaz-Aldana et al.· International Conference on...· 0 citations
To efficiently compute optimal compressor actions in gas networks, we investigate port‐Hamiltonian models consisting of linear and a nonlinear model assumptions. The control actions are derived via adjoint‐based gradients that incorporate the constraints of the underlying optimization problem. We then present results from the implementation of a model predictive control (MPC) strategy. We compare the results of the optimization on different models and focus on the computational efficiency. These actions are then validated and periodically updated based on a physically detailed nonlinear model, which captures the detailed system dynamics. This design is applied to a daily demand profile in a network with multiple consumers and sources.
Andres Ortegón‐Villacorte, Jan Rohleff· Proceedings in Applied Mathe...· 0 citations
This work presents a Physics-Informed Neural Network (PINN) framework for multiphase steady-state production systems and its application to constrained production optimization. The PINN is constructed to approximate the coupled momentum and energy equations of a flowline–riser configuration with state-dependent thermophysical properties obtained from tabulated PVT (Pressure-Volume-Temperature) data via differentiable bilinear interpolation. The network is trained by enforcing the governing equations and boundary conditions, yielding continuous pressure and temperature fields along the spatial domain without requiring labeled data. Once trained, the neural network weights are frozen and embedded into a production optimization problem, where choke settings and well activation decisions are optimized under global water-handling limits and local operability constraints, including bottom-hole pressure requirements and hydrate avoidance conditions evaluated along the entire flow path. The problem is cast as a mixed-integer nonlinear program, with physical feasibility enforced through a differentiable PINN surrogate.
L. K. Miyatake, Eduardo Camponogara, Alexey Pavlov· International Conference on...· 0 citations