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

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

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

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.

Data-driven stochastic model predictive control for spacecraft attitude tracking

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.

Reduced-order state-space reformulation for task-space predictive control of an under-actuated hydraulic boom

Hydraulic booms used in material handling are typically commanded in cylindrical task-space coordinates, while dynamic models used for control are commonly formulated in joint coordinates. This mismatch leads to unnecessarily high-dimensional system representations when predictive control is applied to underactuated suspended loads. This paper addresses this modeling inconsistency by introducing a reduced-order state-space reformulation of grapple sway dynamics directly in cylindrical task-space velocity coordinates. The proposed input-consistent state transformation eliminates the dependence of the dynamics on input accelerations by embedding actuator–sway coupling within modified velocity states, yielding a nonlinear model driven solely by cylindrical velocity commands. Based on this representation, a nonlinear model predictive control (NMPC) framework is developed for simultaneous goal reaching, sway suppression, and obstacle avoidance. The NMPC cost function is designed to capture the practical trade-off between rapid boom motion and suppression of suspended load oscillations. In addition, approximate hydraulic actuator dynamics identified from a high-fidelity AMESim simulator model of a forwarder crane are incorporated to better reflect realistic boom behavior. Simulation studies in representative boom operation scenarios demonstrate that the proposed formulation enables effective sway regulation and accurate task-space motion control using a reduced set of states without requiring full joint-space models or payload sensing. The results indicate that the proposed cylindrical state-space reformulation simplifies predictive control design for underactuated hydraulic booms while preserving the essential dynamics of the suspended load.

Koopman Operator-Based Optimal Control for High-Speed Autonomous Vehicle Path Tracking: An Experimental Study

This paper presents a Koopman-operator-based optimal control framework for high-speed lateral path tracking and validates it through closed-loop experiments on a full-size autonomous electric vehicle. The path-tracking error dynamics are identified from real driving data using extended dynamic mode decomposition with control. The lifting dictionary combines the measured physical states with thin-plate-spline radial basis functions, while maximum-absolute scaling is used to improve numerical conditioning. Road curvature and longitudinal velocity are included as measurable exogenous inputs. Because steady-state autonomous highway driving provides limited dynamic excitation, and because artificial steering excitation is unsafe in public traffic, the identification dataset combines autonomous lane-centering recordings with open-loop excitation maneuvers performed by a human driver. Two optimal controllers are evaluated: an infinite-horizon linear quadratic regulator and an input-constrained model predictive controller with curvature-and-velocity feedforward. Both Koopman-based controllers are compared with analytical single-track-model baselines using a common weight-mapping scheme. In highway tests at 80 km/h, the Koopman-based model predictive controller reduces the lateral-position root-mean-square error by up to 43.7% relative to the analytical model predictive controller, while the Koopman-based linear quadratic regulator reduces it by up to 19.2% relative to its analytical counterpart. Most of the improvement is obtained with 20 radial basis functions, after which the tracking performance saturates. The largest tested Koopman configuration runs in under $20~\mu $ s on an automotive-grade embedded target, demonstrating improved tracking accuracy without sacrificing real-time feasibility.